Review of Searches for Rare Processes and Physics Beyond the Standard Model at HERA
aa r X i v : . [ h e p - e x ] M a y EPJ manuscript No. (will be inserted by the editor)
Review of Searches for Rare Processes and Physics Beyond theStandard Model at HERA
David M. South and Monica Turcato Deutsches Elektronen Synchrotron, Hamburg, Germany Hamburg University, Institute of Experimental Physics, Hamburg, GermanyReceived: date / Revised version: date
Abstract.
The electron-proton collisions collected by the H1 and ZEUS experiments at HERA comprisea unique particle physics data set, and a comprehensive range of measurements has been performed toprovide new insight into the structure of the proton. The high centre of mass energy at HERA has alsoallowed rare processes to be studied, including the production of W and Z bosons and events withmultiple leptons in the final state. The data have also opened up a new domain to searches for physicsbeyond the Standard Model including contact interactions, leptoquarks, excited fermions and a numberof supersymmetric models. This review presents a summary of such results, where the analyses reportedcorrespond to an integrated luminosity of up to 1 fb − , representing the complete data set recorded by theH1 and ZEUS experiments. The Standard Model (SM) of particle physics [1,2,3], whichdescribes the fundamental building blocks of nature andtheir interactions, is one of the success stories of the last50 years in science. The theoretical development and sub-sequent experimental confirmation of the SM, which de-scribes the elementary particles and their weak, electro-magnetic and strong interactions, has been made possibleby a variety of particle accelerators and their associatedexperimental programmes operated during this time. Thesuccessful exploration of the electroweak sector, from thediscovery of weak neutral currents in the bubble chamberexperiments of the early 1970’s to the subsequent obser-vation of the weak bosons at the SPS at CERN in theearly 1980’s, greatly influenced the direction of researchand detector design, as well as the type and energy of ma-chines developed in the following decades. Different typesof programmes have been formed more recently, based onmaking precision measurements such as the LEP experi-ments at CERN, BaBar at SLAC and Belle at KEK, to allout discovery machines such as the Tevatron at Fermilabor the LHC at CERN. In the last few years, the LHC hasproduced one of the major physics results of this excitinghalf century of particle physics, with the observation [4,5]of a new narrow resonance consistent with the long soughtHiggs boson [6,7,8].The HERA accelerator at DESY is a unique achieve-ment, in that it is the world’s only electron -proton col-lider to be constructed, thus providing an unrivalled physics The term “electron” is used generically to refer to bothelectrons and positrons, unless otherwise stated. programme to the high energy physics community. Bring-ing into collision point-like leptons with finite sized hadrons,HERA may be thought of as a powerful electron micro-scope, a tool to make precise measurements of the struc-ture of the proton and to investigate the nature of strongforce binding it together. The experimental data from the ep collisions at HERA also allow rare processes to bestudied, typically those involving the electroweak gaugebosons, and to search for physics beyond the StandardModel (BSM), in analyses complementary to those at othercolliders and sometimes unique to ep physics.This review presents a summary of the measurementsof rare processes and BSM searches based on experimentaldata taken by the H1 and ZEUS experiments at HERA.The majority of the presented analyses utilise the com-plete data sets of the experiments, which in combinationamounts to an integrated luminosity of 1 fb − . A brief in-troduction to the kinematics of ep scattering is followed bya description of HERA and the DESY accelerator facilityand the H1 and ZEUS experiments. An outline of particleidentification, event reconstruction and simulation is thengiven, describing the key methods employed in the dataanalysis performed by each experiment.To effectively perform searches for rare processes andnew physics in the data, it is important to have a goodunderstanding and level of confidence in the descriptionof SM physics. Therefore, a summary of the main experi-mental results on deep inelastic scattering (DIS) at largemomentum transfer is given in section 8, which are per-formed in a similar kinematic region to the majority of a Now at European X-ray Free-Electron Laser facility GmbH,Hamburg, Germany. D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA the results presented in this review. This is particularlyimportant for the first category of searches, where devia-tions from SM expectation of DIS events may reveal newphysics, namely searches for contact interactions and lep-toquarks as described in section 9. Dedicated searches forfirst, second and third generation leptoquarks are thenpresented in section 10.Rare processes with high transverse momentum lep-tons in the final state are investigated in sections 11 and12, featuring measurements of lepton pair and W pro-duction. Potential new signals are also investigated in thecontext of these analyses in sections 11.3 and 13. The pro-duction of Z bosons is examined by the ZEUS experimentusing the hadronic decay channel in section 14. A modelindependent “general” search for new physics is performedby H1 as described in section 15, where all final states areexamined containing high transverse momentum entities.Searches for new physics in the context of specific modelsare then presented, for excited fermions and supersym-metry in sections 16 and 17, respectively. Finally a novelsearch for magnetic monopoles performed by the H1 ex-periment is presented in section 18, before a summary ofthe presented results is given together with an outlook insection 19. Figure 1 shows a diagram of the interaction ep → ℓX ,where a virtual photon ( γ ), or heavy vector boson ( Z or W ) is exchanged between the incoming electron ( e ) andproton ( p ). As the mediator boson between the electronand the proton can be either a photon or a heavy vectorboson, due to the high centre of mass energy at HERA,QED and weak interactions may be studied simultane-ously, testing the electroweak theory. The outgoing par-ticles are made up of the scattered lepton ( ℓ ) and thosecontained in the hadronic final state ( X ). In the case ofneutral current (NC) interactions, the exchange is medi-ated by a γ or Z , so that an electron ( e ′ ) is present in thefinal state. In charged current (CC) interactions, the weakexchange of the W boson results in a final state neutrino( ν ). The four momenta of the initial state electron andproton are denoted k and P , so that the centre of massenergy √ s is given by: s = ( k + P ) . (1)Neglecting the masses of the incoming particles, this canbe approximated by √ s ≈ E e E p , where E e ( E p ) is theenergy of the initial state electron (proton). The square ofthe four-momentum transfer (which is equal to the masssquared of the virtual boson), q <
0, determines the hard-ness, or in other words, the resolving power of the inter-action. The negative four-momentum transfer squared isdefined as: Q = − q = − ( k − k ′ ) (2) e (k) e´, n (k´) g , Z o , W ± (q = k-k´)p (P) X (q+P) Fig. 1.
The scattering of electrons and protons at HERA. Thefour-momenta of the particles are indicated in the parentheses.The exchanged gauge boson is a photon ( γ ) or Z boson in NCinteractions and a W boson in CC interactions. and the invariant mass W of the hadronic final state X isgiven by: W = ( q + P ) . (3)Interactions at HERA are denoted elastic if the proton re-mains intact, quasi-elastic if the proton dissociates intoa low-mass hadronic system, or inelastic if the protonbreaks up. Deep inelastic scattering (DIS) events are char-acterised as having large momentum transfer Q ≫ m p and are highly inelastic, W ≫ m p , where m p is the massof the proton.The fraction of the proton momentum carried by thestruck parton is given by the quantity Bjorken x , where: x = Q P · q (4)under the assumption of massless quarks. The inelasticity of the interaction, y , is given by: y = q · Pk · P (5)and is equal to the fraction of the incident electron mo-menta carried by the exchange boson in the rest frame ofthe proton. Both x and y take values between 0 and 1 sincethey describe fractions of momenta, as defined above. Theabove quantities are related by: Q ≈ sxy, (6)resulting in a maximum squared four-momentum exchangeequal to the centre of mass energy squared s .The value of Q is a measure of the virtuality of theexchange boson: for Q ≈
0, the photon is considered tobe almost real, and in such interactions the initial stateelectron scatters under very small angles. An interactionat higher Q represents a more energetic exchange, re-sulting in a higher resolution of the parton participatingin the interaction: one of the three valence quarks, a seaquark or a gluon. Hence the exchanged boson acts as aprobe for the determination of the structure of the pro-ton and depending on the scattering angle and energy of . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 3 the outgoing lepton, different Q and x ranges can be in-vestigated, thus examining the electromagnetic and weakcharge distribution inside the proton. x Q / G e V Atlas and CMSAtlas and CMS rapidity plateauD0 Central+Fwd. JetsCDF/D0 Central JetsH1ZEUSNMCBCDMSE665SLAC -1 -7 -6 -5 -4 -3 -2 -1 Fig. 2.
Regions of phase space in the x - Q kinematic planecovered by several collider and fixed target experiments. The advent of the HERA collider in 1992 made it pos-sible to explore a much wider region in x and Q than thatpreviously accessible at fixed target experiments, with mea-surements possible down to 10 − in x and low Q , in par-ticular in the non-perturbative region and up to a Q of10 GeV in the valence (high- x ) region. The kinematiccoverage of the HERA experiments in the x - Q plane isshown in figure 2, compared to that of several fixed tar-get DIS experiments as well as the phase space coveredby the hadron-hadron collision experiments at both theTevatron ( p ¯ p ) and the LHC ( pp ). By exploiting QCD fac-torisation [9] and utilising the DGLAP [10,11,12] partonevolution scheme, the HERA parton distribution functions(PDFs) derived from H1 and ZEUS measurements acrossa large range in x can be used as input to calculate pre-dictions for the LHC at much higher values of Q . We willreturn to these measurements and the calculation and im-pact of the HERA PDFs in section 8. HERA (Hadron Electron Ring Anlage) [13] is so far theonly lepton-proton collider in the world to have been con-structed . It was located at the DESY (Deutsches Electro-nen Synchrotron) laboratory, as pictured in the upper half The conceptual design report of the proposed LHeCproject, a machine to collide a high energy electron beam withthe hadron beams of the LHC, is now available [14].
HERAhall west
PETRA cryogenichall magnettest-hallDESY II/III PIA e -linac+e -linac--H -linacNW N NO OSOSWW proton bypass pe e p Hall NorthH1 Hall EastHERMESHall SouthZEUS
HERA
Hall WestHERA-B e p
VolksparkStadion m m R = m T r a b r e nnb a hn Fig. 3.
The DESY research centre in Hamburg, Germany. Inthe upper photograph, the dashed circles show the path of theunderground ring accelerators PETRA and HERA; the fourlarge halls containing the HERA detectors are indicated bythe smaller, solid circles. The lower diagram details the systemof pre-accelerators employed in order to produce the protonand electron beams that were brought into collision at the H1and ZEUS experiments. of figure 3, and was in operation during the years 1992 to2007. The HERA machine accelerated and brought intocollision 27 . , resulting in a centre of mass energy of 319 GeV.At the time, this energy represented more than an orderof magnitude increase with respect to the previous fixed-target experiments and consequently a new and widerkinematic region was accessible for the first time at HERA.In the final data taking period the proton beam was accel-erated to lower energies, first 460 GeV and then 575 GeV,in order to provide data used for a direct measurement ofthe longitudinal structure function F L (see section 8).The 6 . The proton beam energy was 820 GeV from 1992-1997,resulting in a centre of mass energy of 300 GeV. The datarecorded during this period amounts to less than 10% of thetotal integrated luminosity yield. D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA periment [15,16] was located, the other in the South Hallwhere the ZEUS experiment [17] could be found. TheHERMES experiment [18] in the East Hall studied thespin structure of the nucleon using collisions of the leptonbeam on an internal polarised gas target. The HERA-Bexperiment [19,20] in the West Hall was built to use colli-sions of the proton beam halo with a wire target in orderto produce B -mesons for the study of CP violation in the B − ¯ B system. The layout of the HERA ring and the sys-tem of pre-accelerators at DESY is illustrated in the lowerhalf of figure 3.The proton beam began as negative hydrogen ions(H − ) accelerated in a linear accelerator to 50 MeV. Theelectrons were then stripped off the H − ions to obtainprotons, which were injected into the proton synchrotronDESY III, accelerated up to 7 . .
65 T,where they were then accelerated to the nominal beamenergy of 920 GeV.The electron (positron) pre-acceleration chain began ina linear accelerator, LINAC I (LINAC II), where the lep-tons were accelerated up to 450 MeV. The leptons werethen injected into the electron synchrotron DESY II, ac-celerated to 7 GeV and, similarly to the protons, trans-ferred to the PETRA ring, where they reached an energyof 14 GeV. Injection transfer into the HERA ring followed,where they were accelerated to the nominal lepton-beamenergy of 27 . .
165 T.Up to 210 bunches of leptons and protons were accel-erated in the HERA ring, spaced at 96 ns intervals. Only175 bunches were typically used for collisions, where theremainder were used as pilot bunches to study backgroundrates arising from interactions of the beams with residualgas in the beam-pipe. When the proton bunches were com-pressed by HERA during acceleration, small secondary or satellite bunches were formed, separated from the mainbunch by up to 8 ns.The data taking at HERA may be divided into two dis-tinct periods: HERA I, which was from 1994 until 2000,and HERA II, from 2003 until 2007. A luminosity upgrade[21] of the machine took place between the two data takingperiods and brought an observed increase in the luminos-ity delivered to the experiments from 1 . × cm − s − in the HERA I phase up to a peak value of 5 . × cm − s − , achieved during HERA II e − p running. The in-tegrated luminosity delivered by the HERA accelerator isshown in figure 4.The integrated luminosity collected for analysis by H1and ZEUS amounts to about 0 . − per experiment.This is less than the delivered integrated luminosity, asquality conditions are applied to the data used for anal-ysis, such as requirements on the high voltage status ofthe various detector subsystems (see section 4). The lumi-nosity is measured by both experiments from the rate ofthe well understood QED Bethe-Heitler process ep → epγ . Days of running H E RA D e li v ere d L u m i n o s i t y / pb - electronspositronslow energy HERA-1HERA-2
Fig. 4.
A summary of the integrated luminosity deliveredby the HERA collider during the HERA I (1992-2000) andHERA II (2003-2007) phases. The different electron andpositron running periods are indicated, as well as the datataken at lower proton beam energies in 2007.
As the photon is emitted almost collinear to the incom-ing electron, it is detected using devices located close tothe beam line beyond the main detectors. A photon de-tector [22,23,24] is employed by H1 and the ZEUS exper-iment uses two independent systems, a photon calorime-ter [25,26,27] and a magnetic spectrometer [28]. A recentanalysis [29] of Compton scattering events provided analternative and improved measurement of the luminosityrecorded by the H1 experiment. The integrated luminosi-ties of the data sets are detailed in table 1.Another feature of the HERA II upgrade was the useof a longitudinally polarised lepton beam. As the lep-ton beam circulated in HERA it naturally became trans-versely polarised via the Sokolov-Ternov effect [30,31].The typical polarisation build-up time for the HERA ac-celerator was approximately 40 minutes. At HERA II, spinrotators installed on either side of the H1 and ZEUS de-tectors changed the transverse polarisation of the beaminto longitudinal polarisation and back again. The leptonbeam polarisation was measured using two independentpolarimeters, the transverse polarimeter (TPOL) [32] andthe longitudinal polarimeter (LPOL) [33]. Both devicesexploited the spin-dependent cross section for Compton Note that for some analyses presented in this review theintegrated luminosity may vary from this table. For example,some searches do not require a good polarisation measurementand this results in a higher luminosity yield from HERA II. Insuch cases, the integrated luminosity of the analysed datasetsis given in the text.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 5 scattering of circularly polarised photons off positrons tomeasure the lepton beam polarisation [34].During the HERA II period, the machine was run inboth left handed and right handed polarisation modes,where the average beam polarisation is given by: P e = ( N R − N L ) / ( N R + N L ) (7)and N R ( N L ) is the number of right (left) handed lep-tons in the beam. Accordingly, four distinct data setswere recorded by the experiments at HERA II, by run-ning with either left or right handed polarised electrons orpositrons. The luminosity weighted average polarisationsof the HERA II data sets are also given in table 1. Table 1.
Integrated luminosity L and luminosty-weighted av-erage lepton beam polarisation P e of the H1 and ZEUS data.The centre of mass energy √ s of the data is 319 GeV, exceptfor the 1994-1997 data, which is 301 GeV.Data set H1 ZEUS L [pb − ] P e [%] L [pb − ] P e [%]1994-1997 e + p
36 0 48 01998-1999 e − p
16 0 16 01999-2000 e + p
65 0 63 0HERA II e + p
98 +32 91 +3282 −
38 68 − e − p
46 +37 71 +29103 −
26 99 − A general purpose particle physics experiment is normallycomposed of a series of different detectors surroundingthe interaction region, which is the nominal point wherethe two counter-rotating beams of particles are broughtinto collision. Each detector identifies and measures par-ticles produced in the interaction by taking advantage oftheir different properties. Figure 5 shows a general layoutof a particle physics experiment: a tracking device in amagnetic field is surrounded by an electromagnetic andan hadronic calorimeter, and finally by muon detectors.Particles produced in the interaction region traverse thesedetectors sequentially from the collision point outwards,leaving different signatures depending on their physicsproperties.The first detector surrounding the interaction regionis a tracking system, which records the passage of chargedparticles. This system may be comprised of multiple detec-tors, such as drift chambers and silicon trackers. Chargedparticles leave their energy in these detectors via ionisa-tion, and due to the low material budget only a smallfraction of the particle energy is lost in such devices. Ingeneral neutral particles are not seen as tracks, but pho-tons may convert into an electron-positron pair which can
Fig. 5.
Typical components of a particle physics detector. Dif-ferent types of particle leave different signatures in the detec-tor, allowing particle identification to be performed [35]. then be detected in the tracker. Tracks are reconstructedby detecting the particle energy lost along their path in-side the detector. A magnetic field, which is parallel to thebeam direction, allows the particle momentum and chargeto be determined, based on the curvature of the tracks.The characteristic pattern of energy loss in the trackermay also be used to perform particle identification, allow-ing the separation of electrons, pions, kaons and protonsat low momenta.Moving outwards from the interaction region, the track-ing system is enclosed inside a calorimeter. Calorimetersmeasure both neutral and charged particles by completelydegrading them and absorbing all of the energy they de-posit. A typical design is a sampling calorimeter , in whichlayers of active material such as scintillator or liquified no-ble gas are interleaved by layers of absorber such lead ordepleted uranium. A calorimeter is also able to determineif a particle has electromagnetic or hadronic interaction byexamining the pattern of the energy loss. This allows theseparation of electron and photons from other particleswhich undergo hadronic interactions. A calorimeter is de-signed such that electrons and photons leave all of their en-ergy in the electromagnetic section, which is closer to theinteraction region and typically many radiation lengthsdeep. The electromagnetic interactions occur rapidly withthe nuclei in the absorbing layers via the bremsstrahlungand pair-production processes. As electrons and photonscannot be distinguished using the calorimeter alone, thisis done by spatially matching the electromagnetic energydeposit to a track in the tracking system. Hadrons pene-trate more deeply in the detector, leaving energy depositsnot only in the electromagnetic calorimeter but also in thehadronic section, where they interact strongly with thenuclei of the absorbing layers, elastically and inelastically,resulting in a shower composed of secondary hadrons. Thecharacteristic length of the hadronic shower, the interac-tion length , is much longer than the radiation length forthe same material and the shower, which also contains
D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA an electromagnetic component, is typically much broaderthan a purely electromagnetic interaction, allowing thetwo shower types to be distinguished. A full discussion onthe separation of electromagnetic and hadronic showerscan be found elsewhere [36].Muons do not interact like hadrons via the strong forceand do not radiate via bremsstrahlung as much as elec-trons due to their heavier mass, losing their energy onlyvia ionisation and behaving like a minimum ionising par-ticle. They therefore penetrate beyond the main calorime-ters and additional, dedicated muon detectors are installedas the outermost layer of the detector. In order to makea muon momentum measurement, information from theseoutermost detectors is typically matched to a track mea-sured in the tracking system.A detailed description of the H1 and ZEUS detectorscan be found elsewhere [15,16,17]. Both detectors are de-scribed by a right handed cartesian coordinate system( x, y, z ) with the nominal interaction point defined at theorigin, + x pointing towards the centre of the ring, + y pointing vertically upwards and + z in the direction of theincoming proton beam (also referred to as the forward di-rection). The corresponding spherical coordinate system( r, θ, φ ) is defined so that θ = 0 ◦ is in the proton directionand consequently θ = 180 ◦ is in the electron ( backward )direction.The H1 and ZEUS detectors are illustrated in figure 6.Both designs feature tracking detectors closest to the beampipe, which runs through the centre, surrounded by elec-tromagnetic and hadronic calorimetry, which is enclosedin a muon system. Two striking features can be seen inthe design of both the H1 and ZEUS detectors. Firstly,almost complete coverage is achieved around the inter-action point. This not only allows particles produced inthe ep interaction to be almost completely contained, butalso results in a reliable calculation of any net transversemomentum imbalance in an event, which is important ifthe resulting final state includes neutrinos. Secondly, bothdesigns are very asymmetric, corresponding to the largeasymmetry in the beam energies. Thus the backward re-gion of each detector is mainly dedicated to the detectionof the scattered electron, whereas the forward region con-tains more instrumentation and a deeper coverage. Moredetails on the main H1 and ZEUS detector componentsare given in the following sections. The central and forward tracking detectors, which coverthe regions 20 ◦ < θ < ◦ and 7 ◦ < θ < ◦ respectively,are used to measure charged particle trajectories and toreconstruct the interaction vertex. These detectors are en-closed together with the Liquid Argon (LAr) calorime-ter inside a superconducting magnetic coil with a fieldstrength of 1 .
16 T parallel to the z axis. From the cur-vature of charged particle trajectories in the magneticfield, the central tracking system provides transverse mo-mentum measurements with a resolution of σ P T /P T =0 . P T / GeV ⊕ . Fig. 6.
The H1 (top) and ZEUS (bottom) multi-purpose de-tectors employed at HERA. The proton beam enters the H1(ZEUS) detector from the right (left). also be ascertained from the direction of the curvature,and an accurate measurement of the tracks in an eventprovides spatial information on the interaction vertex. Thecentral and forward tracking detectors are complimentedat the very centre of the H1 detector by the central [37],backward [38] and (during HERA II only) forward silicontrackers, providing improved z -resolution and polar an-gle measurements. Additional track reconstruction is pro-vided in the backward region by the backward drift cham-ber (backward proportional chamber) during the HERA I(HERA II) running period.The LAr calorimeter [39] covers the polar angle range4 ◦ < θ < ◦ with full azimuthal ( φ ) acceptance and is . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 7 composed of two sections: an electromagnetic calorime-ter (EMC) and a hadronic calorimeter (HAC). The pas-sive layers of the EMC are formed from 2.4mm thick leadplates, whereas the HAC uses 16mm thick plates of stain-less steel; liquid argon forms the common sampling layerfor both the EMC and the HAC. Charged particles pro-duced in the shower ionise the argon atoms and the re-sulting electrons are converted to a signal and read out.The LAr is a non-compensating calorimeter, resulting ina 30% loss of the initial hadronic energy to the showeringprocess. To account for this, an offline software techniqueis employed [40]. The energies of electromagnetic showersare measured in the LAr calorimeter with a precision of σ ( E ) /E ≃ / p E/ GeV ⊕
1% and hadronic energy de-posits with σ ( E ) /E ≃ / p E/ GeV ⊕ (SpaCal) [43] covering the backward re-gion 153 ◦ < θ < ◦ completes the measurement ofcharged and neutral particles. Like the LAr calorimeter,it is divided into electromagnetic and hadronic sections,although its primary function is the detection of elec-trons scattered through low angles. Both sections consistof scintillating fibres, which form the sampling material,embedded in a lead matrix absorber. Charged particlesproduced by showering in the lead cause the fibres to scin-tillate, and the resulting light is recorded using photomul-tipliers. The response to electrons is given by σ ( E ) /E =7% / p E/ GeV ⊕
1% and σ ( E ) /E = 13% / p E/ GeV ⊕ ◦ < θ < ◦ . When the streamer occurs withinthe LST, pulses generated on the strips are combined bythe central muon trigger to reconstruct the muon track.In the central (barrel) region, at least 2 hits in the in-ner 4 layers are required. In the endcaps, which completethe iron shell around the detector, at least 3/5 hits are re-quired. The signals from the central muon system are com-bined with tracking information from the central trackingdetector to form the muon momentum measurement. Inthe very forward region (3 ◦ < θ < ◦ ) a set of six dou-ble layers of drift chambers, three either side of a central1 . .
40m to 2 . θ an-gles and so the toroidal magnet is used to bend the pathof traversing muons, enabling an independent momentummeasurement.The H1 detector contains approximately 270 ,
000 read-out channels, which combined with the HERA bunch cross-ing frequency of 96 ns (equivalent to an event rate of This device was installed in 1995, replacing a lead-scintillator sandwich calorimeter [16]. ≈
10 MHz) provides a potential rate of data flow thatis too high for the detector components and electron-ics employed to process. To cope with this, a multi-leveltrigger system is employed. The first level comprises trig-gers built using about 200 different subtriggers , each us-ing basic information from different parts of the detector:calorimeter energies, tracks multiplicities and so on. Thelevel one subtriggers fired by more common physics pro-cesses are only accepted by the central trigger a fractionof the time using a technique called prescaling : for a trig-ger with a prescale of p , only 1 in p events are kept. Leveltwo triggers add additional information and combine ex-isting triggers, often utilising different subdetectors. Thereare two components: a topological trigger, which employspattern recognition using a 2D projection (or topology ) ofthe event in θ and φ and a neural network based system.During HERA II particle identification was employed atlevel three, using the Fast Track Trigger (FTT). Finally,the level four trigger runs on a filter farm and providesmore detailed reconstruction and selection of tracks andclusters. The level 4 farm runs at up to 50 Hz, at whichrate the H1 data events are written out for analysis. Charged particles are detected by ZEUS using the CentralTracking Detector (CTD) [46,47,48], the Microvertex De-tector (MVD) [49] and the straw-tube tracker (STT) [50].The CTD and the MVD are located in a magnetic fieldof 1 .
43 T, provided by a thin superconducting solenoid.The CTD consists of 72 cylindrical drift chamber lay-ers, organised in nine superlayers covering the polar-angleregion 15 ◦ < θ < ◦ . The MVD silicon tracker con-sists of a barrel (BMVD) and a forward (FMVD) section.The BMVD provides polar angle coverage for tracks withthree measurements in the range 30 ◦ < θ < ◦ . TheFMVD extends the polar-angle coverage in the forwardregion down to 7 ◦ . The STT covers the polar-angle region5 ◦ < θ < ◦ and consists of 48 sectors of two differ-ent sizes. Each sector, which is trapezoidal in shape andsubtends an azimuthal angle of 60 ◦ , contains 192 (smallsector) or 264 (large sector) straws of diameter 7 . ◦ or 15 ◦ to each other.A high-resolution, uranium-scintillator calorimeter(CAL) [51,52,53,54] is employed by ZEUS, consisting ofthree parts: the forward (FCAL), the barrel (BCAL) andthe rear (RCAL) calorimeter, covering 99 .
7% of the solidangle around the nominal interaction point. Each partis subdivided transversely into towers and longitudinallyinto one electromagnetic section (EMC) and either one(RCAL) or two (BCAL and FCAL) hadronic sections (HAC).The relative energy resolutions of the CAL, as measuredunder test-beam conditions, are σ ( E ) /E = 18% / p E/ GeVfor electrons and σ ( E ) /E = 35% / p E/ GeV for hadrons.The timing resolution of the CAL is better than 1 ns for
D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA energy deposits exceeding 4 . × silicon-pad detectors at a depth of 3 . ◦ < θ < ◦ ) and RMUON (135 ◦ < θ < ◦ ) are comprised of LSTs, located behind the CAL, andinside and outside the magnetised iron yoke surroundingthe CAL. The FMUON is made up of six planes of LSTsand four planes of drift chambers covering the angular re-gion 5 ◦ < θ < ◦ . Whereas the central and rear muonsystems use the magnetic field of the iron yoke, two irontoroids with a field strength of 1 . x − y in the barrel, y − z inendcaps) with an accuracy of a few mm.Similarly to H1, ZEUS also employs a multi-level trig-ger system. The first level, which deals with the very high10 MHz rate, handles simple event level information, suchas calorimeter energy deposits or the number of tracks inthe event. At the second level more refined informationis available, such as the arrival time of particles in thecalorimeter, which is used to achieve an efficient separa-tion between ep collision events and background. At thethird level, part of the offline reconstruction software isrun in order to select signal events. The design and concept of the HERA detectors are drivenby the physics they are required to measure and the result-ing particle identification and event reconstruction meth-ods employed by the H1 and ZEUS experiments are sim-ilarly defined. This section describes the identification ofthe particles and event level quantities used in the analy-ses presented in this review. A description of the variouskinematic reconstruction methods, which require at leastone of the components detailed below, is given in the fol-lowing section.
Electrons are identified as compact, isolated energyclusters in the electromagnetic part of the calorimeters.Electron candidates are also required to have an associ-ated track, with a distance of closest approach (DCA) to the calorimetic cluster typically less than 12cm. Fur-ther requirements on the electron track are often appliedin the central region of the detector where coverage ismore complete, such as a minimum measured transversemomentum, P T , and a minimum radial starting positionmeasured with respect to the nominal interaction point.The electron cluster is required to be clean, such that theenergy in a cone of radius 1 in pseudorapidity -azimuth( η − φ ) space around the electron cluster is limited to asmall fraction of the electron energy. Inefficient regionsbetween calorimeter modules, where an electron may passthrough the electromagnetic section and into the hadronicsection without interaction, are excluded using fiducialvolume cuts. The electron energy E e and polar angle θ e are determined from the calorimeter cluster; the azimuthalangle φ e is determined from the track. A sample of NCevents with a well contained hadronic final state is usedto perform a calibration of the electron energy, where themeasured electron energy in the calorimeter, E e , is com-pared to that determined via the “double angle method”, E DA , as described in Section 6. Further details on theelectron calibration performed by H1 can be found in [60]and references therein. Photons are identified using the same criteria as elec-trons concerning the isolation of the electromagnetic clus-ter. Conversely to electrons however, a track veto is ap-plied, so that any photon candidates with an associatedtrack are rejected. For example, in the case of H1, a min-imum track-cluster DCA of 12 cm and no tracks within acone of radius 0 . η − φ space around the cluster arerequired. Muons are identified using a wide range of detectorcomponents, where the muon reconstruction algorithmsrequire a track in the tracking system, a minimum ionisingparticle (m.i.p.) energy deposit in the electromagnetic andhadronic calorimeter, which is of the order of 1 − P µT and itsangular variables θ µ and φ µ are given by the associatedtrack. Muons with a transverse momenta lower than a fewGeV do not reach the outer muon detectors and are usu-ally stopped in the calorimeter, but still may be identifiedas muons by the characteristic calorimeter pattern. Giventhe multi-detector nature of muon identification, a seriesof muon classes or grades are usually employed, dependingon which information is available. These grades typicallyuse track quality and DCA arguments, as well as require-ments on the number of hit in the muon system as well asmatching between the measurements available. Jets are narrow cones of hadrons or other particlesproduced from the hadronisation of a quark or a gluon. Inthe detector, they are reconstructed as clusters of energyin the electromagnetic and hadronic calorimeter, whichare recognised as coming from a collimated particle flow. The pseudorapidity is defined as η = − log tan( θ/ Tracking information can also be used at particle momentafor which the resolution of the tracking detector is betterthat that of the calorimeter.The features of jet in a hadronic final state are closelyrelated to those of the partons originating them. However,jets are complex objects which are not uniquely defined inQCD and whose definition relies on the algorithms usedto reconstruct them [61]. These come essentially in twotypes: cone algorithms , in which a jet is defined as a coneof radius R in the η − φ plane, and clustering algorithms , inwhich particles (or energy deposits) are assigned to jets it-eratively according to whether a given energy-angle resolu-tion variable y ij exceeds a fixed resolution parameter y cut .Clustering algorithms are more reliable in hadron-hadronand lepton-hadron collisions, as they are not affected fromambiguities related to the presence of overlapping jets inmulti-jet events.At H1 and ZEUS, jets are reconstructed using the k T clustering algorithm [62], which uses the relative trans-verse momentum k T between the particles as a resolu-tion variable to identify jets. This algorithm is infraredand collinear safe at any order in QCD, can be used withthe same procedure both on theoretical calculations andon experimental data and treats multi-jet events withoutambiguities. A jet is usually kinematically identified by itstransverse energy E jet T and its angular variables η jet and φ jet . Typical values used in the k T clustering algorithmare R < E jet T = 5 GeV. Later publica-tions [63] have also employed the anti − k T algorithm; dis-cussions on the merits of various jet clustering algorithmsare available elsewhere [64].All identified leptons are excluded from the inclusivehadronic final state and any energy around the leptonin a cone of radius of 0 . η − φ space for electrons andradius 1 . P eT to that of the inclusive hadronic final state, P hT . The P T balance, P hT /P eT should be equal to 1 in in-trinsically balanced NC events and the data are adjustediteratively until they are in agreement with the MC simu-lation. The calibration procedure may involve additionalsteps, in particular in the treatment of jets, see for exam-ple [36].The missing transverse momentum , P miss T , is cal-culated using the vector sum of all identified particles anda significant value of this quantity may indicate the pres-ence of a neutrino, or neutrinos, in the event. The vector p miss T is derived from the total visible hadronic momentumvector, p T , by p miss T = − p T , where: p T = ( P x , P y )= X i E i sin θ i cos φ i , X i E i sin θ i sin φ i ! . (8) For example, in CC events a significant imbalance of trans-verse momenta of measured final state particles is ob-served. As a consequence, the P x and P y components of p miss T are non zero, and they can be attributed to the out-going neutrino. Many of the final states examined in thisreview feature neutrinos, and as such P miss T is employedin such analyses. A reliable measurement of this quan-tity is made possible via the near hermetic coverage ofthe H1 and ZEUS detectors around their respective in-teractions points. A related quantity used in several H1analyses is P calo T , the net transverse momentum calculatedfrom all reconstructed particles measured in the calorime-ter. This quantity reflects the missing transverse momen-tum as seen by the trigger. For events containing highenergy muons, where only the (relatively small) muon en-ergy deposited in the calorimeter is included, P calo T ≃ P hT ,otherwise P calo T = P miss T . The reconstruction of the scattered electron together withthat of the hadronic final state is of particular importanceat HERA as it allows the determination of the kinematicvariables introduced in Section 1. Indeed, one of the salientfeatures of the H1 and ZEUS experiments is the possibil-ity to determine NC event kinematics from the scatteredelectron or from the hadronic final state, or using a combi-nation of the two. In the case of NC DIS, exclusively usingthe scattered electron to determine the event kinematicsresults in a less model dependent analysis, which is easierto interpret theoretically. Resolution, measurement accu-racy and effects due to the radiation of photons by theincoming electron influence the choice of the reconstruc-tion method in a given kinematic region. For a broaderdiscussion of the reconstruction methods presented in thissection, see for example [60,65].For NC scattering, the “electron method” is favoured,where the inelasticity and the negative four-momentumtransfer squared are calculated from the scattered electronenergy E e and polar angle θ e as: Q e = P eT − y e , y e = 1 − Σ e E e , x e = Q e sy e , (9a)where P eT = E e sin θ e is the electron transverse momen-tum, Σ e = E e (1 − cos θ e ) = E e − P ez , and E e is the en-ergy of the initial state electron. Using this method, thenegative four-momentum transfer squared may also be ex-pressed as: Q e = 4 E e E e cos θ e . (9b)In the case of CC events, as the scattered neutrinois not detected only the information on the hadronic fi-nal state can be used for the reconstruction of the eventkinematics. The “hadron method” or “Jacquet-Blondelmethod” [66] uses similar relations to those defined ineqation 9a, obtained exclusively from the reconstructed hadronic final state: Q h = P hT − y h , y h = Σ h E e , x h = Q h sy h , (10)where Σ h = P i ( E hi − p hz,i ) is the total hadronic E h − P hz ,summed over all reconstructed hadronic final state par-ticles i , and P hT is transverse momentum of the inclu-sive final state. A combination of P hT and Σ h defines thehadronic scattering angle, γ h , where:tan γ h Σ h P hT (11)which, within the Quark Parton Model (QPM) [67] corre-sponds to the direction of the struck quark.The “sigma method” [68] makes use of both electronand hadronic final state variables and equations 9a and 10are modified as: Q Σ = P T,e − y Σ , y Σ = Σ h E − P z , x Σ = Q Σ sy Σ . (12)The total E − P z of the event, δ , is defined as: δ ≡ E − P z = E e (1 − cos θ e ) + X i ( E hi − p hz,i )= Σ e + Σ h (13)and for events with no photon radiation from the incomingelectron δ = 2 E e = 55 GeV.The “e-sigma method” [69] is most often used for thereconstruction of NC kinematics and is an optimum com-bination of the two methods, providing good resolutionwhilst minimising radiative effects [70]: Q eΣ = Q e , y eΣ = Q e sx Σ , x eΣ = x Σ . (14)Finally, the “double angle method” [71,72] is used toreconstruct the event kinematics from the electron andhadronic scattering angles: y DA = tan ( γ h / θ e /
2) + tan ( γ h / ,Q DA = 4 E e · cot ( θ e / θ e /
2) + tan ( γ h / , (15a) x DA = Q DA sy DA . In this method, the energy of the scattered electron maybe calculated via: E DA = 2 E e sin γ h sin γ h + sin θ e − sin ( γ h + θ e ) , (15b)which is used in the calibration of the electron energy asdescribed in section 5. This method is largely insensitiveto hadronisation and is, to first order, independent of thedetector energy scales. However, the hadronic angle is lesswell-determined than the electron angle due to particleloss in the beampipe, and an additional correction maybe applied [65]. To study different physics models and in particular com-pare these models with experimental data, stochastic tech-niques are employed. These techniques, which use randomnumbers and probability distributions, are termed
MonteCarlo (MC) methods. Simulation is an essential tool forphysics analysis, contributing to a better understandingof the data and of the detector response to physics events.Moreover, the theoretical models implemented in MC pro-grams may be tested by comparing the prediction fromthe simulation to what is observed in the real data. Thesimulation of physics events at HERA, much like at otherparticle physics colliders, can be broken down into threediscreet steps: event generation, detector simulation, andfinally reconstruction of the simulated events. These stepsare briefly described in the following.
Firstly, QCD MC event event generators are used, whichemploy the factorisation theorem [73] to describe the ep hard scatter, characterised by an associated scale allowingthe collision to be factorised into separate stages. Eventgenerators produce all final state partons for a given in-teraction, using all relevant diagrams and parton densityfunctions. The hard sub-process is the main feature of theevent, and is the interaction of a parton extracted from theproton and the photon (or a photon constituent in resolvedphoton events). This process can be calculated in a fixedorder perturbative expansion since it involves a hard scale µ . Hadronisation is the process in which colourless hadronsare formed starting from coloured partons produced in thehard scatter. It is a non-perturbative phenomenon whichis modelled by the simulation programs using phenomeno-logical inputs. The main hadronisation models availableinclude the cluster model (for example, as done by HER-WIG [74]) and the Lund string model [75] (for example,as done by PYTHIA [76] and JETSET [77]). In processesinvolving charged and coloured objects the topology of anevent can be strongly influenced by the emission of gluonsand photons by the initial or final state. These pertur-bative corrections are usually modelled by the so called parton shower method , where the radiation is simulatedby an arbitrary number of branchings of one parton intotwo, such as e → eγ , q → qg , q → qγ or g → q ¯ q . A fi-nal consideration is the beam remnant, which comprisesthe remainder of the initial state particles, following thehard scatter and any initial and/or final state radiation. Ifthis remnant is coloured, it will be necessarily connectedto the rest of the event and needs to be fragmented andreconstructed coherently. The interactions of any unstablepartons produced (mainly quarks and gluons) are furthersimulated until only long lived stable particles exist. Thesimulated event then consists of a list of 4-vectors, describ-ing the final state particles. . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 11 The output of the event generator comprises a list of par-ticles produced in the hard scattering, as well as the par-ticles produced from the parton shower, as explained inthe previous section. In real data the only available in-formation from an electron-proton scattering is the signalthe particles produced in the collision leave in the var-ious detector sub-components as they pass through thedetector. A full detector simulation is therefore performedin order to also describe this at the MC level. The pas-sage of particles through the detector is simulated withthe GEANT3 [78] package. GEANT provides a descrip-tion of all detector components, including the compos-ite material, as well as the shapes and relative positions.The program traces the passage of a particle through thewhole detector, simulating its response whilst taking intoaccount the relevant physics processes such as energy loss,multiple scattering and particle decays in flight. After thedetector response has been simulated, the trigger logic asimplemented in the data taking is added to the simula-tion. The simulated event now resembles a set of hits onwires, energy deposits in the calorimeters, signals in themuons chambers and so on, mimicking the traces left inthe detector by a real ep collision event. As a final step, the same reconstruction program used forthe data is applied to simulated events. This program re-constructs the event variables, like particle momenta andenergies, treating the data and the Monte Carlo in thesame way. All the information coming from the differentdetector sub-components are taken as input by the recon-struction program. MC simulated data are thus identicalto real data, with the addition of the generator level in-formation. This information and the difference betweenthe two levels of simulation also provide a method of cor-recting detector acceptances and resolution effects in thedata.
The cross sections of inclusive NC and CC interactions,which are measured at HERA with high precision, are oneof the most important ingredients for the determination ofthe proton parton distribution functions. The kinematicregion in x and Q covered by the HERA experimentsis shown in figure 2 and comprises a significant part ofthe x region of interest for the LHC experiments. As aconsequence, taking advantage of QCD factorisation andthe use of DGLAP equations [10,11,12,79,80], the PDFsextracted from the HERA data can be used as input forcross section determination at the LHC.The H1 and ZEUS collaborations published [81] a com-bination of their NC and CC cross section measurementsextracted from the full data sample collected at HERA. The details of how the combination was performed, in par-ticular regarding the treatment of the systematic uncer-tainties, are described in detail elsewhere [81]. For the aimsof this paper it is sufficient to say that the cross sectionsmeasured by the two collaborations are combined using a χ minimisation method, which takes into account boththe statistical and systematic uncertainties of the data.In particular, a distinction is made between the correlated and uncorrelated uncertainties among the different points(bins) of the analysis. In addition to the clear improve-ment on the statistical uncertainty obtained by combiningthe data, an improvement on the systematics uncertain-ties is also obtained. Intuitively, correlated systematic un-certainties that affect the measurement in one directionfor H1, and in the other for ZEUS, can be significantlyreduced in the data combination. The fact that the de-tectors and the analysis techniques are different is fullyexploited, where these differences translate into system-atic uncertainties affecting the data in a different way.In this sense, the detectors are used to “cross calibrate”each other. These arguments are explained in full math-ematical detail in the papers illustrating the method em-ployed [82,83]. It is also worthwhile pointing out also thatthis method allows the consistency of the data of the twoexperiments to be checked in a model-independent way,as the main assumption done in the data combination isthat there is a single true value of the cross section corre-sponding to each data point and each process, NC or CC e + p or e − p scattering. Cross sections for NC DIS interactions have been pub-lished [81] for 0 . ≤ Q ≤ , in a largephase space region 6 · − ≤ x ≤ .
65 for values of in-elasticity 0 . ≤ y ≤ .
95 (see figure 2). Covering thevery low Q regions required special experimental tech-niques. The lowest- Q data, Q > .
045 GeV , were col-lected during the HERA I data taking period with theZEUS detector using special tagging devices [84]. The Q range between 0 . and 1 . was covered us-ing special HERA I runs, in which the interaction vertexposition was shifted forward, bringing backward-scatteredelectrons with small scattering angles into the acceptanceof the detectors [82,85,86]. The Q > . regionwas covered with HERA I and HERA II data in differentconfigurations.In performing the analyses, three main different Q regions were considered, as the analysis methods differsubstantially among them. At √ s = 318 GeV, the high Q region is defined for Q between 150 and 30000 GeV ,whereas the low Q region comprises the range 2 < Q <
120 GeV . The very-low Q region, populated only withdata collected at √ s ≤
300 GeV, is defined for Q < . As a breakdown of perturbative QCD (pqCD) isexpected for Q approaching 1 GeV , the data of this lastregion cannot be compared to predictions from pQCD.The most interesting region for BSM searches is thehigh Q region, in particular at very low x , where the cross section is lower and the precision of the measure-ments is worse so that new phenomena can hide in thelarge SM background. In general, searches for deviationsfrom the SM are performed at the limits of the accessi-ble kinematic regions. Therefore, the analysis for the high Q analysis is reported here as representative. The selec-tion techniques of the many other analyses included in thecombined data are described in detail elsewhere ([81] andreferences therein).NC DIS events are generated with the DJANGOH [87]MC simulation program, which is based on HERACLES [88]for the electroweak calculation and LEPTO [89] for thehard matrix element calculation. The colour dipole modelas implemented in ARIADNE [90] is used to generatehigher order QCD dynamics. The JETSET program isused to simulate the hadronisation process in the ’string-fragmentation’ model.Events are selected by requiring the DIS electron tobe reconstructed in the final state. The electron recon-struction is based on an algorithm combining informationfrom the calorimeter energy deposits and tracks measuredin the central tracking detectors. The electron is requiredto have an energy E ′ e >
10 GeV and to be isolated fromother energy deposits in the calorimeter. If the electron isfound in the acceptance region of the tracking detectors, atrack matched to the energy deposit in the calorimeter isrequired. The matching is performed considering the dis-tance of closest approach between the track extrapolatedto the calorimeter surface and the energy cluster position.A matched track is not required if the electron emergedoutside the acceptance of the tracking detectors.The most important background in the NC DIS anal-ysis comes from photoproduction events, when an energydeposit in the calorimeter associated to a charged track iswrongly identified as the scattered DIS electron. In orderto suppress this background, a cut on the total E − P Z as defined in equation 13 is used in the event selection,by requiring events to have 38 < δ <
65 GeV. As alreadymentioned in section 6, conservation of energy and lon-gitudinal momentum implies that δ = 2 E e = 55 GeV,if all final-state particles are detected and perfectly mea-sured. Undetected particles that escape down the forwardbeampipe have a negligible effect on δ . However, particleslost down the backward beampipe could lead to a sub-stantial reduction in δ . This is the case for photoproduc-tion events, where the electron emerges at a very smallscattering angle, or for events in which an initial-statebremsstrahlung photon is emitted. In order to further re-duce the photoproduction background, the selected NCevents are required to have y < .
9. For the puposes of thisreview, it is worth noting that this requirement cuts outpart of the kinematic region interesting for BSM searches.Further cuts are applied in order to suppress the back-grounds from beam-gas and cosmic interactions. After allcuts, the remaining background contamination estimatedusing photoproduction MC is about 0 . σ ± NC is defined in terms of the inclu-sive NC cross section as: σ ± r,NC = d σ ( e ± p ) dxdQ · Q x πα Y + (16)where the fine-structure constant, α , is defined at scalezero and Y ± = 1 ± (1 − y ) . The combined high Q inclu-sive NC e + p reduced cross sections at √ s = 318 GeV, asextracted from the combined HERA data, are shown infigure 7. The cross sections are shown as a function of x indifferent Q bins and are compared to the HERAPDF2.0predictions [81] at next-to-next-to-leading (NNLO). Thecombined low Q HERA inclusive NC e + p reduced crosssections at √ s = 318 GeV are shown in figure 8. The datadescription by the SM prediction is generally good, exceptfor the turnover of the cross section at low x and low Q . H1 and ZEUS Q = 150 GeV s r , NC + Q = 200 GeV Q = 250 GeV Q = 300 GeV Q = 400 GeV Q = 500 GeV Q = 650 GeV Q = 800 GeV Q = 1000 GeV Q = 1200 GeV Q = 1500 GeV Q = 2000 GeV Q = 3000 GeV Q = 5000 GeV Q = 8000 GeV -2 -1 Q = 12000 GeV -2 -1 x Bj Q = 20000 GeV -2 -1 Q = 30000 GeV -2 -1 x Bj HERA NC e + p 0.5 fb –1 √ s = 318 GeVHERAPDF2.0 NNLO Fig. 7.
The combined high Q HERA inclusive NC e + p re-duced cross sections at √ s = 318 GeV, plotted as a function of x at fixed Q , with overlaid predictions of the HERAPDF2.0NNLO. The bands represent the total uncertainties on the pre-dictions. The combined reduced cross section as a function of Q at different x values is shown in figure 9. In the high Q region, the e − p cross section is significantly larger thanthe e + p . This is due to the parity-violating component ofthe NC interactions, namely to the exchange of a Z bosonbetween the electron and the proton. This component issuppressed at low Q due to the large mass of the Z boson and becomes relevant only for Q ∼ M Z .In figure 9 the HERA data are compared to the re-sults of fixed-taget experiments, which populate the re-gion of lower Q and higher x values. The HERA and thefixed-target results are in good agreement, as shown by . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 13 H1 and ZEUS Q = 2 GeV s r , NC + Q = 2.7 GeV Q = 3.5 GeV Q = 4.5 GeV Q = 6.5 GeV Q = 8.5 GeV Q = 10 GeV Q = 12 GeV Q = 15 GeV Q = 18 GeV Q = 22 GeV Q = 27 GeV Q = 35 GeV Q = 45 GeV -3 -1 Q = 60 GeV -3 -1 Q = 70 GeV x Bj Q = 90 GeV -3 -1 Q = 120 GeV -3 -1 x Bj HERA NC e + p 0.5 fb –1 √ s = 318 GeVHERAPDF2.0 NNLO Fig. 8.
The combined low Q HERA inclusive NC e + p re-duced cross sections at √ s = 318 GeV, plotted as a function of x at fixed Q , with overlaid predictions of the HERAPDF2.0at NNLO order in pQCD. The bands represent the total uncer-tainties on the predictions. Dotted lines indicate extrapolationinto kinematic regions not included in the fit. H1 and ZEUS x Bj = 0.00005, i=21x Bj = 0.00008, i=20x Bj = 0.00013, i=19x Bj = 0.00020, i=18x Bj = 0.00032, i=17x Bj = 0.0005, i=16x Bj = 0.0008, i=15x Bj = 0.0013, i=14x Bj = 0.0020, i=13x Bj = 0.0032, i=12x Bj = 0.005, i=11x Bj = 0.008, i=10x Bj = 0.013, i=9x Bj = 0.02, i=8x Bj = 0.032, i=7x Bj = 0.05, i=6x Bj = 0.08, i=5x Bj = 0.13, i=4x Bj = 0.18, i=3x Bj = 0.25, i=2x Bj = 0.40, i=1x Bj = 0.65, i=0 Q / GeV s r , NC x i HERA NC e + p 0.5 fb –1 HERA NC e p 0.4 fb –1 – √ s = 318 GeVFixed TargetHERAPDF2.0 e + p NNLOHERAPDF2.0 e p NNLO – -3 -2 -1 Fig. 9.
The combined HERA data for the inclusive NC e + p and e − p reduced cross sections together with fixed targetdata [91,92] and the predictions of HERAPDF2.0 NNLO [81].The bands represent the total uncertainty on the predictions. the comparison with theoretical predictions based on theHERA data alone [81]. The level of agreement between the two fixed-target experiment results shown in the fig-ure [91,92] was investigated in [92] and found to be good,taking into account the normalisation uncertainties of thedata and the systematic uncertainties quoted in the analy-ses. The HERA data significantly extend the region wherethe reduced cross section can be measured with very goodprecision.Scaling violations, as predicted by the DGLAP equa-tions, are also clearly visible in figure 9, where in the low x region the reduced cross section is not independent of Q ,but shows a slope that becomes steeper with decreasing x . These violations are due to QCD effects not present inthe na¨ıve QPM model. The large kinematic range coveredby HERA clearly demonstrates the scaling violations andallows them to be used for the extraction of the gluon den-sity in the proton. On the other hand, it has to be notedthat the gluon content of the proton cannot be measureddirectly at HERA. This means that phenomenological as-sumptions are needed in the extraction of the gluon den-sity from the data, introducing an important source ofuncertainty in the extraction of the proton PDFs.The HERA inclusive NC DIS cross sections are an im-portant input to the determination of the proton struc-ture functions. The double-differential cross section of theelectron-proton NC DIS as a fucntion of x and Q can beexpressed in terms of the proton structure functions F , F and F L , as [81]: d σ ( e ± p ) dxdQ = 2 πα xQ (cid:8) Y + F ∓ Y − xF − y F L (cid:9) . (17)It follows that from the reduced cross section, ˜ σ ± NC , theproton structure functions can be constrained: σ ± r,NC = F ∓ Y − Y + xF − y Y + F L . (18)The structure functions F , F and F L are process de-pendent. F is non-zero only for weak interactions and isgenerated by parity-violating interactions, i.e. by the ex-change of a W boson in CC DIS or a Z boson in NCDIS between the electron and the proton. Therefore, for Q ≪ M Z : σ ± r,NC = F ∓ − y Y + F L (19)The F L term is related to the longitudinally polarisedvirtual boson exchange process. This term vanishes at low-est order QCD but has been predicted [93] to be non-zerowhen including higher order QCD terms. The contributionof F L to the reduced NC cross section is relevant only forvalues of y larger than approximately 0 . F L has been performed atHERA by determining the reduced cross section, σ ± r,NC , atdifferent values of √ s by reducing the proton beam energyfrom E p = 920 GeV to E p = 460 GeV and E p = 575 GeV,as described in section 3. This method had been previouslyused to extract F L in fixed-target experiments [91,92,94,95]. From equation 6, y = Q /sx and therefore the cross sections can be measured at the same values of x and Q but at different values of y , allowing an experimentalseparation between F and F L in equation 19. The sensi-tivity to F L is increased by measuring the cross sectionsin the high y region, but in this region the electron energyis low and the background from photoproduction is large.The separation between NC DIS and the photoproductionbackground is therefore one of the main challenges of thehigh y analysis.The structure function F L as measured by the H1 [96]and ZEUS [97] collaborations is shown in figure 10. Thedata are compared with several QCD predictions at NNLO,which describe the measurements reasonably well. (cid:215) x .
28 0 . .
59 0 .
88 1 .
29 1 .
69 2 .
24 3 . .
02 5 . .
87 9 .
58 12 . . . . . . . . H1 Collaboration L F ] [GeV Q HERAPDF1.5 NNLOCT10 NNLOMSTW08 NNLO ABM12 NNLONNPDF2.3 NNLOJR09 NNLO H1 ZEUS
Fig. 10.
The proton structure function F L averaged over x at different Q (solid points). The average value of x for each Q is given above each data point. The inner error bars rep-resent the statistical uncertainties, the full error bars includethe statistical and systematic uncertainties added in quadra-ture, including all correlated and uncorrelated uncertainties.The data are compared to NNLO predictions from a selectionof PDF sets as indicated ([96] and references therein). A precise direct measurement of F L would allow, ac-cording to the Altarelli-Marinelli relation [93], a direct ex-traction of the gluon density in the proton, which is con-strained indirectly via scaling violations. The F L measure-ment was used [96] to perform a gluon density extractionbased on a NLO approximation, and the agreement withthe gluon as determined from scaling violations was foundto be reasonably good. Although the scaling violations al-low a much better constraint of the gluon in the proton,the comparison with the direct extraction from the F L measurement provides an independent check of its valid-ity. Although more at a qualitative than at a quantitativelevel, this measurement represents an improvement on theknowledge of the gluon density in the proton.From equation 18 it follows that the structure function xF can be extracted from the difference between the e + p and e − p reduced cross sections: xF = Y + Y − ( σ − r , NC − σ +r , NC ) . (20) It is useful to consider the simplified picture as expressedin the QPM, where F L = 0. In the QPM, xF is directlyrelated to the valence quark distributions in the proton,which, assuming symmetry between the quarks and anti-quarks in the sea, can be expressed as: xu v = xU − x ¯ U ,xd v = xD − x ¯ D ; (21)where xU , x ¯ U , xD and x ¯ D represent the sums of partondistributions for up-type and down-type quarks and anti-quarks, respectively. Below the b -quark mass threshold,they are related to the quark distributions as follows: xU = xu + xc, x ¯ U = x ¯ u + x ¯ c,xD = xd + xs, x ¯ D = x ¯ d + x ¯ s, (22)where xs and xc are the strange- and charm-quark distri-butions.In the HERA kinematic regime the dominant contri-bution to xF comes from its photon- Z exchange inter-ference term, xF γZ . In the QPM, this is expressed by therelation: xF γZ ≈ x u v + d v ) , (23)which shows that xF is directly related to the valencequark distributions in the proton. The measurements of xF γZ therefore make it possible to determine the behaviourof the valence quark distributions at low x . The structurefunction xF γZ as extracted from the HERA combined NCDIS cross sections is shown in figure 11 and compared topQCD predictions from HERAPDF2.0. Bj x -1
10 1 Z g x F H1 and ZEUS = 1000 GeV Q -1 HERA 1 fbHERAPDF2.0 NLO
Fig. 11.
The structure function xF γZ averaged over Q ≥ at the scale Q = 1000 GeV together with theprediction from HERAPDF2.0 NLO. The band represents thetotal uncertainty on the prediction. The CC DIS process ep → νX was measured at HERAfor the first time in 1993. The Q dependence of the CC . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 15 DIS cross section is sensitive to the W boson mass, whichenters the CC propagator. One of the aims of the first mea-surements of CC DIS was the determination of this mass,which was extracted from a fit to the differential CC DIScross section as a function of Q , leaving it as a free pa-rameter of the fit. The fact that the obtained value wasconsistent to the mass of the W boson as measured by thehadron colliders at that time demonstrated the presenceof the W propagator [98,99]. The measurement of CC DISinteractions in ep collisions, e + p → ¯ νX ( e − p → νX ), pro-vides a complementary view with respect to NC DIS forthe understanding of the proton structure and the SM.While NC DIS is mediated by the exchange of photonsand Z bosons and is sensitive to all quark flavours, onlydown-type quarks and up-type antiquarks (down-type an-tiquarks and up-type quarks) contribute at leading orderto e + p ( e − p ) CC DIS. Thus this process is a powerfulprobe of flavour-specific PDFs, as described in more de-tail in the following. Although part of this informationcould already be obtained from the previous fixed-targetneutrino experiments, NC and CC DIS became accessibleat the same machine for the first time at HERA, and inan extended kinematic region.The precision of the measurement of the CC cross sec-tions at HERA has been significantly improved by combin-ing the data of the two experiments H1 and ZEUS. Crosssections for CC interactions have been published [81] for200 ≤ Q ≤ and 1 . · − ≤ x ≤ .
40 atvalues of y between 0 .
037 and 0 . W boson production, respectively.In CC DIS, the struck quark gives rise to one or morejets of hadrons and the energetic final state neutrino es-capes detection, leaving a large imbalance in the trans-verse momentum observed in the detector. Therefore, CCDIS events are selected by requiring a large missing trans-verse momentum in the event, P miss T , as defined in equa-tion 8.Backgrounds to CC DIS arise from high E T events inwhich the finite energy resolution of the calorimeter orenergy that escapes detection leads to significant missingtransverse momentum. Non- ep events such as beam-gasinteractions, beam-halo muons or cosmic rays can alsocause substantial imbalance in the measured transversemomentum and constitute additional sources of background.Moreover, single W boson production events and di-leptonevents could also constitute a potential background in casethe lepton(s) are poorly reconstructed.CC events are selected in the kinematic region Q >
200 GeV and y < .
9, with large missing transversemomentum, P miss T >
12 GeV, and a primary vertex re-
Fig. 12.
A charged current event with Q = 53060 GeV and x = 0 .
59 observed in the ZEUS data. The transverse momen-tum imbalance in the event is visible in the figure, as most ofthe activity appears in the upper part of the detector. constructed in the nominal interaction region. The vertexrequirement significantly reduces the non- ep background.Background from NC events with a poorly measured scat-tered electron or hadronic jets, leading to significant miss-ing transverse momentum, are removed by rejecting eventswith an isolated electromagnetic cluster in the calorime-ter and a longitudinal balance δ >
30 GeV. Other clean-ing cuts are used to reduce the remaining backgrounds,based on for example the number of tracks fitted to thevertex compared to the total, or on the azimuthal colli-mation of the energy flow in the event, using the ratio V ap /V p [102], where V p and V ap are the transverse energyflow parallel and antiparallel to the hadronic final state p hT , respectively, and are determined from the transversemomentum vectors p iT of all the particles i which belongto the hadronic final state according to: V p = X i p hT · p iT P hT for p hT · p iT > V ap = X i p hT · p iT P hT for p hT · p iT < ep events is found to be negligible, while other back-grounds from photoproduction, single W boson produc-tion and lepton pairs contribute up to 20% in the lowest- Q and lowest x bins. One of the selected CC events, asseen by the ZEUS detector, is shown in figure 12.Similarly to NC, cross sections are extracted and com-pared to the theoretical predictions from pQCD, based onHERAPDF2.0. The reduced cross sections for unpolarised CC e ± p scattering are defined as: σ ± r, CC = 2 πxG F (cid:20) M W + Q M W (cid:21) d σ e ± p CC dxdQ . (26)The combined inclusive CC reduced cross sections at √ s =318 GeV, as extracted from the combined HERA data,are shown in figure 13. The precise predictions describethe CC cross sections well. The CC data are in generalless precise than the NC data. H1 and ZEUS s r , CC Q = 300 GeV + Q = 500 GeV Q = 1000 GeV Q = 1500 GeV Q = 2000 GeV Q = 3000 GeV -2 -1 Q = 5000 GeV -2 -1 Q = 8000 GeV x Bj -2 -1 Q = 15000 GeV -2 -1 Q = 30000 GeV x Bj HERA CC e + p 0.5 fb –1 √ s = 318 GeVHERAPDF2.0 NNLO Fig. 13.
The combined HERA inclusive CC e + p reduced crosssections at √ s = 318 GeV with overlaid predictions from HER-APDF2.0 NNLO. The bands represent the total uncertaintieson the predictions. The combined inclusive CC reduced cross sections asa function of x in different Q bins are shown in figure 14.The difference between the e − p and the e + p cross sectionscan be intuitively understood at leading order by consid-ering the valence quark composition of the proton and thecharge of the exchanged vector boson in e − p and e + p in-teractions and is explained more formally below. The dataare well described by pQCD predictions.The cross sections of CC DIS also provide an importantinput for the determination of the proton structure. Inanalogy to equation 18, CC structure functions are definedsuch that: σ ± r, CC = Y + W ± ∓ Y − xW ± − y W ± L (27)In the QPM [67], W ± L = 0, while W ± and xW ± are ex-pressed as sum and differences of quark and anti-quarkdistributions, depending on the charge of the lepton beam: W +2 ≈ x ¯ U + xD, xW +3 ≈ xD − x ¯ U ,W − ≈ xU + x ¯ D, xW − ≈ xU − x ¯ D, (28) H1 and ZEUS x Bj = 0.008 (x15000)x Bj = 0.013 (x3000)x Bj = 0.032 (x700)x Bj = 0.08 (x170)x Bj = 0.13 (x20)x Bj = 0.25 (x2)x Bj = 0.40 (x0.1) Q / GeV s r , CC HERA √ s = 318 GeV HERAPDF2.0 NNLO √ s = 318 GeVCC e + p 0.5 fb –1 CC e p 0.4 fb –1 – CC e + pCC e p – -4 -3 -2 -1 Fig. 14.
The combined HERA data for inclusive CC e + p and e − p reduced cross sections at √ s = 318 GeV with overlaidpredictions of HERAPDF2.0 NNLO. The bands represent thetotal uncertainty on the predictions. and consequently: σ + r, CC ≈ ( x ¯ U + (1 − y ) xD ) ,σ − r, CC ≈ ( xU + (1 − y ) x ¯ D ) . (29)The combination of NC and CC DIS measurements there-fore makes it possible to determine both the combined sea-quark distributions, x ¯ U and x ¯ D , and the valence quarkdistributions, xu v and xd v .Equation 29 also provides the formal explanation forthe numerical difference between the cross section for e − p and e + p collisions (see figure 14), which is due to the pres-ence of the helicity factor (1 − y ) . As this factor multipliesthe valence quark distribution in the e + p cross section for-mula, it results in a suppression of the cross section at high y . For the e − p cross section, the (1 − y ) helicity factormultiplies the anti-quark distribution, which is part of thesea and is already suppressed at high Q and high x , andcontributes little compared to the quark term. The H1 and ZEUS combined NC and CC cross sections asa function of Q are shown in figure 15. The NC processesdominate the cross section at low Q . This is due to thefact that in the low Q region the major contribution tothe cross section is given by the exchange of a photonbetween the electron and the proton; W or Z exchangeis suppressed due to the high mass of the vector boson,which enters the propagator term, Q / ( Q + M W/Z ). At . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 17 higher Q , of the order of the mass squared of the W or Z boson, Q ≃ , CC and NC processesare equally important, providing experimental evidenceof electroweak unification. It can also be seen that the e − p cross section is higher than the e + p data for both NCand CC at higher values of Q due to the couplings of thequarks in the proton to the exchanged boson. The data arecompared with the predictions of HERAPDF2.0 at next-to-leading order (NLO), which provide a good descriptionof the measurements. / GeV Q ) ( pb / G e V / d Q s d -7 -5 -3 -1 H1 and ZEUS y < 0.9 = 318 GeVs -1 p 0.4 fb - HERA NC e -1 p 0.5 fb + HERA NC e p - HERAPDF2.0 NC e p + HERAPDF2.0 NC e -1 p 0.4 fb - HERA CC e -1 p 0.5 fb + HERA CC e p - HERAPDF2.0 CC e p + HERAPDF2.0 CC e 2 / GeV Q ) ( pb / G e V / d Q s d -7 -5 -3 -1 Fig. 15.
The combined HERA NC and CC e − p and e + p crosssections together with predictions from HERAPDF2.0 NLO.The bands represent the total uncertainty on the predictions. The combined HERA data are used as sole input for theextraction of the PDF set HERAPDF2.0 [81]. The frame-work already established for the extraction of the HERA-PDF1.0 [103] is used. The x and Q dependences of theNC and CC DIS cross sections were used to determinethe free parameters of the assumed shape of the partondistribution functions at a given value of Q .As pQCD is not applicable below Q of the order ofthe inverse of the proton radius squared, an intrinsic un-certainty is present in performing the QCD fits, due to thechoice of the scale at which to start the DGLAP evolution.In the analysis performed to extract the HERAPDF2.0PDF set, to safely remain in the kinematic region wherepQCD is expected to be applicable, only cross sectionsfor Q starting from Q = 3 . are used in theanalysis. The Q range of the cross sections entering thefit is therefore 3 . ≤ Q ≤ . The correspond-ing x range is 0 . · − ≤ x ≤ .
65. In addition to experimental uncertainties, model and parameterisationuncertainties are also considered.To extract the proton PDFs, predictions from pQCDare fitted to the data. These predictions are obtained bysolving the DGLAP evolution equations [10,11,12,79,80]at LO, NLO and NNLO in the ¯
M S scheme [104,105]. TheDGLAP equations yield the PDFs at all scales µ and x ,if they are provided as functions of x at some startingscale, µ . This is chosen to be µ = 1 . as forHERAPDF1.0 [103], since in the used formalism µ has tobe lower than the charm-quark mass parameter squared.The renormalisation and factorisation scales were chosento be µ = µ = Q .The values of the charm and beauty mass parametersare chosen after performing χ scans of NLO and NNLOpQCD fits to the HERA inclusive data and the H1 andZEUS charm and beauty data. The procedure is describedin detail elsewhere [106].A detailed description of the HERAPDF2.0 PDFs isbeyond the scope of this paper and further information isgiven in the publication [81]. Here as an example the quarkand gluon distributions are shown in figure 16 at a scale Q = 10 GeV . The gluon distribution domainates the low x region, while at high x , as expected, the valence quarkdistribution are prevalent, and the u -type quarks are twiceas much as the d -type, due to the QED couplings, whichare proportional to the quark electrical charge. -4 -3 -2 -1
10 1
HERAPDF2.0 NNLO uncertainties: experimental model parameterisation HERAPDF2.0AG NNLO x x f = 10 GeV m v xu v xd 0.05) · xS ( 0.05) · xg ( H1 and ZEUS
Fig. 16.
The parton distribution functions xu v , xd v , xS =2 x ( ¯ U + ¯ D ) and xg of HERAPDF2.0 NNLO at µ = 10 GeV .The gluon and sea distributions are scaled down by a factor 20.The experimental, model and parameterisation uncertaintiesare shown. The dotted lines represent HERAPDF2.0AG NNLOwith the alternative gluon parameterisation, see [81].8 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA HERAPDF2.0 has small experimental uncertainties dueto the high precision and coherence of the input data, andmakes precise predictions which describe the input datawell, as can be seen also in the examples reported above.The precision data on the inclusive ep scattering from theH1 and ZEUS experiments are one of the main legacies ofHERA. W boson The presence of a polarised electron beam during the sec-ond phase of the data taking period at HERA also pro-vides the opportunity to investigate the helicity structureof the Standard Model. The most striking evidence canbe seen in CC DIS processes. The electroweak Born-levelcross section for the CC reaction, e + p → ¯ νX ( e − p → νX ),with a longitudinally polarised positron beam can be ex-pressed as a function of the charged current structure func-tions W ± , W ± and W ± L [107]: d σ CC ( e ± p ) dxdQ = (1 ± P e ) G F πx (cid:18) M W M W + Q (cid:19) (cid:20) Y + W ± − Y − xW ± − y W ± L (cid:21) , (30)where, P e is the polarisation of the lepton beam, as givenin equation 7.It can be seen from equation 30 that the cross sectionfor the process e − p → νX ( e + p → ¯ νX ) has a linear depen-dence on the beam polarisation, and vanishes in the SM for P e − = 1 ( P e + = − e + p DIS cross section be-comes zero for a fully negatively polarised positron beam,a non-zero cross section at P e = − W boson, W R , and right-handedneutrinos, ν R . The H1 and ZEUS data have been used toconstrain the mass of such boson [60,110], assuming thecoupling strength and propagator dependence on the massof the boson to be the same as in SM CC interactions,and the outgoing right-handed neutrinos to be light. TheZEUS collaboration obtains M W R >
198 GeV at 95% con-fidence level (CL) [110], while the H1 collaboration givesa 95% CL limit of M W R >
214 GeV and M W R >
194 GeVfor e − p and e + p collisions, respectively [60].The HERA results shown in this section confirm theexcellent agreement between the data and the predictionsof the SM. However, there are parts of the phase spacewhich are not measured with very high precision, or typesof processes for which the cross sections as predicted bythe SM are very low and would not manifest themselvesin significant changes to the NC and CC inclusive crosssections.Searches for rare processes and BSM physics at HERAfocus therefore on processes with striking features but low [%] e P -100 -50 0 50 100 [ pb ] CC s p Scattering – HERA Charged Current e > 400 GeV Q y < 0.9 X n fi p + e X n fi p (cid:190) e HERAPDF 1.5 HERAPDF 1.5 H1 ZEUS H1 ZEUS Fig. 17.
The measured CC DIS cross sections versus the leptonbeam polarisation as measured by the H1 and ZEUS collabo-rations. The prediction from HERAPDF1.5 is also shown.
SM cross sections, like particle production at high trans-verse momenta, or specific model-predicted signatures likeSUSY, or heavy resonances like leptoquarks, and in gen-eral on deviations from SM cross sections in the regionswhich are less well measured, such as high Q and high x . The high Q NC DIS interactions e ± p → e ± X at HERAdescribed in the previous section provide the means tosearch for new physics beyond the SM at short distances,using the concept of four-fermion contact interactions (CI).As opposed to s -channel direct searches, where the massof any resonant particle is limited to the available cen-tre of mass energy via M X = √ xs , the search for CI reliesupon the indirect effects of the interference of the SM pho-ton and Z boson field with the field of any new particleproduced. Therefore, CI may manifest as deviations fromthe SM expectation in the measured differential cross sec-tion dσ/dQ and any observed deviation may be related tonew heavy particles with masses M X much larger than theelectroweak scale. In the low energy limit √ s ≪ M X suchphenomena can be described by an effective four-fermionCI model, and different implementations of such a modelare described in the following.The most general chiral invariant Lagrangian for NCfour-fermion CI in ep scattering may be written as [111,112,113,114]: L = X q X a,b = L,R = η qab (¯ e a γ µ e a )(¯ q b γ µ q b ) , (31) . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 19 where η qab are the CI coupling coefficients, a and b indicatethe left-handed and right-handed fermion helicities andthe first sum is over all quark flavours. In the kinematicregion of interest at HERA the valence ( u and d ) quarksdominate.For general models of fermion compositeness or sub-structure the CI coupling coefficients are defined as: η qab = ǫ qab πΛ (32)where Λ is the compositeness scale and the coefficients ǫ qab describe the chiral structure of the coupling and maytake the values ± M LQ ≫ √ s ,the coupling λ is related to the CI coupling coefficients via: η qab = ǫ qab λ M (33)The classification of leptoquarks is discussed in sec-tion 10, and follows the Buchm¨uller-R¨uckl-Wyler (BRW)model [115] where the coefficients ǫ qab depend on the lep-toquark type [116] and take values 0, ± . ± ± hierarchy problem , is the existence of largeextra dimensions [117,118,119]. In such a model it is pro-posed that whilst particles, including strong and electroweakbosons, are confined to four dimensions, gravity can prop-agate into additional n spatial dimensions, which are com-pactified with a radius R . The theory predicts a new grav-itational scale M S , related to the Planck scale by M P ∼ R n M nS , which for R ∼ n = 2 can be of orderTeV. Consequently, at high energies the strengths of thegravitational and electroweak interactions may be compa-rable [120]. The addition of the graviton-photon interfer-ence and graviton- Z interference to the SM cross section isdescribed in [121]. The graviton-exchange contribution tothe total eq → eq scattering cross section can thus be de-scribed [122,123] as a contact interaction with an effectivecoupling strength: η G = λM S (34)where the coupling λ is conventionally set to ± eq → eq scattering cross section: f ( Q ) = 1 − h R i Q (35) where h R i is the mean squared radius of the electroweakcharge distribution of the quark, or quark radius . Thisform factor modifies the Q dependence of the SM crosssection similarly to the above CI models.Several results on searches for contact interactions havebeen published by both H1 and ZEUS using partial HERAdata sets [120,121,124,125]. In this review we focus onthe H1 result [126] that uses their full data sample, corre-sponding to an integrated luminosity of 446 pb − as de-scribed in table 1. As some of the models described aboveexhibit chiral sensitivity, the longitudinally polarised datasets are analysed separately.To investigate contact interactions the measured H1NC differential cross sections dσ/dQ at high four-momentumtransfer squared Q >
200 GeV are compared to the SMprediction. The standard H1 NC event selection is em-ployed [60]. For the analysis of contact interactions, theSM prediction at high Q and high x are of special rele-vance. The use of a PDF set to determine the SM predic-tion in this kinematic region based mostly on the HERAdata is not appropriate, as the SM predictions would alsoinclude the effects from any potential contact interactionspresent in the data. Therefore, the PDF set CTEQ6mPDF [127] is used. The CTEQ6m set was obtained byfitting several experimental data sets. At high x this PDFis mostly constrained by fixed target experiments and alsoby W -boson production and jet data from the Tevatronexperiments, which are not sensitive to possible eq con-tact interaction processes. CTEQ6m does include early e ± p scattering data at high Q from the H1 and ZEUSexperiments, but as the e + p ( e − p ) data sets analysed hereare 6 (10) times larger the residual correlations betweenthe HERA data and the CTEQ6m PDF are small and areneglected in the following. The CTEQ6m parton densitiescan be therefore be regarded as unbiased with respect topossible contact interaction effects. CTEQ6m is chosen asit describes many experimental data and in particular, theHERA data in the region Q <
200 GeV , which are notused in this analysis. The analysis was also verified usingan alternative PDF not based on HERA high Q data,a dedicated H1 PDF set, obtained from a next-to-leadingorder QCD fit to the H1 data [82] with Q <
200 GeV ,excluding the high Q data used in this analysis. Both theSM expectation and limits derived using the dedicated H1PDF agree well with those obtained using the CTEQ6mPDF within the uncertainties. The ratio of the measuredcross sections to those from the SM prediction is shownin figure 18, where a good agreement is observed both inthe full data set and each of the polarised data sets fromthe HERA II.A quantitive test is performed to evaluate the impactof each of the different CI models on the SM predictionand the level of agreement to the data using a χ minimi-sation fitting function [125]. The fit to the experimentaland theoretical cross sections fully takes into account allstatistical and systematic uncertainties.The H1 data are found to be consistent with the SM ex-pectation based on the CTEQ6m PDF, yielding a χ /dof =16 . / . /
17) for the e + p ( e − p ) data, where 17 is the ] [GeV Q / d Q S M s / d / d Q s d Graph - p NC 0.16 fb - H1 e p - CTEQ6m e - p NC 0.28 fb + H1 e p + CTEQ6m e H1 ] [GeV Q / d Q S M s / d / d Q s d = - e (P - p NC 0.10 fb - H1 e p - CTEQ6m e 32.5%) = + e (P - p NC 0.09 fb + H1 e p + CTEQ6m e H1 ] [GeV Q / d Q S M s / d / d Q s d = + e (P - p NC 0.04 fb - H1 e p - CTEQ6m e 37.6%) = - e (P - p NC 0.08 fb + H1 e p + CTEQ6m e H1 (a)(b)(c) Fig. 18.
The ratio of the measured cross section to the SM prediction determined using the CTEQ6m PDF set for e + p → eX and e − p → eX scattering. Figure (a) shows the full H1 data with an average longitudinal polarisation of P e ∼
0. Figures (b)and (c) show the polarised H1 data divided into the different lepton charge and polarisation data sets. The error bars representthe statistical and uncorrelated systematic errors added in quadrature. The bands indicate the PDF uncertainties of the SMcross section predictions. number of Q bins. For each of the CI models describedabove, the effective scale parameters and couplings asso-ciated to the new physics scale are determined by a fitto the differential NC cross section. All scale parametersare found to be consistent with the SM and limits are cal-culated at the 95% CL using the frequentist method asdescribed in the H1 HERA I publication [125].Lower limits on the compositeness scale Λ in the con-text of the general CI model are presented in table 2.The results are presented for nine scenarios, which dif-fer in their chiral structure as determined by the CI cou-pling coefficients η qab . Depending on the model and thesign of the coefficients, limits on Λ are obtained in the range 3 . Λ − V A ) to 7 . Λ − V V ). In a similar anal-ysis by ZEUS [120] using their HERA I data alone, limitsof 3 . . Λ − V A and Λ − V V ,respectively. For comparison, in a recent ATLAS analy-sis where the background process to contact interactionsarises from Drell-Yan production qq → ℓℓ , limits are de-rived at the 95% CL on the LL, LR and RR scenarios inthe range 15 . . M LQ /λ at the 95% CL are presentedin table 3, for each of the 14 leptoquarks in the BRWmodel. The observed limits in this analysis are in the range M LQ /λ > .
41 - 1 .
86 TeV. Leptoquarks coupling to u . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 21 Table 2.
Lower limits from H1 at the 95% CL on the compos-iteness scale Λ . The Λ + limits correspond to the upper signsand the Λ − limits correspond to the lower signs of the chi-ral coefficients ǫ qLL , ǫ qLR , ǫ qRL and ǫ qRR , where the CI couplingcoefficient is given by η qab = ǫ qab π/Λ . H1 Search for General Compositeness ( L = 446 pb − ) Model ǫ qLL ǫ qLR ǫ qRL ǫ qRR Λ + [TeV] Λ − [TeV]LL ± ± ± ± ± ± ± ± ± ∓ ∓ ± ± ∓ ± ∓ ± ± ± ± ] [GeV Q / d Q S M s / d / d Q s d - p NC 0.16 fb - H1 e = 0.90 TeV S
1, M = + l = 0.92 TeV S
1, M = - l - p NC 0.28 fb + H1 e = 0.90 TeV (cid:9) S
1, M = + l = 0.92 TeV (cid:9) S
1, M = - l H1 H1 Search for Large Extra Dimensions
Fig. 19.
The measured NC cross section d σ/ d Q normalisedto the SM expectation. H1 e ± p scattering data are comparedwith curves corresponding to 95% CL exclusion limits obtainedfrom the full H1 data on the gravitational scale, M S , for bothpositive ( λ = +1) and negative ( λ = −
1) couplings. The er-ror bars represent the statistical and uncorrelated systematicerrors added in quadrature. quarks are probed with higher sensitivity, correspondingto more stringent limits than those coupling to d quarksdue to the valence quark content of the proton and theQED couplings of the electron to the quarks, which reflectthe electric charge of the different quarks. For a Yukawacoupling of electromagnetic strength, λ = 0 .
3, scalar andvector leptoquark masses up to 0 .
33 TeV and 0 .
56 TeVare excluded, respectively.The S L and ˜ S L / leptoquarks have identical quantumnumbers to down and up squarks, respectively. The cou-plings associated to these leptoquarks therefore correspondto the Yukawa couplings λ ′ k and λ ′ j in the frameworkof R p violating supersymmetry and the limits on theseleptoquarks presented in table 3 are also applicable to the Table 3.
Lower limits from H1 at the 95% CL on M LQ /λ for 14 scalar (S) and vector (V) leptoquarks, where L and Rdenote the lepton chirality and the subscript (0, 1 /
2, 1) is theweak isospin. In this case the CI coupling coefficient is η qab = ǫ qab λ /M LQ . For each leptoquark type, the relevant coefficients ǫ qab and fermion number F = L +3 B are indicated. Leptoquarkswith identical quantum numbers except for weak hyperchargeare distinguished using a tilde, for example V R and ˜ V R . H1 Search for Heavy Leptoquarks ( L = 446 pb − ) LQ ǫ uab ǫ dab F M LQ /λ [TeV] S L ǫ uLL = + S R ǫ uRR = + S R ǫ dRR = + S L / ǫ uLR = − S R / ǫ uRL = − ǫ dRL = − S L / ǫ dLR = − S L ǫ uLL = + ǫ dLL = +1 2 0.71 V L ǫ dLL = − V R ǫ dRR = − V R ǫ uRR = − V L / ǫ dLR = +1 2 0.51 V R / ǫ uRL = +1 ǫ dRL = +1 2 1.44˜ V L / ǫ uLR = +1 2 1.58 V L ǫ uLL = − ǫ dLL = − the ratio M ˜ q /λ ′ [126]. Dedicated leptoquark searches per-formed at HERA are discussed in the following sections.Lower limits in a model with large extra dimensions onthe gravitational scale M S in 4 + n dimensions are derivedassuming a positive or negative coupling. For a λ = +1( λ = −
1) coupling mass scales M S < .
90 TeV ( M S < .
92 TeV) are excluded at the 95% CL. The correspondingcross section predictions normalised to the SM expectationare compared to the e ± p data in figure 19. Since the adventof the LHC and the higher energy centre of mass data thatit provides these limits have been surpassed, for exampleby ATLAS, where limits are set on M S > . R q < . · − m is found, assuming point-like leptons.The same limit from ZEUS is R q < . · − m, whichis derived in a similar analysis using their HERA I dataset [120].
10 Leptoquarks
The electron-proton collisions at HERA provide a uniqueopportunity to search for new particles coupling directlyto a lepton and a quark. Leptoquarks (LQs) are an exam-ple of such particles, colour-triplet bosons which appearin many extensions of the SM [129,130,131,132,133,134,135,136,137,138,139]. They can be produced at HERA di-rectly via s -channel resonant production, or indirectly via u -channel virtual LQ exchange, as shown in figure 20. Thecoupling at the electron-quark-LQ vertex is described by Table 4.
The 14 LQ types of the Buchm¨uller-R¨uckl-Wyler classification in the commonly used notation. The LQ subscriptsrefer to the weak isospin and the superscripts refer to the lepton chirality. The spin J , fermion number F and charge Q of eachleptoquark is indicated, as well as the dominant resonant production process in ep scattering and possible decay modes, thecorresponding coupling and the branching ratio to charged leptons β ℓ .LQ type J F Q
Production and Coupling β ℓ decay modes ℓ − u λ L / S L − / e − L u L → (cid:26) ν ℓ d − λ L / S R − / e − R u R → ℓ − u λ R S R − / e − R d R → ℓ − d λ R ℓ − u − λ L / S L − / e − L u L → (cid:26) ν ℓ d − λ L / − / e − L d L → ℓ − d −√ λ L V L / − / e − L d R → ℓ − d λ L − / e − R u L → ℓ − u λ R V R / − / e − R d L → ℓ − d λ R V L / − / e − L u R → ℓ − u λ L ℓ + d λ L / V L / e + R d L → (cid:26) ¯ ν ℓ u λ L / V R / e + L d R → ℓ + d λ R V R / e + L u R → ℓ + u λ R ℓ + d − λ L / V L / e + R d L → (cid:26) ¯ ν ℓ u λ L / / e + R u L → ℓ + u √ λ L S L / / e + R u R → ℓ + u λ L / e + L d L → ℓ + d − λ R S R / / e + L u L → ℓ + u λ R S L / / e + R d R → ℓ + d λ L a dimensionless parameter λ . LQs carry both lepton ( L )and baryon ( B ) quantum numbers and the fermion num-ber F = L + 3 B is conserved. The s -channel productiondominates for LQ masses lower than the centre of mass en-ergy, while for masses larger than √ s both the s - and the u -channels, as well as the interference with SM processes,are important. In the first case, LQs appear as peaks inthe spectra of the final state lepton-jet invariant mass. Inthe second case, heavy LQ exchange could lead to mea-surable low-energy exchange and so to deviations of themeasured cross sections with respect to SM predictions.For LQ masses lower than √ s , F = 0 ( F = 2) LQs domi-nate in e + p ( e − p ) collisions, while for higher masses both e + p and e − p have similar sensitivity to all LQ types.In the framework of the phenomenological Buchm¨uller-R¨uckl-Wyler (BRW) model [115], LQs are classified into14 types [116] with respect to the quantum numbers spin J , weak isospin I and chirality C (left-handed L , right-handed, R ). The 14 different LQs are detailed in table 4.Scalar ( J = 0) LQs are denoted as S CI and vector ( J = 1)LQs are denoted V CI in the following. LQs with identicalquantum numbers except for weak hypercharge are distin-guished using a tilde, for example V R and ˜ V R . (cid:1) LQ q j ℓq i ˆ s −→ eλ eq i λ ℓq j (cid:2) LQ ¯ q i ℓ ¯ q j ˆ u −→ e λ eq i λ ℓq j Fig. 20.
Leptoquark production in ep collisions: s -channel res-onant production (left) and u -channel virtual exchange (right)with subsequent decay to a lepton-quark pair. Whereas all 14 LQs couple to electron-quark pairs, fourof the left-handed LQs, namely S L , S L , V L and V L , mayalso decay to a neutrino-quark pair. The branching ratioto charged leptons is given by: β ℓ = Γ ℓq / ( Γ ℓq + Γ ν ℓ q ) (36)where Γ ℓq ( Γ ν ℓ q ) denotes the partial width for the LQdecay to the charged lepton ℓ (neutrino ν ℓ ) and a quark . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 23
100 200 300 E ve n t s / G e V -2 -1
10 110 NC dataSM NCCC dataSM CC H1 p - e -1 = 103 pb = -26% e P [GeV] LQ M
100 200 300 E ve n t s / G e V -2 -1
10 110 NC dataSM NCCC dataSM CC H1 p + e -1 = 82 pb = -38% e P [GeV] LQ M
100 200 300 E ve n t s / G e V -3 -2 -1
10 110 NC dataSM NCCC dataSM CC H1 p - e -1 = 46 pb = +37% e P [GeV] LQ M
100 200 300 E ve n t s / G e V -2 -1
10 110 NC dataSM NCCC dataSM CC H1 p + e -1 = 98 pb = +32% e P [GeV] LQ M H1 Search for First Generation Leptoquarks
LL LL (a) (b)(c) (d)
Fig. 21.
The reconstructed leptoquark mass in the search for first generation leptoquarks in the 2003-2007 H1 data, which wastaken with a polarised lepton beam. The left-handed electron data (a) and left-handed positron data (b) are shown in the toprow; the right-handed electron data (c) and right-handed positron data (d) are shown in the bottom row. The luminosity L andaverage longitudinal lepton polarisation P e of each data set is indicated. The NC (solid points) and CC (open points) data arecompared to the SM predictions (histograms), where the shaded bands indicate the total SM uncertainties. q . The branching fraction of decays into a neutrino-quarkpair is then given by β ν ℓ = 1 − β ℓ . In particular, for S L and V L the branching fraction of decays into an electron-quark pair is predicted by the model to be β ℓ = 0 . first gen-eration leptoquark . If the lepton number is not conserved,the production of second and third generation leptoquarks is possible, leading to a final state containing a second orthird generation lepton together with the quark.The BRW model assumes lepton number conservation,although a general extension of this model allows for the In the case of S L and V L LQs, which are superpositions oftwo states, this branching ratio is less trivial. decay of LQs to final states containing a quark and a lep-ton of a different flavour, that is a muon or tau lepton,introducing lepton flavour violation (LFV). Non-zero cou-plings λ eq i to an electron-quark pair and λ µq j ( λ τq j ) toa muon(tau)-quark pair are assumed. The indices i and j represent quark generation indices, such that λ eq i denotesthe coupling of an electron to a quark of generation i , and λ ℓq j is the coupling of the outgoing lepton (where ℓ = µ or τ ) to a quark of generation j . When second and thirdgeneration LQs are considered, the branching ratio β to agiven charged lepton flavour LQ → µ ( τ ) q is calculated as: β = β ℓ × β LF V (37)where β LF V = Γ µ ( τ ) q Γ µ ( τ ) q + Γ eq (38) and Γ ℓq = m LQ λ ℓq × ( π scalar LQ π vector LQ (39)where Γ ℓq denotes the partial LQ decay width for the de-cay to a lepton ℓ = e, µ, τ and a quark q . Assuming leptonuniversality, and that only one LFV transition is possible, β LF V = 0 .
5. An overview of this extended model for theLQ coupling to u and d quarks is provided elsewhere [140]. Searches for first generation leptoquarks have been regu-larly performed by both H1 and ZEUS during the HERAdata taking [141,142,143,144,145], and two papers pub-lished in 1997 using up to 20 pb − of the first data takenrevealed a handful of outstanding events observed by bothcollaborations at masses above and around 200 GeV [146,147].The final H1 and ZEUS first generation leptoquarksearches are summarised in this section, which betweenthem include the full 1 fb − of HERA data [148,149]. Thepolarisation P e of the lepton beam in the HERA II datataking period is exploited to enhance the chiral sensitivityof leptoquarks by analysing the positively and negativelypolarised data samples separately.First generation leptoquarks lead to final states whichare similar to those of NC and CC DIS, in that the LQdecays into either an electron or neutrino and a quark.As the experimental signature of LQ production is similarto that of NC and CC events, the data selection closelyfollows that used in the standard inclusive DIS analysesperformed by H1 and ZEUS as described in section 8.The NC and CC DIS processes are modelled using theDJANGOH generator and the smaller photoproductioncontribution is estimated using PYTHIA.In the NC-like event topology ep → eX , the H1 anal-ysis [148] is performed in the region Q >
133 GeV , E e ′ >
11 GeV and 0 . < y < .
9, where the electron re-construction method is used (see equation 9a). The ZEUSanalysis [149] employs both the electron and double anglemethods (see equation 15) and the phase space is definedas Q > , E e ′ >
10 GeV, x > . y e < . P T >
15 GeV in the region | η | < E − P z in the event to reduce the residualphotoproduction background.In the CC like event topology ep → νX , events are se-lected in the H1 analysis by requiring significant missingtransverse momentum P miss T >
12 GeV, which is due tothe undetected neutrino, in the inelasticity region 0 . 85. The ZEUS analysis phase space is P miss T > 22 GeV, Q > 700 GeV , y < . 9. An identified hadronicjet with P T > 10 GeV in the region | η | < P miss T and the ratio V ap /V p [102]. Both H1 andZEUS use the hadronic reconstruction method describedin equation 10 for the CC like event topology.The lepton scattering angle in the lepton-jets centreof mass frame, θ ∗ , is used in the ZEUS analysis to iso-late a potential leptoquark signal further. The decay ofa scalar resonance results in a flat distribution in cos θ ∗ ,while SM events show an approximately 1 / (1 − cos θ ∗ ) dependence [143]. In a final step a cut of cos θ ∗ < . (GeV) ejs M100 120 140 160 180 200 220 240 260 280 300 320 E ve n t s -1 =-0.27) e , P -1 p (106 pb - ZEUS eSM =0.3 l =210 GeV, LQ , M L0 SM+S =1 l =400 GeV, LQ , M L0 SM+S X - e fi p - e ZEUS (GeV) ejs M100 120 140 160 180 200 220 240 260 280 300 320 E ve n t s -1 =-0.27) e , P -1 p (106 pb - ZEUS eSM =0.3 l =210 GeV, LQ , M L0 SM+S =1 l =400 GeV, LQ , M L0 SM+S X - e fi p - e ZEUS Fig. 22. Top: The reconstructed invariant mass, M ejs , dis-tribution in the e − p → e − X topology for the left-handed e − p ZEUS sample (dots), compared to the SM prediction (solid his-togram) and to the predictions of the BRW-based LQ model in-cluding a S L LQ state with a mass of 210 GeV with a couplingstrength λ = 0 . λ = 1 . θ ∗ < . The leptoquark mass is reconstructed by H1 as: M LQ = p Q /y (40)and uses the measured kinematics of the scattered electron(hadronic final state) in the analysis of NC (CC) topolo-gies. In the ZEUS analysis, the LQ mass is reconstructed . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 25 from the momentum and energy of the jet and the lepton: M ljs = q E ljs − p ljs , (41)where E ljs is the sum of the energies of the jet and thelepton, and p ljs is the vector sum of their momenta.In the analysis of their complete data sets a good agree-ment between the data and the SM is observed by both H1and ZEUS and no evidence for LQs at HERA is observed.The SM expectation is dominated by DIS processes in allevent samples, with small additional contributions fromphotoproduction.Mass spectra of the four H1 HERA II data sets takenwith a longitudinally polarised lepton beam are shown infigure 21, where both the NC-like and CC-like event sam-ples are presented [148]. The shape and normalisation ofall samples are well described. Similarly good agreement isobserved in the equivalent mass distributions in the ZEUSanalysis [149].Figure 22 shows as an example the left-handed e − p ZEUS data without (top) and with (bottom) the cos θ ∗ < . S L LQ state with a massof 210 GeV and coupling strength λ = 0 . λ = 1 . M LQ − y ( M ljs − cos θ ∗ ) plane, wherethe NC and CC data samples with different lepton beamcharge and polarisation are kept as distinct data sets.Limits are determined from a statistical analysis whichuses the method of fractional event counting [151], takinginto account the polarisation and systematic uncertain-ties, the most relevant of which are the electromagneticand hadronic energy scales and the PDF uncertainty. Fulldetails on the limit calculation employed can be found inthe individual publications [148,149].Upper limits from ZEUS on the coupling λ obtainedat 95% CL are shown as a function of leptoquark mass infigure 23, displayed as groups of scalar and vector LQs forboth F = 2 and F = 0.Limits corresponding to LQs coupling to a u quarkare better compared to those for LQs coupling to the d quark only, as expected from the larger u quark densityin the proton. Corresponding to the steeply falling par-ton density function for high values of x , the LQ produc-tion cross section decreases rapidly and exclusion limitsfrom HERA are less stringent towards higher LQ masses.For LQ masses near the kinematic limit of 319 GeV, thelimit corresponding to a resonantly produced LQ turnssmoothly into a limit on the virtual effects of both an off-shell s -channel LQ process and a u -channel LQ exchange.The presented limits extend beyond those from previ-ous leptoquark and contact interaction analyses by H1 [125, 142] and ZEUS [120,145] based on smaller HERA datasets. For a coupling of electromagnetic strength λ = √ πα em =0 . 3, LQs produced in ep collisions decaying to an electron-quark or a neutrino-quark pair are excluded at 95% CL upto leptoquark masses between 290 GeV ( ˜ S R ) and 699 GeV( V L ), depending on the leptoquark type. Similar limits arederived by H1, where LQs decaying to an electron-quarkor a neutrino-quark pair are excluded at 95% CL up toleptoquark masses between 277 GeV ( V R ) and 800 GeV( V L ), depending on the leptoquark type.Within the framework of the BRW model, the ˜ S L / LQ decays exclusively to an electron-quark pair, resultingin a branching fraction for decays into charged leptons of β ℓ = 1 . 0, whereas the S L LQ also decays to neutrino-quark, resulting in β ℓ = 0 . 5. The H1 and ZEUS limits on˜ S L / and S L from the analysis of the full HERA data arecompared to those from other experiments in figure 24The H1 limits at high leptoquark mass values are alsocompared with those obtained in the contact interactionanalysis described in section 9, which is based on singledifferential NC cross sections d σ/ d Q measured using thesame data. The additional impact of the CC data can beseen in the case of the S L LQ, where a stronger limit isachieved in this analysis, whereas for the ˜ S L / LQ the twoanalyses result in a similar limit.Indirect limits from searches for new physics in e + e − collisions at LEP by the OPAL [152] and L3 [153] experi-ments are indicated, as well as the limits from the DØ [154,155] experiment at the Tevatron and from searches by theATLAS [156] and CMS [157] experiments based on their √ s = 7 TeV data. The limits from hadron colliders areprimarily based on searches for LQ pair-production andare independent of the coupling λ . For example, for a lep-toquark mass of 640 GeV, the H1 LQ analysis rules outthe S L LQ for coupling strengths larger than about 0 . √ s = 8 TeV data LHC are appearing, extending theselimits into the kinematic regime beyond 1 TeV [158] for β = 1 . The introduction of lepton flavour violation [159] to lepto-quark models would mean that the processes ep → µX or ep → τ X , mediated by the exchange of a second or thirdgeneration leptoquark, would be observable at HERA withfinal states containing a muon or the decay products ofa tau lepton back-to-back in the transverse plane with ahadronic system X . Searches for such signatures have beenpreviously performed at HERA by both H1 and ZEUS us-ing HERA I data [140,141,160]. The analysis performedby H1 using their complete √ s = 319 GeV data set (seetable 1) is described in the following. The event selectionsfor both the searches are described below; full details canbe found in the publication [161]. (TeV) LQ M l -2 -1 L1/2 S R1/2 S L1/2 S~ exc l ud e d F=0 scalar LQ limit) -1 p (498 pb – ZEUS e ZEUS (TeV) LQ M l -2 -1 L0 S R0 S R0 S~ L1 S exc l ud e d F=2 scalar LQ limit) -1 p (498 pb – ZEUS e ZEUS (TeV) LQ M l -2 -1 L0 V R0 V R0 V~ L1 V exc l ud e d F=0 vector LQ limit) -1 p (498 pb – ZEUS e ZEUS (TeV) LQ M l -2 -1 L1/2 V R1/2 V L1/2 V~ exc l ud e d F=2 vector LQ limit) -1 p (498 pb – ZEUS e ZEUS (a) (b)(c) (d) Fig. 23. Exclusion limits from ZEUS for the 14 leptoquarks in the framework of the Buchm¨uller, R¨uckl and Wyler modelon the coupling λ as a function of leptoquark mass for the scalar leptoquarks with F = 0 (a) and F = 2 (b) and the vectorleptoquarks with F = 0 (c) and F = 2 (d). Domains above the curves are excluded at 95% CL. [GeV] LQ M 200 400 600 800 1000 -2 -1 l Search for First Generation Scalar Leptoquarksd) n u, - (e L0 S H1 limitH1 CI analysis limitZEUS limitCMS pair productionATLAS pair productionDØ pair productionL3 indirect limit [GeV] LQ M 200 400 600 800 1000 -2 -1 l Search for First Generation Scalar Leptoquarksd) + (e L1/2 S~ H1 limitH1 CI analysis limitZEUS limitCMS pair productionATLAS pair productionDØ pair productionOPAL indirect limit Fig. 24. Exclusion limits from H1 and ZEUS in the framework of the Buchm¨uller, R¨uckl and Wyler model on the coupling asa function of leptoquark mass for the S L (left) and ˜ S L / (right) leptoquarks, which have branching fraction to charged leptonsof β ℓ = 0 . β ℓ = 1 . 0, respectively. Domains above the curves and to the left of the vertical lines are excluded at 95% CL.Published limits from the Tevatron (DØ), LEP (L3 and OPAL) and the LHC experiments (CMS and ATLAS, √ s = 7 TeVdata) are also shown for comparison, as well as constraints on LQs with masses above 350 GeV from the H1 contact interaction(CI) analysis.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 27 Leptoquarks with couplings to first and second gener-ation leptons may decay to a muon and a quark, thereforeevent topologies with an isolated, high transverse momen-tum muon back-to-back to a hadronic system in the trans-verse plane are selected. An initial sample of events withmuons and jets is selected by requiring at least one P µT > ◦ < θ µ < ◦ and at least one jet. Events with isolated muons are thenselected; the angular distance, D = p ( ∆η ) + ( ∆φ ) , ofthe muon to the nearest track and to the nearest jet arerequired to be greater than 0 . . 0, respectively. Lim-itations on the calorimetric energy in a cone around themuon are also introduced [161]. To reduce the muon-pairSM background exactly one isolated muon is required, asexpected in LFV LQ signal events.NC DIS background is suppressed by applying a cut onthe calorimetric momentum imbalance, P calo T > 25 GeV,and by rejecting events with identified isolated electrons.The back-to-back event topology in the azimuthal planeis also exploited to remove the SM background: the differ-ence between the azimuthal angle of the hadronic systemand the muon, the acoplanarity ∆φ µ − X , is required to begreater than 170 ◦ . Further SM background reduction isachieved by exploiting the calorimetric energy imbalance V ap /V p < . δ > 40 GeV.After all selection cuts, in the analysis of µX finalstates one event is observed in the data which compareswell to the SM prediction of 2 . ± . 4. The largest contri-bution comes from muon-pair events, which are modelledby GRAPE.Leptoquarks with couplings to first and third genera-tion leptons may decay to a tau and a quark and in thesearch for third generation leptoquarks, tau leptons areidentified using the muonic and one-prong hadronic de-cays of the tau . Hadronic tau decays, both one-prong andthree-prong, are described in more detail in section 11.2.Muonic tau decays, τ → µν µ ν τ , result in final states sim-ilar to the high P T muon signatures described above andthe same selection is therefore applied in that channel.The one-prong hadronic decay of the tau leads to ahigh P T , narrow “pencil-like” jet, so that the typical LFVsignal event topology is a di-jet event. An initial di-jetevent sample for the analysis of this decay channel isformed by selecting events with at least two jets in thepolar angle range 5 ◦ < θ jet < ◦ and with P jet1 T > 20 GeV and P jet2 T > 15 GeV. The undetected neutrinosfrom tau lepton decays result in an overall P T imbalanceand therefore a minimum missing transverse momentum P miss T > 12 GeV is required.A tau jet is characterised by a narrow energy depositin the calorimeter and a low track multiplicity within theidentification cone of the jet. Tau jets are identified in thedi-jet sample, where the candidates are required to be inthe polar angle range 20 ◦ < θ jet < ◦ and to have a The electronic decays of the tau τ → eν e ν τ result in finalstates very difficult to distinguish from SM NC DIS, where themissing transverse momentum is aligned with the electron. Assuch, they are not considered in the analysis. maximum jet radius R jet of 0 . 12 [162], where R jet = 1 E jet X h E h p ∆η (jet , h ) + ∆φ (jet , h ) , (42)and E jet is the total jet energy. The sum runs over allhadronic final state particles in jets with energy E h . Atleast one track with P T larger than 2 GeV not associatedwith an identified electron or muon is required within thejet radius of the tau jet.A single tau jet is required in the final sample, with se-lection requirements including isolation from from tracksand other jets by an angular distance D > . 0, a trackmultiplicity of one in a cone of radius R = 1 . P hT is required to be larger than 30 GeV and the acoplanaritybetween the tau jet and hadronic system in the transverseplane ∆φ τ − X is required to be greater than 160 ◦ . Anal-ogous to the muon channel, a cut of δ > 40 GeV is alsoapplied to exploit the longitudinal balance of the event.After all selection cuts, in the analysis of τ X finalstates where the tau lepton decays hadronically, 6 eventsare observed in the data, in good agreement with theSM prediction of 8 . ± . 1. The main SM contributionis from remaining NC DIS events, which are modelled bythe RAPGAP [163] event generator.The reconstructed leptoquark-candidate mass in thesearch for ep → µX and ep → τ X events is shown in fig-ure 25, compared to the SM prediction and an example LQsignal with arbitrary normalisation. The LQ kinematicsare reconstructed using the double angle method (equa-tion 15). The direction of the detected lepton and thehadronic final state are used to reconstruct the Bjorkenscaling variable x and subsequently the LQ mass follow-ing equation 40.As the observed number of events is in agreement withthe SM prediction and therefore no evidence for LFV isfound, the results of the search are interpreted in terms ofexclusion limits on the mass and the coupling of LQs me-diating LFV. The LQ production mechanism at HERA in-volves a non-zero coupling to the first generation fermions λ eq i > 0. For the LFV leptoquark decay, it is assumed thatonly one of the couplings λ µq j and λ τq j is non-zero andthat λ eq i = λ µq j ( λ τq j ). A modified frequentist methodwith a likelihood ratio as the test statistic is used to com-bine the individual data sets and the ep → τ X searchchannels [164]. In order to avoid the need to generatemany signal MC samples at each leptoquark mass, cou-pling and branching ratio, a weighting technique is usedto provide predictions across the full range of LQ produc-tion parameters [140]. As in the search for first generationleptoquarks, the lepton beam polarisation enters the limitcalculation for the HERA II data.Figure 26 shows the 95% CL upper limits on the cou-plings to the first generation quarks, λ µq and λ τq , for F = 0 LQs as a function of the mass of the LQ leadingto LFV in ep collisions. These limits extend beyond those [GeV] LQ M E ve n t s All SM=150 GeV LQ M (arb. norm.) H1 Data ) -1 Search for Leptoquarks at HERA (410 pb q mfi LQ fi q – e H1 [GeV] LQ M E ve n t s All SM=150 GeV LQ M (arb. norm.) H1 Data ) -1 Search for Leptoquarks at HERA (410 pb q tfi LQ fi q – e H1 Fig. 25. The reconstructed leptoquark mass in the H1 search for ep → µX (left) and ep → τ X (right) events. The data are thepoints and the total uncertainty on the SM expectation (open histogram) is given by the shaded band. The dashed histogramindicates the LQ signal with arbitrary normalisation for a leptoquark mass of 150 GeV. from H1 and ZEUS based on the HERA I data alone [140,141,160]. Similar limits are found for F = 2 LQs and thesecan be found in the H1 publication along with limits in-volving heavier quark flavours [161].For λ = √ πα em = 0 . 3, LFV leptoquarks producedin ep collisions decaying to a muon-quark or a tau-quarkpair are excluded at 95% CL up to leptoquark masses of712 GeV and 479 GeV, respectively. In both cases, the LQwith the highest sensitivity is V L . As described above, themost appropriate value for the branching ratio when com-paring to results from hadron colliders is β = 0 . β = 0 . t + τ [165] and b + τ [166] final states,where the best limit for β = 0 . M LQ > 560 GeV at95% CL. 11 Multi-lepton production at high transversemomentum Multi-lepton final states may be produced in electron-proton collisions at HERA, proceeding mainly via photon-photon γγ → ℓ + ℓ − interactions [167], as shown in fig-ure 27. The dominant contribution, shown in figure 27(a),is from lepton pair production via the interaction of twophotons radiated from the incident electron and proton.Lepton pairs may also originate from internal conversionof a photon or a Z boson, radiated either from the in-cident electron line (figure 27(b)) or from the quark line(figure 27(c)).As this is a purely QED (Quantum Electrodynamic)process, the cross section is precisely calculable in the SM. Multi-lepton events are simulated using the GRAPE eventgenerator, which includes all leading order electroweakmatrix elements. The final state leptons provide a cleanevent signature, which is well described by the SM andthe investigation of the high-mass, high- P T regions, wherethe SM expectation is low, may reveal some signal of newphysics.The following section concerns final states with elec-trons and muons. Studies of tau-pair production are de-scribed in section 11.2. Measurements of both multi-electron [168] and muon pair[169] production at high transverse momentum have previ-ously been performed by H1 using their HERA I data set.Since then, both H1 and ZEUS have published [170,171]their final results on the search for multi-lepton events,using the full available statistics of the complete HERAdata set. The integrated luminosity in the H1 analysiscorresponds to 463 pb − , of which 285 pb − are from e + p collisions and 178 pb − from e − p collisions. In theZEUS analysis, the integrated luminosity corresponds to480 pb − , of which 278 pb − are from e + p collisions and202 pb − from e − p collisions.The analysis strategy and event selection used in theH1 and ZEUS analyses are similar. First, electron or muoncandidates are identified in a wide angular region using aloose selection criteria. Then, at least two central (20 ◦ <θ ℓ < ◦ ) lepton candidates are required in the event.Electrons are identified in the polar angle range 5 ◦ < θ e < ◦ with an energy greater E e > ◦ < θ e < ◦ in the H1 analysis and in the region 5 ◦ < θ e < ◦ inthe ZEUS analysis. Muons are identified in the polar angle . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 29 200 400 600 -3 -2 -1 [GeV] LQ M e q l = q ml d) + ( L1/2 S~ u) + ( L1/2 S d) + u, + ( R1/2 S 200 400 600 -3 -2 -1 E x c l u d e d a t % C L F = 0 H1 q mfi LQ fi q – e ) -1 Search for Leptoquarks at HERA (410 pb ℓℓℓ ℓ 200 400 600 -3 -2 -1 [GeV] LQ M e q l = q ml d) + ( L0 V d) + ( R0 V u) + ( R0 V~ d) + u, + ( L1 V 200 400 600 -3 -2 -1 E x c l u d e d a t % C L F = 0 H1 q mfi LQ fi q – e ) -1 Search for Leptoquarks at HERA (410 pb ℓℓℓℓ ℓ 200 400 600 -3 -2 -1 [GeV] LQ M e q l = q tl d) + ( L1/2 S~ u) + ( L1/2 S d) + u, + ( R1/2 S 200 400 600 -3 -2 -1 E x c l u d e d a t % C L F = 0 H1 q tfi LQ fi q – e ) -1 Search for Leptoquarks at HERA (410 pb ℓℓℓ ℓ 200 400 600 -3 -2 -1 [GeV] LQ M e q l = q tl d) + ( L0 V d) + ( R0 V u) + ( R0 V~ d) + u, + ( L1 V 200 400 600 -3 -2 -1 E x c l u d e d a t % C L F = 0 H1 q tfi LQ fi q – e ) -1 Search for Leptoquarks at HERA (410 pb ℓℓℓℓ ℓ (a) (b)(c) (d) Fig. 26. Exclusion limits on the coupling constants λ ℓq = λ eq as a function of leptoquark mass M LQ for F = 0 leptoquarks:limits on second generation ( ℓ = µ ) scalar (a) vector (b) LQs; limits on third generation ( ℓ = τ ) scalar (c) vector (d) LQs. Regionsabove the lines are excluded at 95% CL. The notation q indicates that only processes involving first generation quarks areconsidered. The parentheses after the LQ name indicate the fermion pairs coupling to the LQ, where pairs involving anti-quarksare not shown. ℓ + ℓ − ℓ + ℓ − ℓ + ℓ − (a) (b) (c) Fig. 27. Lepton pair production in e + p collisions at HERA. Examples of Feynman diagrams are shown for the photon-photoninteraction (a) and γ / Z conversion (b) and (c). The hadronic final state can be a proton (elastic production) or a higher masssystem (quasi-elastic and inelastic production).0 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA range 20 ◦ < θ µ < ◦ and are required to have transversemomentum P µT > P T > 10 GeV and the otherwith P T > D > . η − φ plane. Accord-ing to the number and flavours of the identified leptons,the events are classified into mutually exclusive topologiescontaining up to 4 leptons.The main source of SM background in each analysis de-pends on the number and flavour of the identified leptonsin the event sample. NC DIS and QED Compton scat-tering (QEDC, ep → eγX ) constitute a significant back-ground only for event topologies in which two leptons, oneof which is an electron, are found in the final state. TheNC DIS background is modelled in the H1 (ZEUS) anal-ysis using the RAPGAP (DJANGOH) event generator.The smaller QEDC background contribution is modelledusing WABGEN [172] (GRAPE) in the H1 (ZEUS) anal-ysis. Background contributions to the SM expectation arenegligible in events in which two muons or more than twoleptons are observed.The number of selected events in the H1 analysis [170]in the various topologies are compared to SM predictionsin table 5, where a good agreement is observed for all eventsamples. In the table, the number of events from genuinepair production is shown, together with the number ofevents from NC DIS and QED Compton, which constitutethe most significant source of background. Events withhigh invariant mass of the two highest P T leptons M are observed in the data, where the SM expectation islow. All events with M > 100 GeV are seen in the e + p data only. Two of the high mass events observed by H1are shown in figure 28. A high scalar sum of the leptontransverse momenta P P T GeV, which is summed overall identified leptons in the event, may be an indicationof new physics and five events are seen in the H1 data,compared to a SM expectation of 1 . ± . 20. All eventsare seen in the e + p data, where 0 . ± . 12 are expectedfrom the SM. The P P T GeV distribution from the H1analysis is shown in figure 29.Similarly for the ZEUS analysis [171], the number ofselected events in the various topologies studied are com-pared to the SM prediction in table 5, where a good agree-ment is observed for all event samples. The P P T and M distributions of all topologies combined are shownin figure 29, where the shape and normalisation are welldescribed by the SM predictions. Some interesting eventsare also observed in the ZEUS data at high- M and high- P P T : in particular, two events are present in the datawith P P T > 100 GeV compared to a SM prediction of1 . ± . 15. Two of the highest mass events observed byZEUS are shown in figure 28.A combination of the H1 and ZEUS multi-lepton anal-yses has also been performed, using a data sample with atotal integrated luminosity of 0 . 94 fb − [173]. Five of thefinal state topologies are combined, namely ee , µµ , eµ , eee and eµµ . The combination is performed in a commonphase space, corresponding to a tightening of the selec-tion cuts of the two experiments. For example, in the H1analysis the electron energy threshold in the central regionwas raised from 5 GeV to 10 GeV. Both the number ofthe observed events and the cross sections for multi-leptonproduction measured by the two experiments were com-bined. This allows a better sensitivity to rare processes inthe high M and high P P T regions to be achieved andan improved precision of the measured cross sections.The event yields of the combined analysis are shown intable 5, where a good agreement is observed with the SM.The P P T distributions for the full combined e ± data, aswell as separately for the e + p and e − p data, are shown infigure 30. In general, a good agreement is found betweenthe data and the SM predictions. For P P T > 100 GeV,seven data events are observed in total, compared to 3 . ± . 26 expected from the SM. These seven events were allrecorded in e + p data, for which the SM expectation is1 . ± . 17. Events are observed in all topologies with M > 100 GeV, as detailed in table 6. Both experimentsrecorded these events in e + p collisions only [173].The cross sections for lepton pair production were alsomeasured by both collaborations [170,171] in the pho-toproduction regime, in which the virtuality Q of thephoton emitted by the beam lepton is low. Photoproduc-tion events were selected by requiring a total E − P z of δ < 45 GeV, which singles out events in which the scat-tered lepton is lost in the beam pipe and corresponds tophase space cuts of Q < and y < . 82. The eventyield in this cross section phase space is also presented forthe combined analysis in table 5 in the rows marked ( γγ ) e and ( γγ ) µ . The cross section is evaluated in each bin i using the formula σ i = N data i − N bgr i L · A i , (43)where N data i is the number of observed events in bin i , N bgr i the expected contribution from background processesin bin i , L the integrated luminosity of the data and A i is the signal acceptance in bin i and is calculated usingGRAPE.The combined H1-ZEUS cross section measurement isevaluated using a weighted mean of the values measuredby the two collaborations [173]. The total visible elec-tron pair production cross section for the process ep → ee + e − X is measured in the restricted phase space as: σ e + e − = 0 . ± . 04 (stat . ) ± . 03 (sys . ) pb , where the first uncertainty is statistical and the secondsystematic. The total visible muon pair production crosssection for the process ep → eµ + µ − X is measured as: σ µ + µ − = 0 . ± . 05 (stat . ) ± . 06 (sys . ) pb . As the SM cross sections for e + e − and µ + µ − production in γγ interactions are expected to be the same, the electronand muon pair production cross sections given above are . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 31 Table 5. Observed and predicted multi-lepton event yields for the different event topologies in the H1, ZEUS and combinedanalysis. The total SM event yield is given by the sum of the signal, lepton pair production in γγ interactions, and thebackground, mainly from NC DIS and QEDC events. For the combined analysis, performed in a common phase space, the eventyields shown for the γγ subsamples are those used in the cross section measurement. The uncertainties on the predictions includemodel uncertainties and experimental systematic uncertainties added in quadrature. The limits on the background estimationsare quoted at 95% CL. Searches for Multi-lepton Events at HERAH1 Analysis ( L = 463 pb − ) Event sample Data Total SM Pair production NC DIS + QEDC ee 368 390 ± 46 332 ± 26 58 ± µµ 201 211 ± 32 211 ± < . eµ 132 128 ± ± . ± . eee 73 70 ± . ± . . ± . eµµ 97 102 ± 14 102 ± < . eeµ . ± . 26 1 . ± . 20 0 . ± . eeee . ± . 07 0 . ± . < . ZEUS Analysis ( L = 480 pb − ) Event sample Data Total SM Pair production NC DIS + QEDC ee 545 563 +29 − +21 − ± µµ 93 106 ± 12 106 ± < . eµ 46 42 ± +3 − . ± eee 73 75 +5 − +4 − < eµµ 47 48 ± ± < . eeee . +0 . − . . ± . < . eeµµ . +0 . − . . ± . < . Combined H1 and ZEUS Analysis ( L = 0 . 94 fb − ) Event sample Data Total SM Pair production NC DIS + QEDC ee 873 895 ± 57 724 ± 41 171 ± µµ 298 320 ± 36 320 ± < . eµ 173 167 ± 10 152 ± ± eee 116 119 ± ± < eµµ 140 147 ± 15 147 ± < . γγ ) e 284 293 ± 18 289 ± 18 4 ± γγ ) µ 235 247 ± 26 247 ± < . combined into a single visible lepton pair production crosssection of: σ ℓ + ℓ − = 0 . ± . 03 (stat . ) ± . 03 (sys . ) pb , which is in good agreement both with the SM predictionfrom GRAPE of 0 . ± . 02 pb, as well as the individualH1 and ZEUS measurements [173]. The differential crosssections for lepton pair photoproduction as a function ofthe transverse momentum of the leading lepton, P ℓ T , andof the invariant mass of the lepton pair, M ℓℓ , are alsomeasured and found to be in good agreement with SMpredictions, as shown in figure 31. The dominant tau-pair production mechanism is the sameas for multi-electron and multi-muon production, γγ → τ + τ − , as illustrated in figure 27. Tau particles can decayinto leptons, τ → µν µ ν τ , or τ → eν e ν τ , or into hadrons, τ → hν τ , which happens about 2 / leptonic if both tauleptons decay leptonically, semi-leptonic if one tau leptondecays hadronically and one leptonically, and hadronic ifboth tau leptons decay into hadrons. From the experi-mental point of view, leptons from a tau decay cannot bedistinguished from prompt electron or muon production, P =20 GeVP =16 GeVP =25 GeV T TT P eT = 63 GeV P µT = 61 GeV P µT = 2 . p eT = 34 GeV p eT = 6 GeV p eT = 32 GeV eee p µT = 36 GeV p µT = 34 GeV p eT = 14 GeV eµµ Fig. 28. Events observed in the H1 (top) and ZEUS (bottom) multi-lepton analyses. The measured transverse momentum ofthe leptons is indicated. Top left: an event observed by H1 in the HERA I data containing three electrons. The invariant mass ofthe two highest P T electrons is measured as M = 118 GeV. Top right: an eµµ event observed in the H1 HERA II data where M = 127 GeV, formed by the electron and one of the muons. Bottom left: a three electron event observed by ZEUS with M = 113 GeV. Bottom right: an eµµ event observed by ZEUS where the muon pair form an invariant mass M = 77 GeV. as the accompanying neutrino is not detected and henceevents in which the two taus decay to leptons of the sameflavour are rejected when examining tau-pair production.In the hadronic tau decay, due to the mass and chargeof the tau lepton, most likely only one or three chargedhadrons are produced . These decays modes are referredto as (tau decay branching ratio 49%) and (tau decay branching ratio 14%), respectively. Thehadronic decay products of the tau lepton look like a col-limated jet, featuring only one or three tracks, which arevery close to each other. A τ jet can therefore be distin- The branching ratio for tau decays into more than threecharged hadrons is small (about 2%). guished from QCD jets based on its shape and on thecharge and multiplicity of its tracks. Neural networks andmultivariate analysis techniques are typically employed toseparate identified tau jet candidates from the large QCDbackground. One of the main differences between the anal-ysis of tau-pair production and other di-lepton analyses isthat a significant part of the tau-lepton momentum is car-ried away by the tau neutrino. This result in the tau decayproducts having a significantly lower P T compared to theoriginal tau lepton.The H1 [162] and ZEUS [174] collaborations have bothstudied tau-pair production looking at the leptonic ( eµ ),semi-leptonic ( e jet or µ jet) and hadronic (jet jet) decay . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 33 [GeV] T P S E ve n t s -2 -1 [GeV] T P S E ve n t s -2 -1 All SMPair Prod.H1 Data ) -1 p, 463 pb-p and e+Multi-Leptons at HERA (e H1 -2 -1 ZEUS M (GeV) E v e n t s S p Tl (GeV) E v e n t s ZEUS 480 pb -1 Total SM NC DISQEDCDi- t -2 -1 Fig. 29. The distribution of the scalar sum of the transverse momenta of all the leptons in the multi-lepton final states from theH1 (left) and ZEUS (right) analyses, as well as the invariant mass of the two highest- P T leptons in the ZEUS analysis (centre),for the complete data sets and for all lepton topologies combined. The points correspond to the observed data events and thehistogram to the SM expectation. The total uncertainty on the SM expectation is given by the shaded band. The individualcomponents of the SM are as indicated within the figures. Table 6. Observed and predicted multi-lepton event yields for masses M > 100 GeV for the different event topologies in theH1 and ZEUS combined analysis. Event yields are shown for all data and divided into e + p and e − p collisions. The uncertaintieson the predictions include model uncertainties and experimental systematic uncertainties added in quadrature. The limits onthe background estimations correspond to the selection of no event in the simulated topology and are quoted at 95% CL. Multi-lepton Events at HERA with M > 100 GeVCombined H1 and ZEUS Analysis e + p collisions ( L = 0 . 56 fb − ) Event sample Data Total SM Pair production NC DIS + QEDC ee . ± . 18 0 . ± . 11 0 . ± . µµ . ± . 08 0 . ± . < . eµ . ± . 05 0 . ± . < . eee . ± . 09 0 . ± . < . eµµ . ± . 04 0 . ± . < . e − p collisions ( L = 0 . 38 fb − ) Event sample Data Total SM Pair production NC DIS + QEDC ee . ± . 13 0 . ± . 11 0 . ± . µµ . ± . 10 0 . ± . < . eµ . ± . 03 0 . ± . < . eee . ± . 07 0 . ± . < . eµµ . ± . 05 0 . ± . < . e ± p collisions ( L = 0 . 94 fb − ) Event sample Data Total SM Pair production NC DIS + QEDC ee . ± . 28 1 . ± . 16 1 . ± . µµ . ± . 12 0 . ± . < . eµ . ± . 07 0 . ± . < . eee . ± . 12 1 . ± . < . eµµ . ± . 06 0 . ± . < . 014 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA [GeV] T P 10 15 20 25 30 35 40 45 50 [ pb / G e V ] T / d P s d -4 -3 -2 -1 [GeV] T P 10 15 20 25 30 35 40 45 50 [ pb / G e V ] T / d P s d -4 -3 -2 -1 SM Pair Prod. ) -1 H1+ZEUS (0.94 fb M [GeV] 20 30 40 50 60 70 80 90 100 / d M [ pb / G e V ] s d -4 -3 -2 -1 M [GeV] 20 30 40 50 60 70 80 90 100 / d M [ pb / G e V ] s d -4 -3 -2 -1 SM Pair Prod. ) -1 H1+ZEUS (0.94 fb ep → e ℓ + ℓ − XP ℓ T > 10 GeV , P ℓ T > ◦ < θ ℓ ,ℓ < ◦ D ℓ ,ℓ η − φ > . y < . , Q < ℓ ℓℓ ℓ ℓℓ Multi-Leptons at HERA Fig. 31. The cross section for lepton pair photoproduction in a restricted phase space as a function of the leading leptontransverse momentum P ℓ T (left) and the invariant mass of the lepton pair M ℓℓ (right). The total error bar is shown, representingthe statistical and systematic uncertainties added in quadrature, which is dominated by the statistical. The bands represent theone standard deviation uncertainty in the SM prediction, dominated by the photon-photon process. modes. The tau-pair signal is modelled using the GRAPEevent generator, which is also used to model the back-ground expectation from other di-leptons. In order to re-duce the significant SM background contribution from NCDIS and photoproduction events, the analyses are restrictedto elastic or quasi-elastic tau-pair production, ep → eXτ + τ − ,where X is the proton or a resonant state. This is effec-tively done by vetoing any additional objects in the finalstate beyond the tau decay products and the scatteredelectron, which may also be present.The main background contribution after applying theabove elasticity requirements is due to exclusive diffractiveevents, both in DIS and photoproduction, which is mod-elled using the RAPGAP event generator. Non-diffractiveDIS background is modelled by H1 (ZEUS) using RAP-GAP (DJANGOH) and photoproduction is modelled byboth experiments using PYTHIA.The H1 analysis of tau-pair production is based ontheir HERA I data sample [162], corresponding to an in-tegrated luminosity of 106 pb − . Electrons are selectedwith E e > P eT > P µT > ◦ <θ ℓ < ◦ , and are required to be isolated from jets of atleast one unit in angular distance D = p ( ∆η ) + ( ∆φ ) .Jets composed of one or three tracks with E jet T > ◦ < θ jet < ◦ are reconstructedby a dedicated algorithm, which uses multiple neural net-works to discriminate between tau jets and the QCD back-ground [162].In total, 30 tau-pair events are selected in the H1 anal-ysis, compared to a SM prediction of 27 . ± . 1, of which16 . ± . γγ → τ + τ − events. The num-ber of events collected in the different tau-pair topologiesare summarised in table 7. The distributions of the visibleinvariant mass, as well as the polar angle and transverse Table 7. Observed and predicted event yields for the differentevent topologies in the H1 and ZEUS di-tau analyses. Thetotal MC expectation includes the sum of tau-pair production,NC DIS and photoproduction, as well as electron and muonpair production. The experimental systematic uncertainties arequoted on the total MC expectations. Tau-pair Production at HERAH1 Analysis ( L = 106 pb − ) Tau decay Data Total SM Tau-pairproduction eµ . ± . e jet 2 6 . ± . µ jet 10 7 . ± . . ± . . ± . ZEUS Analysis ( L = 334 pb − ) Tau decay Data Total SM Tau-pairproduction eµ . +1 . − . . +0 . − . e jet 7 8 . +1 . − . . +0 . − . µ jet 4 8 . +2 . − . . +0 . − . jet jet 10 14 . +2 . − . . +0 . − . Total 25 34 . +3 . − . . +0 . − . momentum of the identified tau candidates were also ex-amined and show no deviation from the SM predictions.A tau-pair event in the final H1 sample is shown in fig-ure 32, where one of the tau leptons decays into a muonand the other undergoes a 3-prong hadronic decay. In thiscase, the scattered electron is not detected in the event. . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 35 Z R X Y h + h − h + µ − µ − h + h + h − Z R YX Fig. 32. A tau-pair event observed in the H1 detector, where one tau lepton decays leptonically to a muon and the other taulepton decays to three charged hadrons, a so called 3-prong decay. The ZEUS analysis of tau-pair production is based ontheir HERA II data sample [174], corresponding to an inte-grated luminosity of 334 pb − . Electrons are selected with P eT > ◦ < θ e < ◦ ,isolated from the rest other calorimetric energy depositsby a distance D > . 8. Muons are selected as tracks inthe central detectors matched to segments in the muonchambers, with P µT > ◦ < θ µ < ◦ . The muon track is required to be sepa-rated by a distance D > . E jet T > | η jet | < 2. A multivariatediscrimination technique [175] is used to discriminate taujets from QCD jets.A total of 25 events are observed in the data, comparedto a SM expectation of 34 . +3 . − . , of which 23 . +0 . − . arefrom tau-pair production. The events are classified intothe different tau decays topologies in table 7. Figure 33shows the visible invariant mass, M visible ττ , calculated fromthe two tau candidates, and the scalar sum of their visibletransverse momenta, P P visible T,ττ . No event with a visiblemass M visible ττ greater than 50 GeV is observed in the data.The highest visible-mass candidate observed in the ZEUSdata, found in the e − µ topology, has M visible ττ = 49 GeV.The SM prediction describes the data well and no excess isobserved in either the high mass or high P P visible T,ττ regions.H1 performs a measurement of the cross section for theelastic production of τ + τ − pairs in the kinematic region P τT > ◦ < θ τ < ◦ . The cross section is cal-culated according to equation 43, where the acceptance iscalculated using GRAPE. The H1 measured visible crosssection for elastic tau pair production ep → epτ + τ − inte-grated over the kinematic phase space defined above is: σ τ + τ − = 13 . ± . . ) ± . . ) pb , where the first uncertainty is statistical and the secondsystematic. The result is in good agreement with the SMexpectation from GRAPE of 11 . ± . P τT > ◦ < θ τ < ◦ . Thevisible measured cross section in the ZEUS phase spaceis: σ τ + τ − = 3 . ± . . ) ± . . ) pb , which is in reasonable agreement with the SM expectation5 . ± . The production in ep collisions of a single doubly-chargedHiggs boson H ±± could be a source of events containingmultiple high P T leptons at HERA [176]. Figure 34 showsthe possible diagrams for single H ++ production in e + p collisions at HERA. Following the observed excess of highmass events observed in multi-electron events in the H1HERA data [168], these events were investigated in thiscontext [177]. The compatibility of these events with ahypothetical doubly-charged Higgs coupling to ee is ad-dressed and further searches for a H ±± boson coupling to eµ and eτ are performed.The ee analysis is based on the multi-electron eventselection described in section 11 and [168], where a like-charge requirement [177] is added to the two highest elec-trons (positrons), which are assigned to the hypothetical H −− ( H ++ ). After the addition of the charge requirement,3 events are observed in the data with M ee > 65 GeV, inagreement with the SM expectation of 2 . ± . 11. Onlyone of the high mass events seen in the original multi-electron analysis [168] survives the additional selection re-quirements. (GeV) visible tt M E v e n t s (a) (GeV) visible tt T, p S E v e n t s -1 ZEUS 0.33 fb Total SM (GRAPE) - t + t fi gg (b) ZEUS Fig. 33. Distribution of ZEUS tau-pair candidates as a function of (a) the visible invariant mass of the tau pair, M visible ττ ,and (b) the scalar sum of transverse momenta of the two tau candidates, P p visible T,ττ . The data (points) are compared with thepredictions of the sum of the MC expectations. The tau-pair expectation is given by the hatched histogram. The shaded bandrepresents the systematic uncertainty on the SM expectation. Events with one electron and one muon with minimaltransverse momenta of P eT > 10 GeV and P µT > H ±± → eµ decay. Electronsare selected in the polar angle range 20 ◦ < θ e < ◦ toreduce the NC DIS background, and muons in the range10 ◦ < θ µ < ◦ , which is more extended into the forwardregion to increase the efficiency for high H ±± masses. Thesame charge criteria is applied to the eµ final states as usedin the ee search. For M eµ > 65 GeV one event is observed,compared to a SM expectation of 4 . ± . H ++ boson decaying into eτ is per-formed in three final states, depending on whether thetau-lepton decays into an electron, a muon or hadroni-cally . Events are selected which contain either two elec-trons ( ee ), or an electron and a muon ( eµ ), or an elec-tron and a hadronic tau-jet ( eh ). The two leptons, or theelectron and the hadronic tau-jet (see section 11.2) arerequired to be in the angular range 20 ◦ < θ < ◦ , andhave an angular separation of D > . P T of 10 (5) GeV is required for theleading (second) lepton or hadronic tau-jet. A significantamount of missing transverse and longitudinal momentumis expected due to the neutrinos produced in the tau lep-ton decay. Events in the ee class are required to have amissing transverse momentum P miss T > P miss T > 11 GeV for the eh class and additionalcuts are applied on the longitudinal balance of the eventto reduce large NC DIS background [177]. Finally, events The search for the eτ decay is only performed for using thelarger e + p data set, so here only a H ++ is considered. are rejected if the track associated with one of the Higgsdecay product candidates has a negative charge, which isopposite to that of the incoming lepton beam. Followingall eτ selection cuts, only one event is observed in thedata (in the eh class), compared to a SM expectation of2 . ± . H ±± is found in the data. Upper limits on the coupling h eℓ are derived at 95% CL using a modified frequentist ap-proach [178] taking into account systematic uncertaintiesand assuming that the H ±± couples with 100% branchingratio to only ee , eµ or eτ .The H1 limits on h ee are not competitive to thoseset by the OPAL experiment [179]. The eµ ( eτ ) analy-sis allows masses below 141 GeV (112 GeV) to be ruledout at 95% CL for a coupling h eµ ( h eτ ) of electromag-netic strength h eℓ = 0 . 3, which extends beyond the lim-its from LEP [180,181,182]. More recent analyses fromhadron colliders, which investigate H ±± pair productionand are independent of the coupling strength, have pushedthese limits further, first beyond the 200 GeV regime atthe Tevatron (for example, an analysis of eµ final statesfrom CDF, M H ±± > 210 GeV [183]) and later at the LHCwhere the most stringent limits are from ATLAS [184,185]and currently exclude masses up to 468 GeV (400) in ananalysis of eµ ( eτ ) final states. The limits from the H1 re-main unique in that they derived from a search for single H ±± production. . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 37 [GeV] T P S E ve n t s -2 -1 [GeV] T P S E ve n t s -2 -1 SMSM Pair Prod. ) -1 H1+ZEUS (0.56 fb p+e Multi-Leptons at HERA [GeV] T P S E ve n t s -2 -1 [GeV] T P S E ve n t s -2 -1 SMSM Pair Prod. ) -1 H1+ZEUS (0.38 fb e p - [GeV] T P S E ve n t s -2 -1 [GeV] T P S E ve n t s -2 -1 SMSM Pair Prod. ) -1 H1+ZEUS (0.94 fb p – e Fig. 30. The scalar sum of the transverse momentum P P T for combined di-lepton and tri-lepton event topologies for e + p (top), e − p (middle) data and for all data (bottom) in the com-bined H1 and ZEUS analysis. The points correspond to theobserved data events and the histogram to the SM expecta-tion. The total uncertainty on the SM expectation is given bythe shaded band. The component of the SM expectation arisingfrom lepton pair production is given by the striped histogram. e + p g p (X)l – H ++ e + p g p (X)l – H ++ l e + p g p (X)H ++ l – H Fig. 34. Diagrams for the single production of a doubly-charged Higgs boson in e + p collisions at HERA via a coupling h eℓ . 12 Events with isolated leptons and missingtransverse momentum Events containing high energy charged leptons (electron,muon or tau-leptons) together with missing transverse mo-mentum produced in high energy particle collisions areinteresting as they may be a signature of BSM physics.When such an event containing an isolated muon was ob-served by H1 in the first 4 pb − of e + p data, a detailedinvestigation into the potential physics source was per-formed [186]. After this initial H1 event was discoveredduring the visual scanning of high Q events with large P miss T , which was routinely done during data taking for CCDIS analysis, such events would regularly appear through-out HERA I and II data taking.In this analysis, processes are considered signal if theyproduce events containing a genuine isolated lepton andgenuine missing transverse momentum in the final state.Within the SM, single W boson production with sub-sequent leptonic decay W → ℓν , as illustrated in fig-ures 35(a)-(c), is the main SM process at HERA that pro-duces events with high energy isolated leptons and miss-ing transverse momentum. The inclusive hadronic state,which results primarily from the hadronisation of thestruck quark q ′ , is denoted by X . The SM prediction for W production via ep → eW X is modelled by both H1 andZEUS using the EPVEC event generator, which employsthe full set of LO diagrams [101], including W productionvia the W W γ triple gauge boson coupling as illustratedin figure 35(b). This prediction is corrected to NLO byapplying a reweighting to the LO cross section dependenton the transverse momentum and rapidity of the W bo-son [187,188,189,190]. The NLO corrections range from In principle, the beam remnant may also contribute to thehadronic final state, although in the case of W production thisis typically low P T and continues down the beampipe followingthe e ± p collision.8 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 30% at low W transverse momentum (resolved photon in-teractions) to around 10% at high W transverse momen-tum (direct photon interactions).Two further processes contribute to signal events. Firstly,the equivalent charged current W production process ep → νW X , as illustrated in figure 35(c), which is calculatedat LO with EPVEC and contributes an additional 7% tothe predicted signal cross section. Secondly, Z produc-tion with subsequent decay to neutrinos, as illustrated infigure 35(d), where the outgoing electron is the isolatedlepton in the event and genuine missing transverse mo-mentum is produced by the Z decay neutrinos. This pro-cess, which is only relevant when the identified isolatedlepton in the final state is an electron, is also calculatedusing EPVEC and found to contribute less than 3% to thepredicted signal cross section.Final states with isolated electrons or muons and miss-ing transverse momentum, referred to as the electron chan-nel and muon channel respectively, are discussed in the fol-lowing. Analyses of events with isolated tau leptons andmissing transverse momentum are covered in section 12.2. Events with isolated electrons or muons and missing trans-verse momentum have been observed at HERA, and re-sults from the analyses have been regularly published byboth collaborations [191,192,193,194], culminating in thefinal results using the complete HERA data set [195,196].The integrated luminosity in the H1 analysis correspondsto 474 pb − , of which 291 pb − are from e + p collisions and183 pb − from e − p collisions. In the ZEUS analysis, theintegrated luminosity corresponds to 504 pb − , of which296 pb − are from e + p collisions and 208 pb − from e − p collisions.The H1 and ZEUS event selections are very similar.Lepton candidates identified by H1 (ZEUS) are requiredto lie within the polar angle range 5 ◦ < θ ℓ < ◦ (15 ◦ <θ ℓ < ◦ ) and to have transverse momentum, P ℓT > 10 GeV. The lepton is also required to be isolated withrespect to jets and other tracks in the event using thedistances in η – φ space to the nearest jet D jet > . D track > . 5. A large transverse momen-tum imbalance P miss T > 12 GeV is required and a cuton P calo T > 12 GeV is also imposed to ensure a hightrigger efficiency. As muons deposit little energy in thecalorimeter P calo T ≃ P XT in events with isolated muons,and therefore the P calo T requirement effectively acts as acut on the hadronic transverse momentum P XT > 12 GeVin the muon channel. To ensure that the two final statesare exclusive, events in the electron channel must containno isolated muons.SM background processes contribute to the analysismainly through misidentification or mismeasurement. NCDIS events ( ep → eX ), in which genuine isolated high P T electrons are produced, form a significant background inthe electron channel search when fake P miss T arises frommismeasurement. The NC DIS background is modelled inthe H1 (ZEUS) analysis using the RAPGAP (DJANGOH) event generator. Charged current (CC) DIS events ( ep → ν e X ), in which there is real P miss T due to the escapingneutrino, contribute to the background when fake isolatedelectrons or muons are observed and is modelled by bothH1 and ZEUS using DJANGOH. Lepton pair production( ep → eℓ + ℓ − X ) contributes to the background via eventswhere one lepton escapes detection and/or measurementerrors cause apparent missing transverse momentum andis modelled by both H1 and ZEUS using the GRAPE eventgenerator.In order to reject the NC background contribution inthe electron channel, further cuts are applied on the calori-metric energy imbalance, V ap /V p [102], and the longitudi-nal momentum imbalance, δ miss = 2 E e − δ , where δ isthe total E − P z in the event as defined in equation 13and E e is the electron beam energy. In the case of H1,the cut on δ miss is only performed if the event containsexactly one electron, which has the same charge as thebeam lepton. A cut on the difference in azimuthal an-gle between the lepton and the direction of the hadronicsystem, ∆φ ℓ − X < ◦ , is used to reject NC DIS back-ground, which has a back–to–back topology. Further back-ground rejection in the electron channel is achieved using ζ e = 4 E e E e cos θ e / 2, where E e is the energy of the fi-nal state electron . Lepton pair background is removedfrom the muon channel by rejecting azimuthally balancedevents using V ap /V p and by requiring ∆φ µ − X < ◦ ,as well as by rejecting events with two or more isolatedmuons. Finally, the lepton–neutrino transverse mass: M ℓνT = q ( P miss T + P ℓT ) − ( p miss T + p ℓT ) (44)is required to be larger than 10 GeV in in the H1 analysisto further reject NC (lepton pair) background in the elec-tron (muon) channel. Full details of the event selectionscan be found in the individual publications [195,196].A total of 53 events are observed in the H1 analysis, ingood agreement with the SM prediction of 54 . ± . 4, whichis dominated by the expectation from signal processes of40 . ± . . ± . . ± . P XT cut, which is applied due tothe P calo T requirement of the trigger (see section 5).For large transverse momentum, P XT > 25 GeV, whichis atypical of SM W production, a total of 18 events arefound in the data, compared to a SM prediction of 13 . ± . 2, of which 17 are found in e + p collisions compared toa SM prediction of 8 . ± . 3. The P XT distribution for thecombined H1 electron and muon channels is shown for the e + p data sample in figure 36. The observation of an excessof data events over the SM prediction, but only in the e + p data, is also a feature of earlier H1 publications [191,192]. For NC events, where the scattered electron is identified asthe isolated high transverse momentum electron, ζ e is equalto the four momentum transfer squared Q e , as calculated viaelectron method (see section 6).. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 39 q W + n q’e + e + ℓ ℓ + q q’W W n e + e + ℓ ℓ q W + n q’W + e + n e ℓ ℓ + q q’ e + e + Z n – n ℓℓ (a) (b)(c) (d) Fig. 35. Diagrams of processes at HERA which produce an isolated lepton together with missing transverse momentum in thefinal state: Figure (a): ep → eW ( → ℓν ) X ; figure (b): W production via the W W γ triple gauge boson coupling; figure (c): ep → ν W ( → ℓν ) X ; figure (d): ep → eZ ( → ν ¯ ν ) X . The diagrams are shown for e + p collisions. A typical W production event observed in the H1 anal-ysis is displayed in figure 37 (top), featuring a single, iso-lated electron and large missing transverse momentum,which is is clearly visible in the azimuthal plane. A fur-ther event from the H1 analysis is displayed in figure 37(middle), this time featuring an isolated muon, large miss-ing transverse momentum and a prominent hadronic finalstate with large P XT .The results of the ZEUS analysis are summarised intable 8, for the electron and muon channels combined. Inthe full phase space a total of 40 events are observed in thedata broadly in agreement with the SM prediction [196].For large hadronic transverse momentum, P XT > 25 GeV,11 events are found in the data, compared to a SM pre-diction of 12 . ± . 7. Unlike the H1 analysis, no excess isobserved in this region, where for the ZEUS e + p data 6events are seen compared to a SM prediction of 7 . ± . . 98 fb − comprising0 . 39 fb − of e − p collisions and 0 . 59 fb − of e + p colli-sions. A study of the selection efficiency for signal pro-cesses found the H1 and ZEUS analyses to be compatiblein the kinematic region where they are directly compa-rable [197]. Nevertheless, in order to coherently combinethe results from the two experiments, a common phase [GeV] XT P E ve n t s H1 [GeV] XT P E ve n t s H1 All SMSignalH1 Data) -1 p, 291 pb+ events at HERA (e missT + P m e, [GeV] XT P E ve n t s Fig. 36. The hadronic transverse momentum P XT distributionfor the electron and muon channels combined from the H1 anal-ysis of the e + p data sample. The data (points) are compared tothe SM expectation (open histogram). The signal componentof the SM expectation, dominated by real W production, isshown as the striped histogram. The total uncertainty on theSM expectation is shown as the shaded band.0 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA e + e + Z R X Y X Xµ − µ − Z R X Y X Xτ τ Fig. 37. Event displays in the H1 search for events with and isolated lepton and missing transverse momentum. Top: Anelectron event with missing transverse momentum and no visible hadronic final state, typical of low P T single W production.Middle: An isolated muon event, with missing transverse momentum and a prominent hadronic final state. Bottom: An eventwith an isolated tau lepton candidate, missing transverse momentum and a prominent hadronic final state.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 41 Table 8. Results of the ZEUS search for events with isolatedelectrons and missing transverse momentum. The number ofobserved events is compared to the SM prediction. The frac-tion of the SM expectation arising from W production is alsogiven. The quoted errors contain statistical and systematic un-certainties added in quadrature. Search for Events with an Isolated Electron orMuon and Missing Transverse Momentum at HERAZEUS Analysis e + p collisions ( L = 296 pb − ) Data Total SM W production P XT < 12 GeV 7 12 . ± . < P XT < 25 GeV 7 6 . ± . P XT > 25 GeV 6 7 . ± . e − p collisions ( L = 208 pb − ) Data Total SM W production P XT < 12 GeV 9 11 . ± . < P XT < 25 GeV 6 5 . ± . P XT > 25 GeV 5 5 . ± . e ± p collisions ( L = 506 pb − ) Data Total SM W production P XT < 12 GeV 16 23 . ± . < P XT < 25 GeV 13 11 . ± . P XT > 25 GeV 11 12 . ± . space is established [198]. The lepton polar angle accep-tance is the main difference in the common phase spacewith respect to the H1 analysis, where the more restrictedrange of the ZEUS analysis is used, 15 ◦ < θ ℓ < ◦ . Ad-ditionally, the more restrictive cuts on δ miss and V ap /V p are taken from the ZEUS analysis [196]. The minimumlepton–neutrino transverse mass and electron multiplicityrequirements are taken from the H1 analysis [195].The results of the combined H1 and ZEUS analysis aresummarised in table 9. The signal contribution, mainlyfrom real W production, is seen to dominate the totalSM expectation in all data samples. A total of 81 eventsare observed in the data, compared to a SM expectationof 87 . ± . 0. At large hadronic transverse momentum P XT > 25 GeV a total of 29 events are observed in the e ± p data compared to a SM prediction of 24 . ± . 2. Inthe e + p data alone, 23 events are observed with P XT > 25 GeV compared to a SM prediction of 14 . ± . 9. Sev-enteen of these data events are the same events observedin the standard H1 analysis [195], but now compared to alower SM expectation of 6 . ± . e + p analysis remains in the common phase space, it alsoremains a feature only seen in the H1 data.Figure 38 shows a variety of kinematic distributionsof the H1 and ZEUS combined analysis for the complete e ± p HERA I+II data, for the electron and muon chan-nels together. The shape and normalisation of the distri-butions are well described within the uncertainties. The distribution of events in M lνT is compatible with the Ja-cobian peak expected from W production. Similarly, theobserved P XT spectrum is compatible with that expectedfrom W production, peaking at low values of hadronictransverse momentum.A measurement of the visible cross section for the iso-lated lepton and missing transverse momentum topologyin e ± p collisions is performed by H1 using the electronand muon channels in the phase space 5 ◦ < θ ℓ < ◦ , P ℓT > 10 GeV, P miss T > 12 GeV and D jet > . of √ s = 317 GeV. The cross section iscalculated using equation 43, where the EPVEC generatoris used to calculate the acceptance, A , which is predictedto be about the same for e + p and e − p collisions. The totalvisible cross section for events with an isolated lepton andmissing transverse momentum is measured by H1 as: σ ℓ + P miss T = 0 . ± . 05 (stat . ) ± . 04 (sys . ) pb , where the first error is statistical and the second system-atic, in agreement with the SM NLO value of 0 . ± . 04 pbfrom EPVEC.The single W boson production cross section is mea-sured by H1 and ZEUS, individually and in the combinedanalysis described above. The branching ratio correspond-ing to the leptonic W boson decay to any final state withan electron or muon, including the contribution from lep-tonic tau-decay, is also included in the calculation. Thiscross section is also calculated using equation 43, where A is again calculated using EPVEC but is now defined withrespect to the full phase space and the contribution from Z production illustrated in figure 35(d) is considered asbackground. The acceptances for the two experiments arefound to be similar in each P XT bin and vary between 27%and 37% in the electron channel and between 18% and38% in the muon channel [198].The combined H1-ZEUS single W production crosssection, evaluated using a weighted mean of the valuesmeasured by the two collaborations in the common phasespace, is measured as: σ W = 1 . ± . 16 (stat . ) ± . 07 (sys . ) pb , where the first uncertainty is statistical and the secondsystematic. The measurement agrees well with the NLOSM prediction of 1 . ± . 19 pb from EPVEC and themeasurements by H1 and ZEUS in their individual pub-lications [195,196]. The single W boson production crosssection is also measured differentially as a function of P XT ,the results of which are displayed in figure 39, and is alsofound to be in agreement with the SM prediction.Some additional investigations into W bosons are per-formed by H1 using the analysis of their full data set [195].The production of single W bosons at HERA is sensitive toanomalous triple gauge boson couplings [199] via the pro-cess illustrated in figure 35 (b), which can be parametrisedusing two free coupling parameters, κ and λ [200]. In theSM κ = 1 and λ = 0 at tree level and in the following Assuming a linear dependence of the cross section on theproton beam energy.2 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA [deg.] q E ve n t s [deg.] q E ve n t s SMSM Signal ) -1 H1+ZEUS (0.98 fb [deg.] q E ve n t s ℓ [deg.] -X FD E ve n t s [deg.] -X FD E ve n t s SMSM Signal ) -1 H1+ZEUS (0.98 fb [deg.] -X FD E ve n t s ℓ [GeV] n T M E ve n t s [GeV] n T M E ve n t s SMSM Signal ) -1 H1+ZEUS (0.98 fb [GeV] n T M E ve n t s ℓ [GeV] XT P E ve n t s -1 [GeV] XT P E ve n t s -1 SMSM Signal ) -1 H1+ZEUS (0.98 fb [GeV] XT P E ve n t s -1 [GeV] missT P E ve n t s -1 [GeV] missT P E ve n t s -1 SMSM Signal ) -1 H1+ZEUS (0.98 fb [GeV] missT P E ve n t s -1 [GeV] T P E ve n t s -1 [GeV] T P E ve n t s -1 SMSM Signal ) -1 H1+ZEUS (0.98 fb [GeV] T P E ve n t s -1 ℓ (a) (b)(c) (d)(e) (f ) Fig. 38. Distributions of kinematic variables of events with an isolated electron or muon and missing transverse momentum inthe full HERA e ± p data. Shown are: the polar angle of the lepton θ ℓ (a), the difference in the azimuthal angle of the lepton andthe hadronic systems ∆φ ℓ − X (b), the lepton–neutrino transverse mass M ℓνT (c), the hadronic transverse momentum P XT (d), themissing transverse momentum P miss T (e) and the transverse momentum of the lepton P ℓT (f). The data (points) are comparedto the SM expectation (open histogram). The signal component of the SM expectation, dominated by single W production, isshown as the striped histogram. The total uncertainty on the SM expectation is shown as the shaded band.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 43 Table 9. Summary of the combined H1 and ZEUS search for events with an isolated electron or muon and missing transversemomentum for the e + p data (top), e − p data (middle) and the full HERA data set (bottom). The results are shown for the fullselected sample and for the subsample with hadronic transverse momentum P XT > 25 GeV. The number of observed events iscompared to the SM prediction. The SM signal (dominated by single W production) and the total background contribution(mainly NC and CC DIS, together with lepton-pair production) are also shown. The quoted uncertainties contain statisticaland systematic uncertainties added in quadrature. Search for Events with an Isolated Electron or Muon and Missing Transverse Momentum at HERACombined H1 and ZEUS Analysis e + p collisions ( L = 0 . 59 fb − ) Channel Data Total SM SM signal Other SMElectron Total 37 38 . ± . . ± . . ± . P XT > 25 GeV 12 7 . ± . . ± . . ± . . ± . . ± . . ± . P XT > 25 GeV 11 6 . ± . . ± . . ± . . ± . . ± . . ± . P XT > 25 GeV 23 14 . ± . . ± . . ± . e − p collisions ( L = 0 . 39 fb − ) Channel Data Total SM SM signal Other SMElectron Total 24 30 . ± . . ± . . ± . P XT > 25 GeV 4 5 . ± . . ± . . ± . . ± . . ± . . ± . P XT > 25 GeV 2 4 . ± . . ± . . ± . . ± . . ± . . ± . P XT > 25 GeV 6 10 . ± . . ± . . ± . e ± p collisions ( L = 0 . 98 fb − ) Channel Data Total SM SM signal Other SMElectron Total 61 69 . ± . . ± . . ± . P XT > 25 GeV 16 13 . ± . . ± . . ± . . ± . . ± . . ± . P XT > 25 GeV 13 11 . ± . . ± . . ± . . ± . . ± . . ± . P XT > 25 GeV 29 24 . ± . . ± . . ± . ∆κ ≡ κ − ∆κ or λ represents a deviation from the SM. The hadronictransverse momentum spectrum of W events is expectedto be sensitive to anomalous values of ∆κ and λ [199], anda likelihood analysis on the measured P XT distribution isperformed using a Bayesian approach and employing Pois-son statistics [195]. This is done for ∆κ and λ separately,keeping the other parameter fixed to its SM value. Thefollowing limits are derived at 95% CL: − . < ∆κ < . , − . < λ < . . in good agreement with the SM prediction and since thevalue of ∆κ = − W boson, in addition tothe coupling to the electric charge of the W boson. Themost stringent limits on these couplings were obtained by the LEP experiments in single γ , single W and W pairproduction [201,202,203,204].H1 also performs a measurement of the W boson po-larisation fractions at HERA by examining the cos θ ∗ dis-tribution in the decay W → e/µ + ν , where θ ∗ is definedas the angle between the W boson momentum in the labframe and the charged decay lepton in the W boson restframe. The cos θ ∗ distributions for W + bosons are givenby [200]: dNd cos θ ∗ ∝ (1 − F − − F ) · 38 (1 + cos θ ∗ ) + F · (cid:0) − cos θ ∗ (cid:1) (45)+ F − · 38 (1 − cos θ ∗ ) , where the left handed F − , longitudinal F and right handed F + polarisation fractions are constrained by the relation [GeV] XT P [f b / G e V ] X T / d P W s d [GeV] XT P [f b / G e V ] X T / d P W s d ) -1 H1+ZEUS (0.98 fbSM Single W Production at HERA [GeV] XT P [f b / G e V ] X T / d P W s d Fig. 39. The single W production cross section as a functionof the hadronic transverse momentum, P XT , measured usingthe combined H1 and ZEUS data at a centre of mass energy of √ s = 317 GeV. The inner error bar represents the statisticalerror and the outer error bar indicates the statistical and sys-tematic uncertainties added in quadrature. The shaded bandrepresents the uncertainty on the SM prediction. F + ≡ − F − − F . Beginning with the H1 isolated electronor muon and missing transverse momentum event sample,the additional requirement of a reliable charge measure-ment is added, so that the resulting charge misidentifica-tion is well below 1% [195]. The final event sample consistsof 21 electron events and 9 muon events and a SM pre-diction with a W production purity of 76%. To allow thecombination of the different W boson charges, the valueof cos θ ∗ is multiplied by the sign of the lepton charge q ℓ = ± q ℓ · cos θ ∗ is shown in figure 40, compared to the SMprediction. The cross section fit to the model defined inequation 46 is also shown. The optimal values for the W boson polarisation fractions F − and F are simultaneouslyextracted from the fit as 0 . ± . 24 and 0 . ± . 43, re-spectively, in good agreement with the SM values 0 . 62 and0 . 17 as predicted by EPVEC. The search for isolated tau leptons complements the anal-ysis of the electron and muon channels described in sec-tion 12.1. This analysis has previously been performed byH1 and ZEUS using their HERA I data sets, where thetau is identified by its hadronic decay [162,205]. The H1collaboration have updated their search to include theirfull HERA data set, corresponding to an integrated lumi-nosity of 474 pb − [195].The selection of H1 events with isolated tau leptonsand missing transverse momentum is based on the HERA- * q cosq -1 -0.5 0 0.5 1 * ) / pb q c o s / d ( q s d s / * q cosq -1 -0.5 0 0.5 1 * ) / pb q c o s / d ( q s d s / EPVECFitH1 Data F - F 0.43 – = 0.15 0.24 – = 0.68 Single W Production Cross Section H1 ℓ ℓ ℓ ℓ Fig. 40. The H1 measured normalised differential cross section1 /σ dσ/d ( q ℓ · cos θ ∗ ) (points) as a function of q ℓ · cos θ ∗ for on–shell W bosons. The EPVEC prediction is also shown (openhistogram) with a 15% theoretical uncertainty shown by theband. The result of the simultaneous fit of the W polarisationfractions is shown as the dashed histogram. I analysis [162]. Only hadronic decays with one chargedhadron (one-prong) are considered. Tau decays to elec-trons and muons enter the electron and muon channelsdescribed in section 12.1.A tau identification algorithm selects narrow, low mul-tiplicity jets typical for hadronic tau decays, with trans-verse momentum P jet T > ◦ <θ jet < ◦ of the detector. Narrow jets are selected by re-quiring R jet < . 12 (see equation 42). At least one trackmeasured in the central tracking detector with transversemomentum P track T > η − φ spaceof D > . P miss T > 12 GeV and P calo T > 12 GeV, a significant az-imuthal imbalance δ miss = 2 E e − δ > V ap /V p < . P XT > 12 GeV. Some degree of acoplanarity between the tau jetand the remaining hadronic system X ′ in the transverseplane ∆φ τ − X ′ < ◦ is required to suppress events withback–to–back topologies, primarily NC events and photo-production events with jets.The results of the search in the tau channel are sum-marised in table 10. In the final event sample, 18 eventsare selected, compared to a SM expectation of 23 . ± . . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 45 [GeV] missT P E ve n t s [GeV] missT P E ve n t s All SMSignalH1 Data H1 [GeV] X’T P E ve n t s [GeV] X’T P E ve n t s All SMSignalH1 Data H1 [deg.] t q 20 40 60 80 100 120 E ve n t s [deg.] t q 20 40 60 80 100 120 E ve n t s All SMSignalH1 Data H1 [GeV] t T P E ve n t s [GeV] t T P E ve n t s All SMSignalH1 Data H1 (a) (b)(c) (d) Fig. 41. Distributions in the tau channel for the H1 e ± p data sample. Shown is the missing transverse momentum P miss T (a), thehadronic transverse momentum not including the tau-jet candidate P X ′ T (b), the polar angle of the tau-jet candidate θ τ (c) andthe tau-jet candidate transverse momentum P τT (d). The data (points) are compared to the SM expectation (open histogram).The signal component of the SM expectation ( W → τ ν τ ) is shown as the hatched histogram. The total uncertainty on the SMexpectation is shown as the shaded band. pectation is dominated by CC DIS background processes,and the signal contribution is only 11%. Distributions ofthe events in the final sample are shown in figure 41. Mostof the events are observed at very low P X ′ T . At P X ′ T > . ± . 2. In this region the contri-bution of single W boson production to the SM expec-tation is about 38%. The selected data event, shown infigure 37 (bottom), is observed in e − p collisions and ex-hibits P τT = 14 . ± . P X ′ T = 62 ± P miss T = 68 ± P T with respect to H1, P miss T > 20 GeV. Tau candidates are reconstructed with E jet T > − . < η < . . +0 . − . (where 43% is due to single- W production). In the region P XT > 25 GeV, 2 events are observed compared to an ex-pectation of 0 . ± . 05. It can therefore be concluded thatthe data show a general good agreement with the SM pre-dictions and no hint of BSM phenomena is observed atHERA. Recently, a review of single vector boson produc-tion at LHC at √ s = 7 TeV has been published [206].There, all results have been found in agreement betweenthe two main experiments, ATLAS and CMS, and are fur-thermore consistent with the presently available SM pre-dictions. Table 10. Summary of the H1 results of the search for eventswith tau leptons and missing transverse momentum for the e + p data, e − p data and the full H1 data set. The results are shownfor the full selected sample and for the subsample at P XT > 25 GeV. The number of observed events is compared to theSM prediction. The SM signal ( W → τ ν τ ) and the backgroundcontributions are also shown. The quoted uncertainties containstatistical and systematic uncertainties added in quadrature. H1 Search for Events with an Isolated Tau-leptonand Missing Transverse Momentum at HERA e + p collisions ( L = 291 pb − ) Data Total SM SM signal Other SMTotal 9 12 . ± . . ± . 25 10 . ± . P XT > 25 GeV 0 0 . ± . 12 0 . ± . 06 0 . ± . e − p collisions ( L = 183 pb − ) Data Total SM SM signal Other SMTotal 9 11 . ± . . ± . 15 10 . ± . P XT > 25 GeV 1 0 . ± . 11 0 . ± . 03 0 . ± . e ± p collisions ( L = 474 pb − ) Data Total SM SM signal Other SMTotal 18 23 . ± . . ± . 40 20 . ± . P XT > 25 GeV 1 1 . ± . 21 0 . ± . 09 0 . ± . 13 Search for single top production The production of single top quarks at HERA is kinemat-ically possible due to the centre of mass energy, which isabove the top mass threshold. Within the SM, the domi-nant process for single top production is the charged cur-rent reaction ep → νtX [207,208,209], which has a tinycross section of less than 1 fb [210,211], ruling out theobservation of SM single top production at HERA. How-ever, flavour changing neutral current (FCNC) processes( u → t or c → t , mediated by a neutral vector boson, γ or Z ) could lead to a visible single top production crosssection. In several extensions of the SM the top quarkis predicted to undergo FCNC interactions [212,213,214,215] and the observation of top quarks at HERA wouldthus be a clear indication of physics beyond the SM.The diagram for anomalous single top production viaFCNC is shown in figure 42, where the top quark couplingto a U -type quark via a photon ( Z boson) is indicatedas κ γ ( v Z ). As the top quark mass is comparable to thecentre of mass energy at HERA, the initial state quarkoriginating from the proton needs to be at a significantlyhigh value of x for single top production. As the charmquark density at high x is low compared to the density ofthe u and d valence quarks, the contribution to the crosssection given by charm quarks is neglected. For the samereason, production of anti-top quarks is neglected, as thiswould involve anti-quarks in the initial state.The anomalous single top production cross section canbe parametrised in terms describing the effect of the twoFCNC couplings, A σ and B σ , and of their interference, ue et /Z g b + m / + e m n / e n + W Z /v g k Fig. 42. Anomalous single-top production via flavour-changing neutral current transition with coupling κ tUγ . C σ : σ ep → etX = A σ κ γ + B σ v Z + C σ κ γ v Z . (46)Simulation of the anomalous single top signal is done us-ing the package CompHEP [216], which is also used to de-termine the parameters A σ , B σ and C σ . The interferenceparameter C σ has only a small effect, producing variationsof the cross section of less than 1% in the full consideredrange of couplings and is therefore neglected.CompHEP is also used to determine the top decaywidths in the different channels: Γ t → uγ = A Γ κ γ ,Γ t → uZ = B Γ v Z , (47) Γ t → qW = C Γ , where A Γ and B Γ are the partial widths of the top corre-sponding to uγ and uZ unitary FCNC couplings and C Γ is the SM top width.As any top quark immediately and exclusively decaysinto a b quark and a W boson, the experimental signatureof single top production at HERA is either the leptonic, ℓν , or hadronic, q ¯ q , W decay products in combination witha high P T hadronic final state from the b -jet. In the caseof leptonic W decay, this topology is of particular interestas it is the same as the SM W production events dis-cussed in section 12.1, especially those seen with a promi-nent hadronic final state. In the case of hadronic W decay,the experimental signature of single top production is thepresence of three jets in an event, with a mass compati-ble with that of the top quark. Both H1 and ZEUS havepreviously investigated FCNC using their HERA I datasets [194,217] and have published searches for single topevents examining the HERA II data sample [218,219].The main SM background to single top production inthe W leptonic decay channel is from real W production,which has a cross section of about 1 pb and is modelledusing the EPVEC MC generator, which is reweighted to . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 47 [GeV]M E ve n t s [GeV]M E ve n t s All SMANOTOPH1 Data ) -1 Search for Single Top Quarks at HERA (474 pb Electron+Muon Channel without cut on lepton chargeTop Preselection H1 ℓνbℓνb Fig. 43. The distribution of the reconstructed top mass M lνb in the H1 electron and muon channels, after neutrino recon-struction but before the cut on the lepton charge. The dataare shown as points, the total SM expectation as the open his-togram with systematic and statistical uncertainties added inquadrature (shaded band). The prediction from ANOTOP isalso shown with arbitrary normalisation (dashed histogram). NLO QCD. In the W hadronic decay channel, the mainbackground contribution arises from multi-jet productionin photoproduction and NC and CC DIS, which are mod-elled using PYTHIA, RAPGAP and DJANGOH.Single top production is investigated by H1, employingboth leptonic and hadronic W decays [218]. In the leptonicchannel, isolated electrons and muons with a transversemomentum P ℓT > 10 GeV in the polar angle range 5 ◦ <θ l < ◦ are selected in events with a missing transversemomentum P miss T > 12 GeV, where the selection is basedon the H1 analysis described in section 12.1, where 39 (14)electron (muon) events are observed in the data, comparedto a SM prediction of 43 . ± . . ± . 8) [195].To estimate a potential top contribution to this sam-ple, a top quark candidate is reconstructed from its de-cay products (lepton l , neutrino ν and b quark), and thecompatibility with single top quark production via FCNCwas tested using a multivariate discriminant method [218].The kinematic variables of the neutrino are reconstructedusing the transverse and longitudinal momentum balanceof the event. The four-momentum of the b -jet is taken asthe four-momentum of the hadronic final state and themass of the top quark is reconstructed as the sum of thefour-vectors of the isolated lepton, the neutrino and thehadronic final state. The reconstructed top mass M ℓνb forthe electron and muon channel combined is shown in fig-ure 43, where the data are in overall agreement with theSM prediction, and a slight excess of data events is ob-served in the top quark mass range. The prediciton fromANOTOP [217], an anomolous top MC MC generator,is also shown with arbitrary normalisation. The resultsof the multivariate discriminant neural-net based analysis are cross checked against a cut-based top selection, requir-ing the selected top events to have a b -jet with transversemomentum P bT > 30 GeV and M ℓνb > 140 GeV. In thefinal selection, five (four) events are observed in the elec-tron (muon) channel, compared to a SM expectation of3 . ± . . ± . W hadronic decay channel, eventsare selected by H1 containing at least three jets in thepseudorapidity range − . < η jet < . 5, with P jet1 T > 40 GeV, P jet2 T > 30 GeV and P jet3 T > 15 GeV, where thejets are ordered in magnitude of their transverse momenta.Two of the jets are required to have a mass compatiblewith that of the W boson, within the experimental reso-lution: 65 < M jj < 95 GeV. The remaining jet is assumedto be that coming from the b quark and is required tohave P T > 25 GeV. After the preselection, 404 events areselected, compared to a SM prediction of 388 ± 32. Likein the analysis of the leptonic decay channels, a multivari-ate discriminant is used to differentiate the signal fromthe background, and the analysis is cross checked with acut-based selection.The b -jet candidate is required have large transversemomentum P bT > 40 GeV and the reconstructed top quarkmass must lie in the range 150 < M jets < 210 GeV. Thenumber of candidate events selected is 128, compared to123 ± 13 expected from SM processes.A similar analysis is performed by ZEUS on the lep-tonic decay channels of the W boson using their HERA IIdata sample [219]. Events are selected with P miss T > 10 GeV(12 GeV for electron events), containing isolated electronswith P eT > 10 GeV in the angular region 17 ◦ < θ e < ◦ ,or isolated muons with P µT > ◦ < θ µ < ◦ .In the electron (muon) channel, a total of 245 (269)events were observed, compared to 253 ± ± 3) ex-pected from the SM. A cut on the transverse momentumof the hadronic final state, P XT > 40 GeV, is then appliedto the data, resulting in a final sample containing 1 eventin the electron channel compared to a SM prediction of3 . ± . 6, and 3 events in the muon channel, compared toa SM prediction of 3 . ± . W decaychannels examined by H1 and ZEUS is summarised in ta-ble 11, compared to the SM expectation. As no significantdeviation from the SM is observed, upper limits on thesingle top production cross section are derived using themethod of fractional event counting [151]. For all chan-nels combined the H1 upper limit on the cross section forsingle top quark production 95% CL is: σ ( ep → etX, √ s = 319 GeV) < . 25 pb , where the limit is reported at √ s = 319 GeV, taking intoaccount [218] the ratio of 0 . 70 of the predicted cross sec-tions at √ s = 301 GeV and 319 GeV [220].The ZEUS analysis described above is based on theHERA II data sample only, and the results are then com-bined with those of the ZEUS publication on their HERA Idata [194] which also includes the hadronic decay channelof the W boson. The resulting ZEUS limit at 95% CL on Table 11. Summary of the H1 and ZEUS searches for sin-gle top production in FCNC at HERA, where the observednumber of events in each of the different W decay channelsis shown. The number of events predicted by the SM is alsoshown, where the quoted errors contain statistical and system-atic uncertainties added in quadrature. Search for Single Top Production in FCNC at HERAH1 Analysis ( L = 474 pb − ) Decay channel Data Total SM W → eν e . ± . W → µν µ . ± . W → qq 128 123 ± ZEUS Analysis ( L = 370 pb − ) Decay channel Data Total SM W → eν e . ± . W → µν µ . ± . the single top production cross section is: σ ( ep → etX, √ s = 315 GeV) < . 13 pb , reported at the average centre of mass energy √ s = 315 GeVof the complete 0 . − ZEUS data sample.The limits on the cross sections are converted into95% CL limits on the anomalous FCNC coupling k γ us-ing equation 46, which are found by H1 (ZEUS) to be κ γ < . 18 ( κ γ < . 13) for a top mass of 175 GeV. Theselimits may in turn be transformed [219] into limits on thebranching ratios Br( t → uγ ) and Br( t → uZ ) and H1(ZEUS) sets a limit of Br( t → uγ ) < . 64% ( < . t → uZ ). The limits on these branchingratios are displayed in figure 44, compared to those fromother experiments ALEPH [221] at LEP and CDF [222,223] and DØ [224] at the Tevatron.Once again, the extended reach of the LHC data hasextended these limits into a new domain, where searchesby the ATLAS [225,226] and CMS [227] collaborationsnow limit these branching fractions to sub-permille levels. Z production at HERA Although the number of W or Z bosons produced atHERA is expected to be small, their study at HERA pro-vides the means to test the SM, as some anomalous cou-plings of these bosons predict an increase in the produc-tion cross section. A measurement of the W productioncross section at HERA was performed using events with anisolated electron or muon and missing transverse momen-tum, as discussed in section 12.1, where good agreementwas observed with the SM prediction. An analysis of theproduction of Z bosons performed by ZEUS is describedin the following.The full data sample collected with the ZEUS detectoris used to study the production of Z bosons in the process _ Fig. 45. Example of a leading-order diagram of Z boson pro-duction, ep → eZ p and subsequent hadronic decay into aquark q and an antiquark ¯ q . ep → eZ X . Compared to the analyses described in sec-tion 11, which include Z decays to lepton pairs, this anal-ysis examines the hadronic decay mode of the Z , chosenbecause of its large branching ratio and to exploit the ex-cellent resolution of the ZEUS hadronic calorimeter. Theanalysis is restricted to elastic and quasi-elastic Z pro-duction in order to suppress QCD multi-jet background. Adiagram for Z production at LO and the subsequent Z hadronic decay is shown in figure 45. The decay productsof the Z boson form at least two hadronic jets with hightransverse energies. No energy deposit is found around theforward direction, in contrast to what would be expectedin inelastic collisions.The production of Z bosons is simulated using theEPVEC program to generate the events at the partonlevel, and PYTHIA to simulate initial and final state par-ton showers. As a reliable simulation for the SM back-ground events, predominantly due to the diffractive pho-toproduction of jets of high transverse momentum, wasnot available, the background distributions are estimatedfrom the data as described below.The event selection is performed requiring the presenceof at least two jets in the final state with E T > 25 GeVand | η | < 2. The two highest E T jets are required to beseparated by at least 2 radians in the azimuthal plane, asthe two leading jets from the Z boson decays are expectedto be nearly back-to-back in the x − y plane.To identify high Q events, the electron produced inthe DIS scattering in the ep → eZ X process is requiredto be reconstructed in the final state. The electron is re-quired to have an energy E ′ e > p track > Q and photo-production events, as well as background from beam-gasand cosmic interactions. To select elastic and quasi-elasticprocesses, a cut on η max < . η max is defined as the pseudorapidity of the energy deposit inthe calorimeter closest to the proton-beam direction withenergy greater than 400 MeV as determined by calorime-ter cells. This cut also rejects signal events with energydeposits from the scattered electron in the calorimeter . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 49 g u Br -3 -2 -1 uZ B r -2 -1 exc l ud e d b y Z E U S ZEUS -1 ZEUS 0.5 fb ,u(c)Z g u(c) fi ALEPH t ,u(c)Z g u(c) fi CDF t g u fi H1 t u(c)Z fi D0 t g u Br -3 -2 -1 uZ B r -2 -1 Fig. 44. Exclusion limits set by the H1 and ZEUS experiments on the branching ratios Br( t → uγ ) and Br( t → uZ ) from thesearch for single top production at HERA. Limits from other experiments are also shown. around the forward beam pipe, causing an acceptance lossof about 30%.After all selection cuts are applied, 54 events remainin the final data sample. The total selection efficiency, es-timated using the MC simulation, is found to be 22% forelastic and quasi-elastic processes and less than 1% forDIS and photoproduction events. The number of signaland background events is estimated using the M jets distri-bution as measured in the data. To increase the statisticsof the sample, the shape of the M jets distribution outsidethe Z mass region is estimated from the inelastic data,obtained by removing the η max cut, after verification thatthis cut does not distort the distribution. In this way, the M jets distribution in the inelastic region is adopted as abackground template in a fit to the data in the elasticregion, allowing the determination of the number of thesignal events and therefore the cross section. The M jets distribution of the selected events and the fit results areshown in figure 46.The number of observed Z events is measured to be15 . +7 . − . (stat . ), corresponding to a statistical significanceof the signal of 2 . σ . The cross section for the elastic andquasi-elastic production of Z bosons, ep → eZ X , at √ s = 318 GeV, is measured as: σ Z = 0 . ± . 06 (stat . ) ± . 01 (sys . ) pb , in agreement with the SM prediction of 0 . 16 pb. (GeV) jets M40 60 80 100 120 140 E v e n t s -1 ZEUS 496 pb signal + b.g. ) Fit ( ZFit ( b.g. ) +7.0 = 15.0 obs N ZEUS Fig. 46. The M jets distribution and the fit result. The data areshown as points, and the fitting result of signal+background(background component) is shown as solid (dashed) line. Thesignal contribution is also indicated by the shaded area andamounts to a total number of N obs events. The error barsrepresent the approximate 68% CL intervals, calculated as ±√ n + 0 . 25 + 0 . n .0 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 15 A general search for new phenomena The searches for new physics reported so far in this re-view focus on the highest energy regions accessible atHERA, as a large variety of possible extensions to the SMpredict new phenomena which may appear there. Model-independent searches are performed without looking forsignatures as predicted by a particular model of BSMphysics, but just looking for deviations between the pre-dicted and measured cross sections in regions in whichthe SM predictions are reliable. Such model-independentanalyses do not rely on any a priori definition of expectedsignatures for exotic phenomena. Therefore, they addressthe important question of whether unexpected phenom-ena may occur through a new pattern, not predicted bythe SM.In this section, a more general, model-independent ap-proach is described. The analysis is performed by the H1Collaboration using their complete e ± p data set [228],corresponding to an integrated luminosity of 463 pb − ,of which 178 pb − was recorded in e − p collisions and285 pb − in e + p collisions. Following the analysis strategyof a previous H1 publication which used only the HERA Idata set [229], a search for differences between the ob-served number of data events and the SM expectation ina large variety of different event topologies is performed.The analysis includes all high P T final state topologies in-volving electrons ( e ), muons ( µ ), jets ( j ), photons ( γ ) orneutrinos ( ν ) and searches for deviations from the SM pre-diction in phase-space regions where the SM predictionsare reliable. The identification of such particles followsthat described in section 5.Calorimetric energy deposits and tracks are used toidentify electron, photon and muon candidates. Electronand photon candidates are characterised by compact andisolated electromagnetic showers in the LAr calorimeterwith an associated track from the inner tracking systemsin the case of electrons or with no associated track in thecase of photons. The identification of muon candidates isbased on a track measured in the inner tracking systemsassociated with signals in the muon detectors. Calorimet-ric energy deposits and tracks not previously associatedto identified electron and muons are used to reconstructjets using the inclusive k T algorithm. If the event con-tains large P missT it is associated to an outgoing neutrinocandidate and the neutrino four-momentum is calculatedassuming transverse momentum conservation and usingthe relation in equation 13. A detailed description of thefurther identification criteria applied to each type of parti-cle can be found in the H1 publication [228]. Such criteriatypically include strict isolation requirements and employinformation from multiple detector components to ensurea high efficiency and to reduce misidentification.A precise estimate of all processes relevant at hightransverse momentum in ep interactions is needed to en-sure a reliable comparison to the SM. Several MC gen-erators, already introduced for the analyses described inthe previous sections, are therefore combined to simulateevents in all classes. The dominant SM processes at hightransverse momenta are NC DIS, which is simulated using RAPGAP and two-jet photoproduction, simulated usingPYTHIA. Charged current DIS events are simulated us-ing DJANGOH and contributions from elastic and quasi-elastic QED Compton scattering are simulated with theWABGEN generator. Smaller contributions arising fromthe production of single W bosons and multi-lepton eventsare modelled using the EPVEC and GRAPE event gener-ators, respectively.The common phase space for all the selected particlesis defined as 10 ◦ < θ < ◦ and P T > 20 GeV, exceptfor the neutrino, for which the phase space is defined as P miss T > 20 GeV and δ < 48 GeV. All identified particleswith P T > 20 GeV, including the neutrino (where the P T is taken from its reconstructed four-vector), are requiredto be isolated with respect to each other by a minimumdistance in pseudorapidity-azimuth of R > 1. All particlessatisfying these requirements are referred to as bodies , andevents are classified into exclusive classes according to thenumber and the types of bodies they contain, for exam-ple e − j , µ − ν − j , j − j − j − j and so on. All possible classeswith at least two bodies are investigated, with the excep-tion of the µν class, which originates mainly from poorlyreconstructed muons giving rise to missing transverse mo-mentum.The event yields for all the event classes with observedevents or with SM expectations greater than 0.01 are givenin table 12. The class with the lowest SM expectation isthe µ − µ − ν , where the number of expected events givenby the SM MC is 0 . ± . e ± p data sample and a good agreement is observedbetween the data and the SM prediction. The same yieldsare shown in figure 47, separately for e + p and e − p colli-sions. As expected, events with an electron (neutrino) andtwo or more jets are dominated by NC (CC) DIS, whileevents with two or more jets and no reconstructed leptonsare dominated by photoproduction. Event classes wherean electron is observed together with a photon, with orwithout an accompanying jet, arise from QED Comptonprocesses.Classes where more than one lepton is observed aremainly due to lepton pair production from γγ processes,as already seen in the dedicated analyses described in sec-tion 11. Compared to the H1 multi-lepton analysis [170],the leptons in the general search are identified in a widerpolar angle region, down to 10 ◦ in the forward direction,and required to have higher transverse momenta. All themulti-lepton events reconstructed in the dedicated anal-ysis and falling into the kinematic region of this analysisare also selected in the general search. Similarly, events inwhich an electron or a muon are reconstructed togetherwith a neutrino, with or without a jet come mainly fromsingle W boson production, as already seen in the searchesfor events with high P T leptons and missing transversemomentum described in section 12.In addition to the yields, the selected events are alsoanalysed in terms of their topology. The distributions ofthe transverse momenta of all bodies, P P T , and the in-variant mass of all reconstructed bodies, M all , are anal-ysed together with their angular distributions and energy . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 51 Table 12. Observed and predicted event yields for all event classes with observed data events or a SM expectation greaterthan 0 . 01 for all e ± p data. Each event class is labelled with the leading body listed first. The uncertainties on the predictionsinclude model uncertainties and experimental systematic errors added in quadrature. The ˆ P values (see text) obtained in thescan of P P T , M all , cos θ ∗ lead and X lead distributions are also given. H1 General Search for New Phenomena ( e ± p collisions, L = 463 pb − ) Event class Data Total SM ˆ P P P T ˆ P M all ˆ P cos θ ∗ lead ˆ P X lead j − j ± . 57 0 . 33 0 . e − j ± . 090 0 . 99 0 . µ − j 21 19 . ± . . 30 0 . 46 0 . ν − j ± . 33 0 . 31 0 . e − ν 16 21 . ± . . 13 0 . 084 0 . e − e 36 40 . ± . . 35 0 . 041 0 . e − µ 19 21 . ± . . 46 0 . 83 0 . µ − µ 18 17 . ± . . 31 0 . 50 0 . γ − j 563 538 ± 86 0 . 31 0 . 21 0 . γ − e 619 648 ± 62 0 . 93 0 . 99 0 . γ − µ . ± . 04 1 1 1 γ − ν . ± . . 076 0 . 33 0 . γ − γ . ± . . 66 0 . 35 0 . j − j − j ± 725 0 . 54 0 . 65 0 . e − j − j ± 270 0 . . 70 0 . µ − j − j . ± . 18 0 . 12 0 . 072 0 . ν − j − j 355 338 ± 62 0 . 80 0 . 48 0 . e − e − j . ± . 04 1 1 1 e − e − ν . ± . 01 1 1 1 e − e − e . ± . 04 0 . 15 0 . 031 0 . µ − µ − j . ± . 03 1 1 1 e − µ − µ . ± . 07 1 1 1 µ − µ − ν . ± . 005 1 1 1 e − µ − j . ± . 04 1 1 1 e − ν − j . ± . . 24 0 . 57 0 . µ − ν − j . ± . . 27 0 . 30 0 . e − µ − ν . ± . 01 1 1 1 γ − j − j . ± . . 41 0 . 25 0 . γ − e − j 12 19 . ± . . 31 0 . 28 0 . γ − ν − j . ± . . 35 0 . 62 0 . e − j − j − j 19 22 ± . . 84 0 . 80 0 . ν − j − j − j . ± . . 47 0 . 39 0 . γ − ν − j − j . ± . 07 1 1 1 e − ν − j − j . ± . 09 1 1 1 γ − e − j − j . ± . 07 1 1 1 e − e − ν − j . ± . 06 1 1 1 e − µ − ν − j . ± . 05 1 1 1 j − j − j − j 40 33 ± e − j − j − j − j . ± . ν − j − j − j − j . ± . j − j − j − j − j . ± . 092 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA j-je-j-j m -j n n e-e-e m e- m - m -j g -e g m - g n - g g - g j-j-je-j-j-j-j m -j-j n e-e-j n e-e-e-e-e-j m - m m - m e- n - m - m -j m e- -j n e- -j n - m n - m e- -j-j g -e-j g -j n - g e-j-j-j-j-j-j n -j-j n - g -j-j n e- -j-j-e g -j n e-e- -j n - m e-j-j-j-je-j-j-j-j-j-j-j-j n j-j-j-j-jj-je-j-j m -j n n e-e-e m e- m - m -j g -e g m - g n - g g - g j-j-je-j-j-j-j m -j-j n e-e-j n e-e-e-e-e-j m - m m - m e- n - m - m -j m e- -j n e- -j n - m n - m e- -j-j g -e-j g -j n - g e-j-j-j-j-j-j n -j-j n - g -j-j n e- -j-j-e g -j n e-e- -j n - m e-j-j-j-je-j-j-j-j-j-j-j-j n j-j-j-j-jj-je-j-j m -j n n e-e-e m e- m - m -j g -e g m - g n - g g - g j-j-je-j-j-j-j m -j-j n e-e-j n e-e-e-e-e-j m - m m - m e- n - m - m -j m e- -j n e- -j n - m n - m e- -j-j g -e-j g -j n - g e-j-j-j-j-j-j n -j-j n - g -j-j n e- -j-j-e g -j n e-e- -j n - m e-j-j-j-je-j-j-j-j-j-j-j-j n j-j-j-j-j SMH1 Data -2 -1 10 1 10 10 ) -1 p, 285 pb + H1 General Search at HERA (e Events H1 j-je-j-j m -j n n e-e-e m e- m - m -j g -e g m - g n - g g - g j-j-je-j-j-j-j m -j-j n e-e-j n e-e-e-e-e-j m - m m - m e- n - m - m -j m e- -j n e- -j n - m n - m e- -j-j g -e-j g -j n - g e-j-j-j-j-j-j n -j-j n - g -j-j n e- -j-j-e g -j n e-e- -j n - m e-j-j-j-je-j-j-j-j-j-j-j-j n j-j-j-j-jj-je-j-j m -j n n e-e-e m e- m - m -j g -e g m - g n - g g - g j-j-je-j-j-j-j m -j-j n e-e-j n e-e-e-e-e-j m - m m - m e- n - m - m -j m e- -j n e- -j n - m n - m e- -j-j g -e-j g -j n - g e-j-j-j-j-j-j n -j-j n - g -j-j n e- -j-j-e g -j n e-e- -j n - m e-j-j-j-je-j-j-j-j-j-j-j-j n j-j-j-j-jj-je-j-j m -j n n e-e-e m e- m - m -j g -e g m - g n - g g - g j-j-je-j-j-j-j m -j-j n e-e-j n e-e-e-e-e-j m - m m - m e- n - m - m -j m e- -j n e- -j n - m n - m e- -j-j g -e-j g -j n - g e-j-j-j-j-j-j n -j-j n - g -j-j n e- -j-j-e g -j n e-e- -j n - m e-j-j-j-je-j-j-j-j-j-j-j-j n j-j-j-j-j SMH1 Data -2 -1 10 1 10 10 ) -1 p, 178 pb - H1 General Search at HERA (e Events H1 Fig. 47. The data and the SM expectation for all event classes in the H1 general search with observed data events or a SMexpectation greater than 0 . 01 events for e + p collisions (left) and e − p collisions (right). The error bands on the predictionsinclude model uncertainties and experimental systematic uncertainties added in quadrature. ratios, which are sensitive to spin and decay properties ofhypothetical high mass particles. The variables employedare defined inspired by topological analyses of multi-jetevents [230] and use the so-called main body [228] of theevent. Simplifying the picture, this main body is definedaccording to a priority list between bodies of differenttypes ( γ, e, µ, ν, j ) and using criteria based on its trans-verse momentum, in the case where two bodies of the samekind are present in the event. The variable cos θ ∗ lead is thendefined as the cosine of the polar angle of the leading body relative to the incident proton in the centre of mass framedefined by all bodies. The variable X lead is the energy frac-tion of the leading body and is defined for systems withthree or more bodies as: X lead = 2 E ∗ lead P i E ∗ i , (48)where the sum runs over all bodies and the energies areevaluated in the centre of mass frame of all bodies. Thesensitivity of cos θ ∗ lead and X lead to new physics was tested . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 53 -1 -0.5 0 0.5 1 E ve n t s E ve n t s SM g e fi * e H1 Data ) -1 p, 463 pb – H1 General Search at HERA (e H1 -e g * q cos lead lead X E ve n t s X E ve n t s SM qe q fi e W fi * n H1 Data ) -1 p, 463 pb – H1 General Search at HERA (e H1 e-j-j Fig. 48. The cos θ ∗ lead distribution in the γ − e event class (left) and the X lead distribution in the e − j − j event class (right)from the H1 general search. The points correspond to the observed data events and the histograms to the SM expectation. Theerror bands on the SM prediction include model uncertainties and experimental systematic uncertainties added in quadrature.The dashed line represents the distribution corresponding to an exotic resonance with a mass of 200 GeV, with an arbitrarynormalisation. using MC samples of various exotics processes, such as lep-toquarks, excited fermions or anomalous top production.The distribution of the variables P P T , M all , cos θ ∗ lead and X lead from the data are compared to SM predictions and,as also seen in the event yields in table 12, good agree-ment is found in all cases [228]. An example is given infigure 48, where a clear difference is observed between thecos θ ∗ lead ( X lead ) distribution of data and an MC simulatedexotic e ∗ resonance [231] ( ν ∗ resonance [232]) with a massof 200 GeV, in the γe ( e − j − j ) event class.In order to quantify the observed difference betweendata and SM predictions in terms of agreement or dis-agreement, a quantity ˆ P is introduced, according to asearch algorithm described in the first H1 publication [229].The quantity ˆ P is defined such that the smaller the ˆ P value, the more significant the deviation between data andSM predictions. When ˆ P > . 01, the event class is con-sidered to be in agreement with the SM. The values of ˆ P for each of the event classes are also shown in table 12.For some of the classes, such as j − j − j − j , e − j − j − j − j and ν − j − j − j − j , no reliable ˆ P values can be calculateddue to the uncertainties of the SM predictions, so theyare not considered. The fact that small values of ˆ P can beobserved in some classes simply due to the large numberof analysed event classes is taken into account in the anal-ysis. The probability of a given value of ˆ P to be observedin the data is calculated by performing a large number ofMC experiments [228].For the P P T and M all distributions, in general goodagreement is observed between the ˆ P values observed inthe data and those obtained from the MC experiments.The most significant deviation from SM is observed in e + p collisions in the e − e class, with ˆ P = 0 . e ± p data sample. Thiscorresponds to five data events being observed in the in-variant mass region 110 < M all < 120 GeV, where the SMexpectation is 0 . ± . 04. This deviation has already beenobserved in the H1 analysis described in section 11. Theglobal probability to find at least one class in the e + p datasample with a smaller value of ˆ P is 12% as extracted fromMC experiments. It is however interesting to see that thisvery general analysis, performed with a completely dif-ferent method, finds as its most striking deviation fromthe SM an event class already identified as interesting ina dedicated analysis, focused on that particular topology.In the case of the cos θ ∗ lead and X lead distributions, no sig-nificant deviation with respect to the SM is observed. Thefull analysis is also performed at lower ( P T > 15 GeV)and higher ( P T > 40 GeV) transverse momenta, and agood overall agreement between data and the SM is alsofound in these regions.This general analysis of high transverse momentum,high-mass events, comprising different kind of particles inthe final states, demonstrates a very good understandingof the high P T phenomena recorded at the HERA col-lider. It also confirms a slight deviation already observedin a less general model-independent analysis, the searchfor multi-lepton events, quantifying the probability of ob-serving such a deviation as 12%. 16 Searches for excited fermions The existence of excited states of leptons and quarks is anatural consequence of models of composite fermions [233], and their discovery would provide convincing evidence ofa new scale of matter. The high energy electron-proton in-teractions at HERA provide a good environment in whichto search for excited states of first generation fermions.Several results on searches for excited fermions have beenpublished by both H1 and ZEUS using partial HERA datasets [234,235,236,237]. In this review we focus on the H1results [231,232,238] that use the full data HERA sample,corresponding to an integrated luminosity of 475 pb − ,which comprises 291 pb − of e + p collisions and 184 pb − of e − p collisions. The ZEUS analyses are in agreementwith that of H1 within their extracted larger limits.Leading order diagrams for gauge-mediated produc-tion and decay of excited fermions at HERA are shown infigure 49. The single production of an excited electron, e ∗ (excited neutrino, ν ∗ ), in ep collisions may result from the t -channel exchange of a photon or Z boson ( W boson).The single production of an excited quark, q ∗ , proceedspredominantly via gauge boson exchange between the in-coming electron and a quark from the proton . Due tothe helicity dependence of the weak interaction and thevalence quark composition and density distribution of theproton, the ν ∗ production cross section is predicted to bemuch larger for e − p collisions than for e + p and hence onlythe e − p data set is considered in that analysis.The production and decay of such particles is primarilystudied by H1 in gauge-mediated (GM) models [239,240,241], where the excited fermions are assumed to have spin1 / / F ∗ L and F ∗ R . Insuch models, only the right-handed component of the ex-cited fermion F ∗ R is allowed to couple to light fermions,to prevent the light leptons from radiatively acquiring alarge anomalous magnetic moment [242,243]. The result-ing effective Lagrangian [240,241] features a composite-ness scale Λ with units of energy and three form factors f , f ′ and f s associated to the electroweak and strong gaugegroups. For a given excited fermion mass, M f ∗ , and as-suming a numerical relation between f , f ′ and f s , theexcited fermion branching ratios are fixed and the pro-duction cross section depends only on f /Λ .As neither the excited electron or excited neutrino areexpected to have strong interactions, these searches areinsensitive to f s and the assumption is made that the cou-pling parameters f and f ′ are of comparable strength. Forexcited leptons the usual complementary coupling assign-ments f = + f ′ and f = − f ′ are considered, although inthe case of excited electrons f = − f ′ means that the e ∗ does not couple to the photon resulting in a much smallercross section, and as such only f = + f ′ is considered inthat analysis. Only γ , W and Z decays of the q ∗ are con-sidered, so the strong coupling parameter f s = 0 and the The exchange of excited quarks in the u -channel is alsopossible and relevant to the analysis for high q ∗ masses andlow values of the compositeness scale, Λ . In addition to GM interactions, e ∗ production and decayvia contact interactions is also investigated, where it is foundto mediate less than 5% of the decays and is therefore ne-glected [231]. Table 13. Summary of the observed and predicted event yieldsfor the various excited fermion decay channels in the H1 excitedfermion analyses. The uncertainty on the SM prediction in-cludes model and experimental systematic uncertainties addedin quadrature. Typical selection efficiencies for excited fermionmasses ranging from 120 to 260 GeV are also indicated. H1 Search for Excited Fermions at HERAExcited electrons ( e ± p collisions, L = 475 pb − ) Channel Data Total SM Signal Eff. [%] e ∗ → eγ (ela.) 42 48 ± e ∗ → eγ (inel.) 65 65 ± e ∗ → νW → νq ¯ q 129 133 ± 32 20 – 55 e ∗ → νW → νeνe ∗ → eZ → eνν . ± . e ∗ → eZ → eq ¯ q 286 277 ± 62 20 – 55 e ∗ → eZ → eee . ± . 06 60 e ∗ → eZ → eµµ . ± . 05 40 – 15 Excited neutrinos ( e − p collisions, L = 184 pb − ) Channel Data Total SM Signal Eff. [%] ν ∗ → νγ . ± . ν ∗ → eW → eq ¯ q 220 223 ± 47 40 – 65 ν ∗ → eW → eνµ . ± . 05 35 ν ∗ → eW → eνe . ± . ν ∗ → νZ → νq ¯ q 89 95 ± 21 25 – 55 ν ∗ → νZ → νee . ± . 05 45 Excited quarks ( e ± p collisions, L = 475 pb − ) Channel Data Total SM Signal Eff. [%] q ∗ → qγ 44 46 ± q ∗ → qW/Z → qq ¯ q 341 326 ± 78 5 – 55 q ∗ → qW → qeν . ± . q ∗ → qW → qµν . ± . q ∗ → qZ → qee . ± . 08 15 – 30 q ∗ → qZ → qµµ . ± . 11 15 – 30 assumption is made that the coupling parameters f and f ′ are of comparable strength, with the relation f = f ′ .Excited fermion events are simulated using the crosssection formulae for GM interactions [240,241] in the Com-pHEP program [244,245] for ν ∗ and q ∗ events, and usingCOMPOS [246] for e ∗ events. The proton parton densitiesare taken from the CTEQ5L [127] parametrisation andare evaluated at the scale of the four-momentum trans-fer squared, p Q , in the case of excited leptons and at √ ˆ s = √ sx for excited quarks. CompHEP includes the fulltransition matrix for the production and decay modes,while COMPOS uses the narrow width approximation forthe production of e ∗ , also taking into account the naturalwidth of the subsequent e ∗ decay [231].As can be seen from figure 49, a large number of fi-nal states are possible due to the decay of the W or Z produced in the excited fermion decay. Each of these final . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 55 e * ep g / Z e, ng / Z p, X g , Z, W n * ep W n , eX g , Z, W e, n ep g / Z/ W Xq * q g , W, Z (a) (b) (c) Fig. 49. Diagrams showing the production of excited electrons (a), excited neutrinos (b) and excited quarks (c) in ep collisionsat HERA, followed by decays into a SM fermion and a gauge boson. states, which are listed in table 13, are analysed separatelyusing dedicated event selections as detailed in the H1 pub-lications [232,231,238]. These selections are based on theidentification of high P T objects in the forward and centralregions of the detector such as electrons, muons, photonsand jets, as well as missing transverse momentum, sim-ilarly to what is done in the general search described insection 15. The event selections are optimised to maximisethe signal efficiency in each channel. The analysis of theexcited electron decay e ∗ → eγ is separated into inelas-tic and elastic parts using the total hadronic energy inthe event [231]. When multiple objects of the same typeare found in the event, the P T threshold of the second andthird objects are generally lower. Note that e ∗ → νW → νeν and e ∗ → νZ → eνν decays produce identical final statesand they are therefore examined together.The main source of SM background in each channeldepends on the final state. NC DIS is modelled usingRAPGAP and CC DIS is modelled using DJANGOH.Compton events are modelled using WABGEN and theGRAPE (EPVEC) program is used to model the lep-ton pair ( W production) contribution. Cuts to reduce SMbackground are applied similarly to what is done in theanalysis of events with isolated electrons or muons andmissing transverse momentum (see section 12.1), usingquantities such as the total E − P z of the event (equation13) and ξ e = E e cos ( θ e / Q .The event yields observed in all decay channels aresummarised in table 13 and are in agreement with the cor-responding SM expectations. QED Compton is the mainSM background in the e ∗ → eγ search, whereas NC (CC)DIS dominates the SM prediction in the e ∗ → eZ → eq ¯ q ( e ∗ → νW → νq ¯ q ) channel. In the search for excited neutri-nos, the SM predictions are dominated by NC DIS in the ν ∗ → eW → eq ¯ q search and by CC DIS for in the ν ∗ → νγ and ν ∗ → νZ → νq ¯ q searches. The SM contribution in the q ∗ → qγ and q ∗ → qW/Z → qq ¯ q channels is mainly due toNC DIS, whereas W production is the main contributionin the q ∗ → qW → qeν and q ∗ → qW → qµν channels. The in-variant mass distributions of some of the most populous excited fermion decay channels are displayed in figure 50,where the data distributions are seen to be in good agree-ment with the SM expectation.Since no evidence of excited fermions is observed, lim-its are derived at the 95% CL on the scale f /Λ as a func-tion of the excited fermion mass M f ∗ . For each excitedfermion type, the decay channels are combined and thelimits are obtained from the mass spectra using a modifiedfrequentist approach, which takes statistical and system-atic uncertainties into account [178]. For excited electronsa pure gauge-mediated interaction is assumed and for thestandard scenario where f = + f ′ and f /Λ = 1 /M e ∗ , ex-cited electrons with a mass lower than 272 GeV are ex-cluded at 95% CL. With the assumption f /Λ = 1 /M ν ∗ excited neutrinos with masses up to 213 GeV (196 GeV)are excluded for f = − f ′ ( f = + f ′ ). Finally, assuming f = + f ′ , no strong interactions f s = 0 and f /Λ = 1 /M q ∗ ,excited quarks with a mass lower than 259 GeV are ex-cluded at 95% CL.The H1 limits as a function of excited fermion massare shown in figure 51, where they are compared to lim-its from LEP (excited electrons: [247,248], excited neu-trinos: [249], excited quarks: [250]) and the Tevatron (ex-cited electrons: [251]). Analyses from the LHC by ATLASand CMS using their √ s = 8 TeV data have recentlypushed these limits into a new mass regime, where, underthe assumption f = f ′ = 1 and Λ = M f ∗ , excited elec-trons (quarks) are ruled out by ATLAS at the 95% CLfor masses lower than 2 . . 17 Searches for supersymmetry Supersymmetric (SUSY) extensions of the SM [254] intro-duce new elementary particles which are the superpart-ners of SM particles but differ in spin by half a unit [138,139]. The hypothesis of the existence of supersymmetricparticles has had a huge impact on both theory and ex-periments. A large variety of new states and a rich phe- e* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s e* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s All SMe* signalH1 Data ) -1 Search for e* at HERA (475 pb qq n fi W n fi * e H1 e* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s e* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s All SMe* signalH1 Data ) -1 Search for e* at HERA (475 pb qeq fi e Z fi * e H1 * Mass [GeV] n 50 100 150 200 250 300 350 E ve n t s * Mass [GeV] n 50 100 150 200 250 300 350 E ve n t s SMH1 Data ) -1 p, 184 pb - * at HERA (e n Search for qq n fi Z n fi * n H1 * Mass [GeV] n 50 100 150 200 250 300 350 E ve n t s * Mass [GeV] n 50 100 150 200 250 300 350 E ve n t s SMH1 Data ) -1 p, 184 pb - * at HERA (e n Search for qeq fi e W fi * n H1 q* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s q* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s SMq* signal M=240 GeVH1 Data ) -1 Search for q* at HERA (475 pb g q fi * q H1 q* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s q* Mass [GeV] 50 100 150 200 250 300 350 E ve n t s SMq* signal M=240 GeVH1 Data ) -1 Search for q* at HERA (475 pb qqq fi q W/Z fi * q H1 (a) (b)(c) (d)(e) (f ) Fig. 50. Invariant mass distribution of the excited fermion candidates in the e ∗ → νW → νq ¯ q (a), e ∗ → eZ → eq ¯ q (b), ν ∗ → νZ → νq ¯ q (c), ν ∗ → eW → eq ¯ q (d), q ∗ → qγ (e) and q ∗ → qW/Z → qq ¯ q (f) search channels. The points correspond to the observed data eventsand the histograms to the SM expectation after the final selections. The error bands on the SM prediction include modeluncertainties and experimental systematic uncertainties added in quadrature. The dashed line in the e ∗ and q ∗ figures representsthe reconstructed mass distribution of excited fermion events with M f ∗ = 240 GeV with an arbitrary normalisation.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 57 e* Mass [GeV] 100 120 140 160 180 200 220 240 260 280 300 ] - [ G e V L f / -4 -3 -2 -1 e* Mass [GeV] 100 120 140 160 180 200 220 240 260 280 300 ] - [ G e V L f / -4 -3 -2 -1 e* Mass [GeV] 100 120 140 160 180 200 220 240 260 280 300 ] - [ G e V L f / -4 -3 -2 -1 ) -1 Search for e* at HERA (475 pb f = + f’ H1 LEP (direct)LEP (indirect)H1) -1 Tevatron (202 pb = 1 / M L f / e* * Mass [GeV] n 100 120 140 160 180 200 220 240 260 280 300 320 ] - [ G e V L f / -3 -2 -1 * Mass [GeV] n 100 120 140 160 180 200 220 240 260 280 300 320 ] - [ G e V L f / -3 -2 -1 ) -1 p, 184 pb - * at HERA (e n Search for f = - f’ L3 H1 = 1 / M L f / * n H1 q* Mass [GeV] 100 150 200 250 300 350 ] - [ G e V L f / -4 -3 -2 -1 q* Mass [GeV] 100 150 200 250 300 350 ] - [ G e V L f / -4 -3 -2 -1 q* Mass [GeV] 100 150 200 250 300 350 ] - [ G e V L f / -4 -3 -2 -1 ) -1 Search for q* at HERA (475 pb = 0 s f = f’, f H1 DELPHI )=1 g q fi * BR(q H1 = 1 / M L f / q* Fig. 51. Exclusion limits at 95% CL on the ratio f/Λ as afunction of M f ∗ , for excited electrons (top), excited neutrinos(middle) and excited quarks (bottom) with the assumptionsgiven in the text and on the plot. Values of f/Λ above thecurves are excluded. Limits from the LEP and Tevatron col-liders are also indicated. nomenology of the Higgs sector was predicted, which cameinto focus during the running of the LEP and HERAexperiments, and is now thoroughly investigated at theLHC. The masses of the new particles, called sparticles ,are related to the symmetry breaking mechanism. A newquantum number R p = ( − B + L +2 S is defined, denoted R -parity, where B is the baryon number, L the leptonnumber and S the spin of a particle. For particles R p = 1and for their supersymmetric partners R p = − R -parity, only allowing the production of sparticlesin pairs. However, the most general supersymmetric the-ory that is renormalisable and gauge invariant with re-spect to the SM gauge group does not impose R -parityconservation [255,256], allowing couplings between twoSM fermions and a squark (˜ q ) or a slepton (˜ l ). This makesthe resonant, single production of sparticles via R -parityviolating ( R p / ) couplings possible, and the ep collisionsat HERA provide an ideal environment to search for suchnew particles. Searches have been performed at HERA forthree different R p / SUSY signatures with squarks, bosonicstop decays and light gravitinos, which are described inthe remainder of this section. R -parity violatingsupersymmetry In SUSY models with R -parity violation squarks can cou-ple to electrons and quarks via the R p / Yukawa couplings λ ′ jk , and then subsequently decay to a number of dif-ferent final state topologies which may be investigatedat HERA [257]. Searches for such final states have beenperformed by both H1 [258] and ZEUS [259] using theirHERA I data sets. In this review we focus on the most re-cent H1 analysis [260], which employs the full HERA dataset, corresponding to an integrated luminosity 183 pb − for e − p collisions and 255 pb − for e + p collisions.Feynman diagrams of the resonant production and de-cay of squarks at HERA via R p / couplings λ ′ jk are shownin figure 52. For simplicity, it is assumed here that one ofthe λ ′ jk couplings dominates over all the other trilinear R p / couplings. At the high values of Bjorken- x which arerequired to produce squarks of significant mass, the va-lence quarks are the dominant contribution to the protonPDFs. Therefore, e − p scattering gives sensitivity to thecouplings λ ′ k ( k = 1 , , 3) which dominate the produc-tion of ˜ d R -type squarks (i.e. the superpartners ˜ d R , ˜ s R and˜ b R of down-type quarks). Conversely, e + p scattering pro-vides sensitivity to the couplings λ ′ j ( j = 1 , , u L -type squarks (i.e. the su-perpartners ˜ u L , ˜ c L and ˜ t L of up-type quarks). Due to thelarger u -quark density in the proton at large x with respectto the d -quark density, larger production cross sections areexpected in e − p interactions for identical couplings andsquark masses.All sparticles are unstable in R p / SUSY and squarkscan decay directly via the Yukawa coupling λ ′ ijk into SMfermions. The ˜ d kR -type ( k = 1 , , 3) squarks can decay via e − u λ ′ k e − , ν e λ ′ k u, d ˜ d kR e + d λ ′ j e + λ ′ j d ˜ u jL Fig. 52. Feynman diagrams for the single resonant s-channelproduction of right-handed down-type squarks in e − p collisions(left) and left-handed up-type squarks in e + p collisions (right)with subsequent decays into SM particles via Yukawa couplings λ ′ k or λ ′ j , respectively. The right-handed down-type squarkscan decay either into e − u or ν e d , while the left-handed up-typesquarks decay into e + d only. the coupling λ ′ k either into e − u or ν e d , while the ˜ u jL -type ( j = 1 , , 3) squarks decay via the coupling λ ′ j into e + d only, as illustrated in figure 52. Squarks may also de-cay via R p conserving gauge couplings with subsequent R p / decay into SM particles via the Yukawa coupling λ ′ jk .In this case, the ˜ u L -type squarks can undergo a gauge de-cay into states involving a neutralino χ i ( i = 1 , , , χ + i ( i = 1 , 2) or a gluino ˜ g . However, ˜ d R -typesquarks mainly decay to χ i or ˜ g and decays into charginosare suppressed [257]. The resulting final states observed inthe detector from such cascade decays may contain mul-tiple leptons and jets as well as missing transverse mo-mentum. Such a cascade decay is illustrated in figure 53,where a ˜ d kR -type squark decays via a neutralino χ to aselectron-electron pair, and finally the selectron decays toSM fermions.Squark signal events are simulated using cross sectionsobtained in the narrow width approximation from theleading order amplitudes in leptoquark production [115],adjusted to NLO QCD using multiplicative correction fac-tors [261]. The parton densities are evaluated at the hardscale M q . A dedicated MC simulation is performed foreach of the signal topologies: for the direct lepton-quarkdecay channels eq and νq shown in figure 52, events aregenerated using LEGO [262], whereas for the gauge de-cays of squarks such as the one in figure 53, events aregenerated using SUSYGEN3 [263]. To allow for a modelindependent interpretation of the results, the squark de-cay processes are simulated for a wide range of sparticlemasses. Further details on the signal event simulation canbe found in the H1 publication [260].As explained above, the squark decays in this analy-sis can produce a large variety of final states, which areclassified [258] into event topologies, or channels, to beexamined. This classification relies on the number of iso-lated electrons, muons and hadronic jets in the final state,as well as on the presence of missing transverse momen-tum, indicating undetected neutrinos. A list of channelsinvestigated in this analysis can be found in table 14.The channels labelled eq and νq are the squark decaymodes that proceed directly via R p / couplings resultingin event topologies with an isolated electron or neutrinoand a single jet. The remaining channels result from the e − u λ ′ k dχ i , ˜ g ˜ d kR ¯ ud k χ ˜ e − e + λ ′ k Fig. 53. Feynman diagram for squark production and subse-quent cascade decay via gauginos, shown here for the case ofright-handed down-type squarks with subsequent R p / sleptondecay into SM fermions via Yukawa couplings λ ′ k . Decays ofdown-type squarks to charginos are suppressed, and the ˜ d R decays to either χ i (where i = 1 , , , 4) or ˜ g . gauge decays of the squark and are characterised by finalstates with more than one jet, (“multijet”, MJ ) with ad-ditional leptons. The eMJ and νMJ channels involve oneor two gauginos in the decay cascade. In the eMJ chan-nel, an electron or positron can be found in the final stateand a distinction may be made with respect to the inci-dent beam lepton charge and therefore, two discrete chan-nels with the “right” (same) sign lepton charge eMJ (RC)and “wrong” (opposite) sign lepton charge eMJ (WC) areformed. Channels with an electron or neutrino and a fur-ther charged lepton are denoted eeMJ , eµMJ and eνMJ , νµMJ , respectively, and necessarily involve two gauginos.Several SM processes may mimic the final states pro-duced by squark decays and therefore a standard selec-tion of MC generators is employed to compare the ob-served data events to the prediction from the SM. NCDIS events are simulated using RAPGAP and both directand resolved photoproduction of jets, as well as promptphoton production, are simulated using PYTHIA. Inclu-sive CC DIS events are simulated using DJANGOH. Theleading order MC prediction of processes with two or morehigh transverse momentum jets in NC DIS, CC DIS andphotoproduction is scaled by a factor of 1 . W boson production and lepton pair production aremodelled using EPVEC and GRAPE, respectively.Each of the final states listed in table 14 is analysedseparately using a dedicated event selection [260]. Theseselections are based on the identification of high P T elec-trons, muons, jets, as well as missing transverse momen-tum. The final state of a squark decaying into an electronand a high P T jet is identical to that from a NC DIS eventat high x and Q , and therefore the event selection in the eq channel closely resembles the selection described in sec-tion 8: An isolated electron is required in the event with P eT > 16 GeV in the region 5 ◦ < θ e < ◦ , and the eventmust be in the kinematic phase space Q e > , y e < . 9, 40 GeV < δ < 70 GeV and P miss T < 15 GeV. Thesquark mass is reconstructed as M e = √ x e s and a mass . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 59 Table 14. Summary of the observed and predicted event yields for the different decay channels considered in H1 search forsquarks in R p / SUSY, in the e − p and e + p data. The total uncertainties on the SM prediction is determined by adding the effectsof all model and experimental systematic uncertainties in quadrature. The range of signal efficiencies is also given for eachchannel, for squark masses ranging from 100 GeV to 290 GeV and gaugino masses ranging from 30 GeV up to the squark mass. H1 Search for Squarks in R p Violating Supersymmetry e − p collisions, L = 183 pb − e + p collisions, L = 255 pb − Channel Data Total SM Data Total SM Signal Eff. [%] eq ± 336 2946 2899 ± 302 30 – 40 νq ± 358 – – 50 – 60 eMJ (RC) 147 158 . ± . . ± . eMJ (WC) 0 1 . ± . . ± . eeMJ . ± . . ± . eµMJ . ± . 02 0 0 . ± . 03 5 – 15 eνMJ . ± . . ± . νMJ 204 235 . ± . . ± . νµMJ . ± . 02 0 0 . ± . 03 5 – 20 dependent y e cut is added to separate the NC backgroundfrom the signal [260].Squarks decaying into a neutrino and a high P T jetlead to the same signature as CC DIS events with highmissing transverse momentum, and so the event selectionin the νq channel is accordingly based on the analysisof such events. Events with a neutrino are selected byrequiring P miss T > 30 GeV and δ < 50 GeV and the phasespace is restricted to Q h > and y h < . eq channel, a y h cut dependent on thereconstructed mass M h = √ x h s is applied. The νq channelis not relevant for e + p data since the ˜ u L -type squarksproduced in e + p do not undergo this decay.Squarks decaying via neutralinos or charginos are ex-pected to have a higher multiplicity of jets and leptonsin the final state and their signatures correspond to fi-nal states detectable in higher order NC DIS processes.Squark decays with single or multiple neutrinos producedvia neutralino or chargino decays can result in final statessimilar to that of higher order CC DIS processes. The re-maining channels can therefore be divided into two groups,for which common preselections are employed: on the oneside electron-multijet and electron-lepton-multijet final statesand on the other side secondly neutrino-multijet and neutrino-muon-multijet final states. Further cuts are then applieddepending on the number and flavour of the leptons in theevent, as well as the charge, to separate the eMJ ( RC ) and eMJ ( W C ) channels. The event selections are optimised tomaximise the signal efficiency in each channel and are de-scribed in the publication [260]. For each selected eventa squark mass M rec = p E e ( P E i − E e ) is calculated,where the sum includes the energies of the reconstructedelectrons, muons and jets with P jet T > νM J and νµM J channel.The number of events observed in the data in eachchannel is shown in table 14 compared to the SM pre-diction, where a good agreement is observed in all chan- nels. Of the gauge decays, only the eMJ ( RC ) and νMJ channels have significant event yields. The invariant massdistributions of some of the most populous squark decaychannels are displayed in figure 54, where the data arein good agreement with the SM expectation. As no sig-nificant deviation from the SM is observed, all analysischannels are combined to set constraints on various su-persymmetric models as described in the following. Massdependent exclusion limits are obtained [260] on the pro-duction of squarks parameterised by the strength of the R p / couplings λ ′ j and λ ′ k .For the interpretation of the results a version of theMinimal Supersymmetric Standard Model (MSSM) is con-sidered where the masses of the neutralinos, charginos andgluinos are determined via the usual SUSY parameters:the Higgs mass term µ , which mixes the Higgs super-fields; the SUSY soft-breaking mass parameter M ; andthe ratio of the vacuum expectation values of the twoneutral scalar Higgs fields tan β [138,139]. The parame-ters are defined at the electroweak scale and the lightestsupersymmetric particle (LSP) is the neutralino χ . Slep-ton masses M ˜ l are fixed at 90 GeV. Exclusion limits arecalculated for two scenarios with tan β = 2: a photino-likeneutralino ( µ = − 200 GeV, M = 80 GeV) and a zino-like neutralino ( µ = 200 GeV, M = 150 GeV). A com-bination of both scenarios is also achieved by performinga full parameter scan, where the parameters M and µ are varied in the range 70 GeV < M < 350 GeV and − 300 GeV < µ < 300 GeV for tan β = 6. As an example,exclusion limits at 95% CL from the parameter scan forthe λ ′ coupling as a function of squark mass using thefull H1 e + p data are shown in figure 55 (left), comparedto the previous H1 limit [258] and an indirect limit fromatomic parity violation [265]. In the parameter space con-sidered in the analysis, Yukawa couplings of electromag-netic strength, λ ′ j or λ ′ k = √ πα em = 0 . 3, are excludedup to masses of 275 GeV at 95% CL for up-type squarksand up to masses of 290 GeV for down-type squarks. [GeV] e M E ve n t s [GeV] e M E ve n t s All SM=150 GeV Squark M (arb. norm.) H1 Data ) -1 p, 183 pb - SUSY at HERA (e p RSearch for Squarks in eq Channel [GeV] h M E ve n t s [GeV] h M E ve n t s All SM=150 GeV Squark M (arb. norm.) H1 Data ) -1 p, 183 pb - SUSY at HERA (e p RSearch for Squarks in q Channel n [GeV] n rec, M E ve n t s [GeV] n rec, M E ve n t s All SM=150 GeV Squark M (arb. norm.) H1 Data ) -1 p, 183 pb - SUSY at HERA (e p RSearch for Squarks in MJ Channel n [GeV] e M E ve n t s [GeV] e M E ve n t s All SM=150 GeV Squark M (arb. norm.) H1 Data ) -1 p, 255 pb + SUSY at HERA (e p RSearch for Squarks in eq Channel [GeV] rec M E ve n t s [GeV] rec M E ve n t s All SM=150 GeV Squark M (arb. norm.) H1 Data ) -1 p, 255 pb + SUSY at HERA (e p RSearch for Squarks in eMJ Channel (RC) [GeV] n rec, M E ve n t s [GeV] n rec, M E ve n t s All SM=150 GeV Squark M (arb. norm.) H1 Data ) -1 p, 255 pb + SUSY at HERA (e p RSearch for Squarks in MJ Channel n Fig. 54. Selected reconstructed invariant mass distributions from the H1 search for squarks in the e − p data (top row) and e + p data (bottom row). The data (points) are compared to SM MC predictions. The error band represents all model andexperimental systematic uncertainties on the SM prediction (solid histogram) added in quadrature. The dashed histogramindicates the signal from a squark with M ˜ q = 150 GeV with arbitrary normalisation. [GeV] squark M 100 150 200 250 -2 -1 ’ l (APV) ’ l Unconstrained MSSM - H . pb H1 E x c l u d e d a t % C L E x c l u d e d i n p a r t o f p a r a m e t e r s p a c e -1 p 255pb + e = 6 b tan < 300 GeV m -300 < < 350 GeV 70 < M = 90 GeV slepton M > 30 GeV LSP M [GeV] m [ G e V ] / m ) = G e V u ~ m ( ) = G e V t ~ m ( DØ limit (j=1,2) =0 <0, A m =6, b =0.3, tan ’ l mSUGRA excluded for j=1,2excluded for j=3 b < M LSP M H1 -1 p 255pb + e at 95% CL not allowed Fig. 55. Left: Exclusion limits at the 95% CL on λ ′ as a function of the squark mass from a scan of the MSSM parameterspace as indicated in the figure. The dark filled region indicates values of the coupling λ ′ excluded in all investigated scenarioswhereas the light filled region is excluded only in part of the parameter space. An indirect limit from atomic parity violation(APV) is also shown, as well as the the limit from the previous H1 analysis. Right: Exclusion limits at the 95% CL in the m , m / plane in the mSUGRA parameter space indicated in the figure for j = 1 , j = 3 (light filledregion). Curves of constant squark mass are illustrated for m (˜ u ) = 275 GeV and m (˜ t ) = 270 GeV. A constraint obtained by theDØ experiment at the Tevatron is also indicated. The dark filled region labelled as “not allowed” indicates where no radiativeelectroweak symmetry breaking solution is possible or where the LSP is a sfermion.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 61 Fig. 56. Lowest order s -channel diagram for R p / stop produc-tion at HERA followed by (left) the bosonic decay of the stopand (right) the R p / decay of the stop. Constraints are also obtained on the Minimal Super-gravity Model (mSUGRA) [266,267,268,269], which is amodel that assumes gauge coupling unification and radia-tive electroweak symmetry breaking with the choice of 5parameters: the common mass of scalar sparticles m ; thecommon mass of fermionic sparticles m / ; the commontrilinear coupling A ; the sign of the Higgs mixing param-eter µ and tan β as defined above. The masses of squarks,sleptons and gauginos as well as the branching ratios in theanalysis channels are determined by the parameter set forgiven values of the couplings λ ′ k and λ ′ j . A enters onlymarginally in the interpretation and is set to zero. The pa-rameter µ is taken with negative sign. Figure 55 (right)shows example exclusion limits at 95% in the m , m / plane assuming λ ′ j = 0 . β = 6, obtained usingthe full H1 e + p data. The excluded region typically cov-ers masses of m (˜ u ) = 275 GeV and m (˜ t ) = 270 GeV, asindicated in the figures. A constraint from the DØ experi-ment [270] at the Tevatron using di-electron events is alsoindicated, where the region excluded by H1 is considerablylarger. R -parityviolating supersymmetry In most SUSY models the third generation squarks, namelystop (˜ t ) and sbottom (˜ b ), are the lightest squarks. If thesbottom mass is smaller than the stop mass, M ˜ b < M ˜ t ,a stop quark resonantly produced in eq -fusion at HERAvia the R p / coupling λ ′ may then decay bosonically, pro-viding a SUSY scenario and final states complementaryto the R p / squark production described in section 17.1. Inthis scenario, the only possible decay modes are ˜ t → ˜ bW with W → f ¯ f ′ and R p / sbottom decay into SM particles,˜ b → ¯ ν e d . In addition, the R p / decay of the stop into SMfermions, ˜ t → e + d , a more general version of which is de-scribed in the previous section, also contributes. Feynmandiagrams of these two processes are presented in figure 56.The diagram where the W decays leptonically is particu-larly interesting, as it results in a final state similar to thatin the analysis of events with isolated leptons and missingtransverse momentum presented in section 12, which hasprovided hints of physics beyond the SM.The analysis presented below uses data collected withthe H1 detector in e + p scattering during the HERA I pe- Table 15. Summary of the observed and predicted event yieldsfor the various stop decay channels in the H1 analysis. Theuncertainty on the SM predictions includes model and experi-mental systematic uncertainties added in quadrature. For the jeP miss T and jµP miss T channels the W production component ofthe SM is given in the last column. H1 Search for Bosonic Stop Decaysin R p Violating Supersymmetry e ± p collisions, L = 106 pb − Channel Data Total SM W production jeP miss T . ± . 92 2 . ± . jµP miss T . ± . 47 1 . ± . jjjP miss T . ± . 74 – ed ± 131 – riod, corresponding to an integrated luminosity of 106 pb − [271]. Simulation of SUSY signal events is done using SUSY-GEN3 [263], which relies on the LO amplitudes for ed → ˜ bW [272]. The parton densities are taken from the CTEQ5Lparameterisation and evaluated at the scale of the stopmass, M ˜ t . The various SM background contributions areestimated using the same generators as described in sec-tion 17.1.The bosonic stop decay leads to three different finalstate topologies, as illustrated in figure 56 (left). If the W decays into leptons, the signature is a jet, a lepton(electron or muon) and missing transverse momentum( jeP miss T channel and jµP miss T channels). The selection cri-teria in these channels closely resembles those used in theH1 search for events with isolated leptons and missingtransverse momentum based on the HERA I data [192],with the additional requirement of a jet with P jet T > 10 GeVwithin the angular range 7 ◦ < θ jet < ◦ . If the W de-cays into hadrons the event signature is the presence ofthree jets and missing transverse momentum ( jjjP miss T channel). Events with three jets with P jet1 T > 20 GeV, P jet2 T > 15 GeV and P jet3 T > 10 GeV are selected, eachwith polar angle 7 ◦ < θ jet < ◦ . A total missing trans-verse momentum P miss T > 25 GeV is also required. In theanalysis of both the leptonic and hadronic W decay chan-nels a cut on the inelasticity y is employed to separate theSM background from the stop signal [271]. For stop andsbottom masses M ˜ t ≈ M ˜ b + M W , the R p / decay ˜ t → ed , asillustrated in figure 56 (right), becomes dominant. Theseevents are selected using criteria similar, though not iden-tical, to that presented in section 17.1.The number of events observed in the data in eachchannel is shown in table 15, compared to the SM predic-tion. The dominant contribution to the SM expectation inthe jeP miss T and jµP miss T channels arises from the produc-tion of real W bosons, which is also given in table 15. Themain SM contribution in the jjjP miss T ( ed ) channel is dueto CC (NC) DIS events. A good agreement is observed in The W decay into ν τ τ , where τ → hadrons + ν , is notinvestigated.2 D. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA all channels except in the jµP miss T channel, where 8 eventsare observed in the data compared to a SM expectationof 2 . ± . M ˜ t decayingbosonically, the observed event yields are used to deter-mine the allowed range for a stop production cross section σ ˜ t , and to examine the compatibility of the different decaymodes. The calculation takes into account the signal effi-ciency, the ˜ t and W branching ratios BR ˜ t → ˜ bW · BR W → f ¯ f ′ and the relative integrated luminosities of the HERA Idata sets taken at different centre of mass energies [271].The bands in figure 57 (left) represent the allowed crosssection regions σ ˜ t ± ∆σ ˜ t for all bosonic decay channels.It can be seen that the stop interpretation of the excessseen in the jµP miss T channel is not supported by the otherdecay modes.As no stop signal is observed, exclusion limits on thestop production cross section are derived at the 95% CLin the framework of the MSSM [138,139] using a modifiedfrequentist approach based on likelihood ratios [178]. Ascan of the SUSY parameter space is performed, to sys-tematically investigate the dependence of the sensitivityon the MSSM parameters. The SUSY soft-breaking massparameter M is set to 1000 GeV and the Higgs mass termis restricted to 400 < µ < θ ˜ t and θ ˜ b are allowed to vary between 0 . . M ˜ t , λ ′ ) plane is shownin figure 57 (right), for tan β = 10 and M ˜ b = 100 GeV.For M ˜ t = 200 GeV, couplings λ ′ ∼ > . 03 are ruled outand for M ˜ t = 275 GeV the allowed domain is λ ′ ∼ < . In Gauge Mediated Supersymmetry Breaking (GMSB) SUSYmodels, new “messenger” fields are introduced which cou-ple to the source of supersymmetry breaking. The break-ing is then transmitted to the SM fields and their super-partners by gauge interactions [273]. The gravitino, ˜ G ,is the lightest supersymmetric particle (LSP) and can beas light as 10 − eV. The next-to-lightest supersymmetricparticle (NLSP) is generally either the lightest neutralino˜ χ or a slepton ˜ ℓ , which decays to the stable gravitinovia ˜ χ → γ ˜ G or ˜ ℓ → ℓ ˜ G . At HERA, the presence ofthe R p / couplings λ ′ j and λ ′ k could lead to neutralinoproduction in e + p and e − p collisions, respectively, via t -channel selectron exchange, as illustrated in figure 58. Thehard scattering process at large Bjorken- x is dominatedby the valence quarks in the proton, and therefore if theinitial state lepton is a positron (electron) the scatter in-volves a down (up) quark from the proton, as shown inthe left (right) part of figure 58. For a given R p / coupling,the ˜ χ production cross section for an initial state electronis roughly a factor of two larger than that for an initialpositron, reflecting the different parton densities for va-lence up and down quarks in the proton.A search for R p / resonant single neutralino productionvia t -channel selectron exchange, e ± q → ˜ χ q ′ is performed Fig. 58. Diagrams for neutralino production via R p / selectronexchange in e + p (left) and e − p (right) scattering, with subse-quent neutralino decay into a gravitino and a photon. by H1 using their HERA I data set taken at √ s = 319 GeV,corresponding to an integrated luminosity of 64 . − for e + p collisions and 13 . − for e − p collisions [274].It is assumed that the ˜ χ is the NLSP and that the de-cay ˜ χ → γ ˜ G occurs with an unobservably small life-time and dominates over R p / neutralino decays. It is alsoassumed that one of the couplings λ ′ j ( j = 1 , 2) or λ ′ k ( k = 1 , , 3) dominates . The process considered inthis analysis is independent of the squark sector, and sois a complementary approach to those presented in sec-tions 17.1 and 17.2.The GMSB model [275] examined in the analysis ischaracterised by six new parameters in addition to those ofthe SM: the parameter Λ , which sets the overall mass scalefor the SUSY particles; the mass of the messenger parti-cles M ; the number f sets of messenger particles, N ; theintrinsic SUSY breaking scale √ F , which also determinesthe ˜ G mass according to m ˜ G ≃ . · F/ (100 TeV) eV;the ratio of the Higgs vacuum expectation values tan β ;and the sign of the Higgs sector mixing parameter µ . Thesignal topology is simulated using the SUSYGEN3 gener-ator [263].The parton densities are evaluated at the scaleof the Mandelstam variable − t .The final state resulting from the process e ± q → ˜ χ q ′ → γ ˜ Gq ′ contains a photon, a jet originating from the scat-tered quark and missing transverse momentum due tothe escaping gravitino. The SM background almost ex-clusively arises from radiative CC DIS, which features ajet, a photon and a neutrino in the final state and is mod-elled using DJANGOH. Smaller contributions from NCDIS, photoproduction and W production are estimatedusing the DJANGOH, PYTHIA and EPVEC generators,respectively.Events are selected with large missing transverse mo-mentum determined from the calorimetric energy deposits, P calo T > 25 GeV. The events are also required to containat least one hadronic jet in the range 10 ◦ < θ jet < ◦ and an identified photon in the LAr, both with transversemomenta greater than 5 GeV. Photons are identified us-ing a shower shape analysis of energy deposits in the LArcalorimeter and for θ γ > ◦ an electromagnetic clusteris only accepted as a photon candidate if it is not asso-ciated with a charged track in the central tracking sys- The coupling λ ′ is not studied in this analysis becausethe production of a top quark together with a neutralino issuppressed due to the high top quark mass.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 63 Fig. 57. Left: Bands representing the allowed stop cross section regions σ ˜ t ± ∆σ ˜ t as a function of the stop mass as obtainedfrom the analysis of each bosonic stop decay channel. Right: Exclusion limits at the 95% CL on the R p / coupling λ ′ as afunction of the stop mass for M ˜ b = 100 GeV. The limits are derived from a scan of the MSSM parameter space described inthe text. The two full curves indicate the regions excluded in all (dark) or part (light) of the parameter space investigated. tem. In addition, the photon must be isolated from anyreconstructed jet with P jet T > . ± . 5, predominantly from radia-tive CC DIS.Based on a study of this preselection, additional cutsare then applied to reduce the SM background, increasingthe minimum photon transverse momentum P γT to 15 GeVand requiring that the sum of the E − P z in the event islarger than 15 GeV [274]. In the final selection no candi-date event is found in the e + p data, compared to a SMprediction of 1 . ± . 2. In the e − p data sample, 1 candidateevent is observed compared to a SM prediction of 1 . ± . W and Z bosons where the final state electron ismisidentified as a photon.Assuming that the massless gravitino is the only non-interacting particle in the event, the gravitino kinematicsare reconstructed by exploiting the conservation of trans-verse momentum and the constraint ( E − p z ) + ( E ˜ G − p z, ˜ G ) = 2 E e . The four-vector of this particle is then addedto that of the photon to reconstruct the invariant mass m of the decaying neutralino. The data and the SM expecta-tion for this distribution are shown in figure 59. From thesimulation of the SUSY signal, also shown in figure 59, themass resolution is determined to be around 10 GeV. Thecandidate event has a reconstructed invariant neutralinomass of 36 ± R p / coupling λ ′ jk for fixed valuesof the SUSY parameters tan β , N and (sign) µ . As an ex- m (GeV) e v e n t s H1 ● data SM MCGMSB: m( c ~1 )= 125 GeVm( c ~0 )= 125 GeV(arb. norm.) Fig. 59. Distribution of the invariant mass of the photon can-didate and the reconstructed missing particle in the H1 searchfor light gravitinos in events with photons. The data (points)are compared with the SM prediction (solid histogram). Thesignal expected for a neutralino with a mass of 125 GeV isshown with arbitrary normalisation (dashed histogram). ample, figure 60 displays excluded regions in the m ( ˜ χ ), m (˜ e L )– m ( ˜ χ ) plane derived from the H1 e + p (left) and e − p (right) data for various values of λ ′ jk in the param-eter space indicated in the figure. It can be seen that forsmall mass differences between the neutralino and selec-tron, neutralino masses up to 112 GeV are ruled out at95% CL for R p / coupling λ ′ jk = 1. Furthermore, for neu-tralino masses close to 55 GeV, λ ′ j Yukawa couplings ofelectromagnetic strength are excluded. These are the only H1 e + p m( c ~1 ) (GeV) m ( e ~ L ) - m ( c ~ ) ( G e V ) m( c ~0 ) (GeV) m ( e ~ L ) - m ( c ~ ) ( G e V ) l , l =0.3 l , l =0.5 l , l =0.75 l , l =1.0 tan b =2, m < 0, N=1, M/ L =2 GMSB, j=1,2 H1 e - p m( c ~1 ) (GeV) m ( e ~ L ) - m ( c ~ ) ( G e V ) m( c ~0 ) (GeV) m ( e ~ L ) - m ( c ~ ) ( G e V ) l , l =0.5 l , l =0.75 l , l =1.0 tan b =2, m < 0, N=1, M/ L =2 GMSB, k=1,2,3 Fig. 60. Exclusion limits at the 95% CL in the m ( ˜ χ ), m (˜ e L )– m ( ˜ χ ) plane from the H1 search for light gravitinos in eventswith photons, for various values of the coupling λ ′ j ( j = 1 , 2) (left) and λ ′ k ( k = 1 , , 3) (right) in the GMSB SUSY parameterspace indicated on the plot. constraints from HERA on SUSY models independent ofthe squark sector. 18 A direct search for stable magneticmonopoles The existence of magnetic monopoles is one of the openissues in modern physics and their discovery would allowa better explanation of some well established aspects ofnature. The quantisation of the electric charge was ex-plained by Dirac [276] by postulating the existence of par-ticles with a magnetic charge, which shall be a multiple ofthe Dirac charge, g D , given by: g D e ~ c = 12 ⇒ g D e = 12 α e ≈ . , (49)where e is the elementary electric charge and α e is thefine structure constant. With the presence of a magneticmonopole, considering the duality of Maxwell’s equationsthe (very large) magnetic coupling can be expressed as: α m = g D ~ c = 14 α e . (50)The large value of this coupling constant prevents the useof perturbative field theory for a reliable calculation of theexpected rates of processes involving magnetic monopoles.It also implies that the energy released by ionisation by amagnetic monopole is much larger than for minimum ion-ising electrically charged particles, as a magnetic monopole will effectively behave, in terms of ionisation energy loss,as a highly charged stable particle, with a charge ≈ . GeV, there are some GrandUnified scenarios [284,285,286] in which mass values ofthe order of 10 GeV are allowed. Other approaches [287,288,289,290,291] also exist, in which a light monopole isallowed, and postulates on values of the classical radius ofa monopole lead to estimates of a monopole mass of theorder of tens of GeV [292].One of the techniques that can be used in the directsearch for magnetic monopoles is the search for the in-duction of a persistent current within a superconductingloop [293]. This approach is used by the H1 Collabora-tion in a direct search for magnetic monopoles [294], ex-ploiting the idea that heavily ionising magnetic monopolesmay stop in the beam pipe surrounding the interaction re-gion of the H1 detector. Such monopoles, if stable, wouldthen remain permanently trapped in the beam pipe, asthe binding energy between the monopoles and the alu-minium of the beam pipe is expected to be large, of theorder of hundreds of keV [295]. The magnetic field of thetrapped monopoles would induce a persistent current on asuperconducting coil, after their complete passage throughthe coil. In contrast, a passage through the coil of mate-rial with no trapped monopole would induce no current, . M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 65 Fig. 61. Method for the analysis of the H1 beampipe strips in the direct search for magnetic monopoles. The conveyor belttravelled in steps of typically 5 cm until the sample traversed completely the superconducting coil. At each step the conveyorbelt stopped for 1 sec before the current in the superconducting coil (magnetometer current) was read to avoid the effects ofeddy currents. The time for each step was typically 3 secs. as the permanent dipole moment in the material wouldcancel in the passage of the material through the coil.The aluminium beam pipe used in the search was inplace in the H1 delector 1995-1997, during which time itwas exposed to a luminosity of 62 pb − . The beam pipehad a diameter of 9 cm and thickness 1 . − . < z < . . < z < . − . < z < +2 . ∼ − . < z < . ∼ 18 mm, two of which were further divided into32 short segments varying in length from 1 to 10 cm. Thedownstream section (0 . < z < . ∼ 32 mm.All the samples were passed along the axis of the 2GEnterprises type 760 magnetometer [296] hosted at theSouthampton Oceanography Centre, in the United King-dom. After each sample was passed through the coil, thecurrent in the superconducting loop was measured, andthe current induced by the sample estimated as the dif-ference between the currents measured before and afterits passage through the coil. This procedure was repeatedmany times for each sample in order to estimate the re-producibility of the results. The sensitivity of the SQUID magnetometer to a mag-netic monopole was assessed using a long, thin solenoid, asthe magnetic field at the end of a long solenoid is similar tothat produced by a magnetic monopole. A long solenoidcan be considered as composed by two magnetic ”pseu-dopoles”, each of strength g = N · I · S/g D , where N is thenumber of turns per unit length, I the current and S thesection area of the solenoid. The current and radius of thesolenoid can be chosen to mimic the pole strength. Thecalibration was performed by passing a solenoid with dif-ferent current through the magnetometer, measuring theinduced current and subtracting the current induced atzero solenoid current. The current in the magnetometerfollowing the passage of one end of the solenoid was foundto increase linearly with the current in the solenoid.To simulate the magnetometer behaviour at the pas-sage of a magnetic monopole, the long solenoid was at-tached to a beam pipe section and the two passed jointlythrough the coil, allowing the passage of only one end ofthe solenoid through the magnetometer. The results areshown in figure 62, where the passage of the beam pipestrip alone is compared to the passage of the same strip at-tached to a solenoid with a ”pseudopole” strength of 2 . g D and − . g D . A large structure is visible in the centre ofthe figure, and this is due to the magnetic field of thepermanent magnetic dipole moments in the aluminium.A persistent current is induced when the pseudopoles arepresent; when they are absent, the large permanent dipolemoment of the aluminium does not prevent the current togo back to zero. In the inset of the figure, the currentmeasured as the strips leaves the magnetometer coil is shown. The values are equal and opposite, and equal tothat measured with the calibration solenoid alone. Thisdemonstrates the sensitivity of the apparatus to a mag-netic monopole trapped in the beam pipe strip.The sample first analysed corresponds to the 15 stripscut from the region − . < z < . . g D were in-duced. To mitigate these effects, the strips were demagne-tised in a low frequency magnetic field of initial intensityof 0 . . g D had been trapped in the beam pipe strips, whichmade up 93% of the total beam pipe, the rest being lostin the cutting procedure. Figure 63 shows a summary ofthe measurements performed on the whole sample.As no magnetic monopole was observed, upper limitson the production cross section are determined. The crosssection extraction needs the evaluation of the detector ac-ceptance, therefore a model for the production is neededand two differnet models are considered. In each model,a monopole-antimonopole ( M ¯ M ) pair was assumed to beproduced in a photon-photon interaction. In the first model(model A), elastic production of a spin-0 monopole pairin the process e + p → e + M ¯ M p , through the interactionof a photon from the electron and a photon from theproton, was assumed. In the second model (model B),spin-1/2 monopoles were produced in the inelastic process e + p → e + M ¯ M X , through photon-photon fusion with aphoton from the electron and one from a quark in the pro-ton. Events for model A were generated using the programCompHEP [216], while a dedicated program was used formodel B [294]. The generated final state particles weretracked in the H1 interaction region of the beam pipe,and if the range of the monopole in aluminium was lowerthan the thickness of the beam pipe, the monopole wasassumed to stop there. The cross section upper limit wasderived considering that no observation translates into a95% CL upper limit of 3 monopoles pair events produced.The upper limits on the cross sections for model A andB, and for monopoles of different charges are shown infigure 64. H1 +/-2.3 g D No coil z m (m) | C a li b r a t e d M a gn e t o m e t e r C u rr e n t ( g D ) | -1 z m (m) C u rr e n t( g D ) -2.3 g D +2.3 g D -2-10123 0.8 1 1.2 Fig. 62. The absolute value of the calibrated magnetometercurrent versus step position ( z m ) for a strip from the cen-tral beam pipe region ( − . < z < . . g D ( − . g D ). The inset shows the signed mea-surements of the calibrated magnetometer currents versus thestep position for z m > . ± . g D are shownby the arrow on the logarithmic plot and by the numbers inthe margin on the inset linear plot. Sample number P e r s i s t e n t c u rr e n t ( un i t s o f g D ) Downstream pipeDownstream pipe reversedCentral pipeCentral pipe reversed H1 -0.8-0.6-0.4-0.200.20.40.60.8 0 2 4 6 8 10 12 14 16 18 Fig. 63. The persistent currents in the long beam pipe stripsin units of g D , after their passage through the magnetometerversus sample number, measured after the samples had beendemagnetised (see text). Samples 1-16 consist of several longstrips (usually two or three) from the downstream beam pipebundled together. Sample 17 consists of the thirteen long stripsof the central beam pipe bundled together.. M. South, M. Turcato: Review of Searches for Rare Processes and BSM Physics at HERA 67 g D D D D Model A - Efficiencies from elasticspin 0 Boson production H1 Monopole Mass (GeV) C r o ss sec t i on upp e r li m i t ( pb ) -2 -1 g D D D D Model B - Efficiencies from inelasticspin 1/2 Fermion production H1 Monopole Mass (GeV) C r o ss sec t i on upp e r li m i t ( pb ) -2 -1 Fig. 64. Upper limits on the cross section for the production of a monopole-antimonopole pair, determined within the contextof model A (left) and model B (right), for monopole-antimonopole pair production in e + p collisions as a function of monopolemass for monopoles of strength g D , 2 g D , 3 g D and 6 g D or more. The direct search for magnetic monopoles has beenperformed with different techniques in various fields ofphysics. A number of papers on magnetic monopole searcheshave been published, in cosmic rays [297,298,299,300,301,302], in matter [303,304,305,306] and at colliders [307,308,309,310,311,312,313,314]. At colliders, although a uni-versal production mechanism can be postulated, the com-parison of the cross section upper limit obtained in the H1analysis with those of other colliders in different types ofcollisions ( e + e − , p ¯ p , pp ) is difficult. Recently, the ATLAScollaboration has published [315] a search for magneticmonopoles and stable particles with high electric charge,setting a model-independent upper limit on the produc-tion cross section of 0 . . g D ≤ | g | ≤ . g D and electric charge inthe range between 20 and 60 times the elementary charge,with masses between 200 and 2500 GeV. This result isvalid in well-defined fiducial regions of high and uniformevent selection efficiency. The H1 result described aboveremains the only one obtained in e + p collisions at highenergy. 19 Summary and outlook The HERA ep collider at DESY is a unique machine,which has brought a unrivalled insight into the structureof the proton via the precision analysis of deep inelasticscattering over many orders of magnitude in Bjorken x andnegative four-momentum transfer squared Q . The dataharvest collected by the H1 and ZEUS experiments hasalso provided the opportunity to search for rare processes and physics beyond the Standard Model. Combining thedata of both experiments, resulting in a HERA datasetwith an integrated luminosity of 1 fb − , has resulted inan increased sensitivity to such processes and allowed athorough search of the high P T kinematic region.Cross sections of the rare production of W and Z bosons are measured, as well as the production of high P T lepton pairs via two photon exchange. These analyseshave also provided tantalising glimpses at physics beyondthe Standard Model, and although no significant signalexcess is observed in the complete dataset, a number ofinteresting events remain in high P T regions of the H1analyses of their e + p data. The single and pair productionof tau leptons is also observed at HERA, utilising bothleptonic and hadronic decays of the tau.The initial ep state at HERA provides a complimen-tary environment to searches using the e + e − collisions atLEP and the p ¯ p collisions at the Tevatron. In particular,HERA is an ideal place to search for the single, resonantproduction of hypothetical particles such as leptoquarks,both within the kinematic limit given by the available cen-tre of mass energy, and beyond using contact interactionmodels. Model dependent searches, such as for excitedfermions and supersymmetry are also performed, as wellas a general search at high P T , which confirms the resultsfound in dedicated analyses.No significant deviation from the Standard Model isobserved in any of the search analyses performed by H1and ZEUS and, where appropriate, mass dependent modelexclusion limits are derived. Whereas the limits from HERAare competitive and complementary to the analyses fromcolliders of the same generation, the advent of the LHC has meant that many have been superseded at the timeof writing. 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