The Physics Programme Of The MoEDAL Experiment At The LHC
B. Acharya, J. Alexandre, J. Bernabéu, M. Campbell, S. Cecchini, J. Chwastowski, M. De Montigny, D. Derendarz, A. De Roeck, J. R. Ellis, M. Fairbairn, D. Felea, M. Frank, D. Frekers, C. Garcia, G. Giacomelli, M. Giorgini, D. HaŞegan, T. Hott, J. Jakůbek, A. Katre, D-W Kim, M.G.L. King, K. Kinoshita, D. Lacarrere, S. C. Lee, C. Leroy, A. Margiotta, N. Mauri, N. E. Mavromatos, P. Mermod, V. A. Mitsou, R. Orava, L. Pasqualini, L. Patrizii, G. E. Păvălaş, J. L. Pinfold, M. Platkevč, V. Popa, M. Pozzato, S. Pospisil, A. Rajantie, Z. Sahnoun, M. Sakellariadou, S. Sarkar, G. Semenoff, G. Sirri, K. Sliwa, R. Soluk, M. Spurio, Y.N. Srivastava, R. Staszewski, J. Swain, M. Tenti, V. Togo, M. Trzebinski, J. A. Tuszyński, V. Vento, O. Vives, Z. Vykydal, A. Widom, J. H. Yoon
TTHE PHYSICS PROGRAMME OF THE MoEDAL EXPERIMENTAT THE LHC
B. ACHARYA , , J. ALEXANDRE , J. BERNAB´EU , M. CAMPBELL , S. CECCHINI ,J. CHWASTOWSKI , M. DE MONTIGNY , D. DERENDARZ , A. DE ROECK ,J. R. ELLIS , , M. FAIRBAIRN , D. FELEA , M. FRANK , D. FREKERS , C. GARCIA ,G. GIACOMELLI , a † , J. JAK˚UBEK , A. KATRE , D-W KIM , M.G.L. KING ,K. KINOSHITA , D. LACARRERE , S. C. LEE , C. LEROY , A. MARGIOTTA , N.MAURI , a , N. E. MAVROMATOS , , P. MERMOD , V. A. MITSOU , R. ORAVA , L.PASQUALINI , a , L. PATRIZII , G. E. P ˘AV ˘ALAS¸ , J. L. PINFOLD ∗ , M. PLATKEVIˇC ,V. POPA , M. POZZATO , S. POSPISIL , A. RAJANTIE , Z. SAHNOUN , b ,M. SAKELLARIADOU , S. SARKAR , G. SEMENOFF , G. SIRRI , K. SLIWA ,R. SOLUK , M. SPURIO , a , Y.N. SRIVASTAVA , R. STASZEWSKI , J. SWAIN , M.TENTI , a , V. TOGO , M. TRZEBINSKI , J. A. TUSZY ´NSKI , V. VENTO , O. VIVES ,Z. VYKYDAL , and A. WIDOM , J. H. YOON .(for the MoEDAL Collaboration) Theoretical Particle Physics and Cosmology Group, Physics Department,King’s College London, UK International Centre for Theoretical Physics, Trieste, Italy IFIC, Universitat de Val`encia - CSIC, Valencia, Spain Physics Department, CERN, Geneva, Switzerland INFN, Section of Bologna, 40127, Bologna , Italy a Department of Physics & Astronomy, University of Bologna, Italy b Centre on Astronomy, Astrophysics and Geophysics, Algiers, Algeria Institute of Nuclear Physics Polish Academy of Sciences, Cracow, Poland Physics Department, University of Alberta, Edmonton Alberta, Canada Institute of Space Science, M˘agurele, Romania Department of Physics, Concordia University, Montreal, Quebec, Canada Physics Department, University of Muenster, Muenster, Germany IEAP, Czech Technical University in Prague, Czech Republic Section de Physique, Universit´e de Gen`eve, Switzerland Physics Department, Gangneung-Wonju National University, Gangneung, Korea Physics Department, University of Cincinnati, Cincinnati OH, USA Physics Department, University de Montr´eal, Montr´eal, Qu´ebec, Canada Physics Department, University of Helsinki, Helsinki, Finland Physics Department, Imperial College London, UK Department of Physics, University of British Columbia, Vancouver BC, Canada Department of Physics and Astronomy, Tufts University, Medford MA, USA Department of Physics, Northeastern University, Boston, USA Physics Department, Konkuk University, Seoul, Korea † Deceased. We dedicate this paper to Giorgio’s memory. We will strive to make this experimenta great success and a tribute to his memory. He will be sorely missed.KCL-PH-TH/2014-02, LCTS/2014-02, CERN-PH-TH/2014-021, IFIC/14-16,Imperial/TP/2014/AR/1 ∗ Communicating author. 1 a r X i v : . [ h e p - ph ] A ug Abstract
The MoEDAL experiment at Point 8 of the LHC ring is the seventh and newest LHCexperiment. It is dedicated to the search for highly ionizing particle avatars of physicsbeyond the Standard Model, extending significantly the discovery horizon of the LHC.A MoEDAL discovery would have revolutionary implications for our fundamental un-derstanding of the Microcosm. MoEDAL is an unconventional and largely passive LHCdetector comprised of the largest array of Nuclear Track Detector stacks ever deployed atan accelerator, surrounding the intersection region at Point 8 on the LHC ring. Anothernovel feature is the use of paramagnetic trapping volumes to capture both electricallyand magnetically charged highly-ionizing particles predicted in new physics scenarios. Itincludes an array of TimePix pixel devices for monitoring highly-ionizing particle back-grounds. The main passive elements of the MoEDAL detector do not require a triggersystem, electronic readout, or online computerized data acquisition. The aim of this pa-per is to give an overview of the MoEDAL physics reach, which is largely complementaryto the programs of the large multi-purpose LHC detectors ATLAS and CMS.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42. The MoEDAL Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52.1. The Nuclear Track Detector system . . . . . . . . . . . . . . . . . . 72.2. The magnetic monopole trapper detector system . . . . . . . . . . . 82.3. The TimePix radiation monitoring system . . . . . . . . . . . . . . . 93. Interactions of Electrically- and Magnetically-Charged Particles in MoEDAL 103.1. Ionization energy loss in matter . . . . . . . . . . . . . . . . . . . . . 103.1.1. Ionization energy loss for electrically-charged particles . . . . 113.1.2. Ionization energy loss of magnetically-charged particles . . . 133.2. Ionization energy loss in plastic Nuclear Track Detectors . . . . . . . 153.2.1. Track formation in NTDs . . . . . . . . . . . . . . . . . . . . 174. Bound States Between Monopoles and Matter . . . . . . . . . . . . . . . 184.1. Trapping monopoles . . . . . . . . . . . . . . . . . . . . . . . . . . . 184.2. Binding of the monopole-nucleus state to the material matrix . . . . 205. Magnetic Monopoles and Dyons . . . . . . . . . . . . . . . . . . . . . . . 205.1. GUT Monopoles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225.2. Monopole-like structures in the electroweak theory . . . . . . . . . . 245.2.1. Electroweak Monopole . . . . . . . . . . . . . . . . . . . . . . 245.2.2. The Cho-Maison Mass Estimate . . . . . . . . . . . . . . . . 265.2.3. Singularity resolution within string/brane theory . . . . . . . 295.2.4. Electroweak strings . . . . . . . . . . . . . . . . . . . . . . . . 305.3. Vacuum decay and light ’t Hooft-Polyakov monopoles . . . . . . . . 315.4. Monopolium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325.5. Summary of accelerator experiments . . . . . . . . . . . . . . . . . . 366. Electrically-Charged Massive (Meta-)Stable Particles in SupersymmetricScenarios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 R -parity violation . . . . . . . . . . 446.6. Heavy sleptons from Gauge Mediated Supersymmetry Breaking sce-narios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446.7. Metastable charginos . . . . . . . . . . . . . . . . . . . . . . . . . . . 456.8. The Fat Higgs model . . . . . . . . . . . . . . . . . . . . . . . . . . . 476.9. XYons from 5D SUSY breaking . . . . . . . . . . . . . . . . . . . . . 486.10. Current LHC limits on sparticles . . . . . . . . . . . . . . . . . . . 497. Scenarios with Extra Dimensions . . . . . . . . . . . . . . . . . . . . . . 517.1. Extra dimensions and microscopic black holes . . . . . . . . . . . . 517.1.1. Long-lived microscopic black holes . . . . . . . . . . . . . . . 537.1.2. Microscopic black hole remnants . . . . . . . . . . . . . . . . 537.2. Long-lived Kaluza-Klein particles from Universal Extra Dimensions 557.3. D-matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567.3.1. D-particles with magnetic charge . . . . . . . . . . . . . . . . 577.3.2. Electrically-charged D-particles . . . . . . . . . . . . . . . . . 588. Highly-Ionizing Particles in Other Scenarios . . . . . . . . . . . . . . . . . 618.1. Long-lived heavy quarks . . . . . . . . . . . . . . . . . . . . . . . . . 618.2. Massive (pseudo-)stable particles from vector-like confinement . . . 648.3. Fourth-generation fermions . . . . . . . . . . . . . . . . . . . . . . . 658.4. ‘Terafermions’ from a ‘sinister’ extension of the Standard Model . . 668.5. A massive particle from a simple extension to the SM . . . . . . . . 668.6. Fractionally charged massive particles . . . . . . . . . . . . . . . . . 679. Scenarios with Doubly-Charged Massive Stable Particles . . . . . . . . . . 689.1. XY gauginos and warped extra dimension models . . . . . . . . . . . 689.2. Doubly-charged leptons in the framework of walking technicolor models 699.3. Doubly-charged Higgs bosons in the L-R symmetric model . . . . . 709.4. Doubly Charged Higgsinos in the L-R supersymmetric model . . . . 719.5. Doubly-charged leptons in the framework of almost commutative ge-ometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7110. Highly-Ionizing Multi-Particle Excitations . . . . . . . . . . . . . . . . . 7210.1. Q-balls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7210.2. Strangelets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7310.3. Quirks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7411. Stopped Stable and Metastable Particles . . . . . . . . . . . . . . . . . . 7712. Detecting Highly-Ionizing Particles at the LHC . . . . . . . . . . . . . . 7913. Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 81
1. Introduction
In 2010 the CERN (European Laboratory for Particle Physics) Research Boardunanimously approved MoEDAL (Monopole and Exotics Detector at the LHC) [1,2],the 7 th international experiment at the Large Hadron Collider (LHC) [3], which isdesigned to seek out avatars of new physics with highly-ionizing particle signatures.The most important motivation for the MoEDAL experiment is to continue thequest for the magnetic monopole and dyons [4–21] to LHC energies. However, theexperiment is also designed to search for massive, stable or long-lived, slow-movingparticles [22] with single or multiple electric charges that arise in many scenarios ofphysics beyond the Standard Model (BSM) [23–53].Magnetic monopoles that carry a non-zero magnetic charge and dyons possessingboth magnetic and electric charge are among the most fascinating hypotheticalparticles. Even though there is no generally acknowledged empirical evidence fortheir existence, there are strong theoretical reasons to believe that they do exist, andthey are predicted by many theories including grand unified theories and superstringtheory.The laws of electrodynamics guarantee that the lightest magnetic monopolewould be a stable particle, and because monopoles interact strongly with the elec-tromagnetic field they are straightforward to detect experimentally. The scatteringprocesses of electrically charged fermions with magnetic monopoles are dependenton their microscopic properties even at low energies, [54, 55] and therefore theywould provide a unique window to physics at high energies beyond the StandardModel. In particular they would elucidate some of the most fundamental aspectsof electrodynamics (or, more precisely, the electroweak hypercharge) such as itsrelation to other elementary particle interactions.Likewise, the existence of massive, stable or long-lived, slow-moving particleswith single or multiple electric charges would also have drastic implications formodels of particle physics and cosmology. Therefore, a MoEDAL discovery wouldhave revolutionary implications for our understanding of the microcosm, potentiallyproviding insights into such fundamental questions as: Does magnetic charge exist?Are there extra dimensions or new symmetries of nature? What is the mechanismfor the generation of mass? What is the nature of dark matter? How did the BigBang unfurl at the earliest times?MoEDAL is an unconventional and largely passive LHC detector comprised ofthe largest array ( ∼
100 m ) of Nuclear Track Detector (NTD) stacks ever deployedat an accelerator, surrounding the intersection region at Point 8 on the LHC ring.Essentially, MoEDAL is like a giant camera ready to reveal “photographic” evidencefor new physics and also to trap long-lived new particles for further study.In this paper we describe the physics goals of a five-year programme of workthat combines interdisciplinary experimental techniques and facilities — from col-lider and astroparticle physics research — to expand significantly the horizon fordiscovery at the LHC, in a way complementary to the other LHC detectors. The official start to MoEDAL data taking is currently Spring 2015, after the long LHCshutdown.The structure of the paper is as follows. First we describe the MoEDAL detectorand then present the mechanisms by which the MoEDAL detector will register thesignatures of new physics. The bulk of the paper is devoted to describing the physicsprogram of the MoEDAL experiment in various scenarios for BSM physics. In thisarena we start with the consideration of the MoEDAL’s main physics motivation— the search for the magnetic monopole and other manifestations of magneticcharge. We then move to the consideration of singly electrically-charged Massive(pseudo)Stable Particles (SMPs) in a number of scenarios. We consider as a separatecase the search for particles with double or multiple electrical charges in a numberof models.A detailed comparison of MoEDAL’s sensitivity a to those of other experimentsin this arena, for each new physics scenario presented below, is beyond the scope ofthe paper. Rather, we outline here a programme of studies at the discovery frontierwhere MoEDAL would provide a unique and complementary physics coverage tothe existing LHC experiments. We emphasize that, even in those cases where we canexpect a considerable overlap between the new physics reach of MoEDAL and theother LHC experiments, MoEDAL’s contribution would be invaluable, particularlyin the event of a discovery. This is because MoEDAL is an entirely different type ofLHC detector. It is immune to fake signals from Standard Model backgrounds andhas totally different systematics from other LHC detectors.MoEDAL is a passive detector unfettered by the requirement to trigger andis not subject to the limitations imposed by real-time electronic readout systems.Importantly, its NTD system can be directly calibrated for the detection of highly-ionizing particles using heavy-ion beams, which is not possible for the other LHCdetectors. Also, it is the only LHC detector than can detect directly magnetic charge.Last but not least, MoEDAL will have a permanent record of any new particle thatit detects and may even be able to capture that new particle for further study.We note that in this work we consider only collider-based searches for newphysics scenarios signalled by highly-ionizing phenomena. Cosmological and astro-physical constraints on such scenarios, along with the various assumptions required,are not explored here. Comprehensive reviews of non-accelerator searches are pre-sented elsewhere [22] [56].
2. The MoEDAL Detector
The MoEDAL detector is deployed around the intersection region at Point 8 ofthe LHC in the LHCb experiment’s VELO (VErtex LOcator) [57] cavern. A three-dimensional depiction of the MoEDAL experiment is presented in Fig. 1. It is aunique and largely passive LHC detector comprised of four sub-detector systems. a Defined to be a convolution of the efficiency and acceptanceFig. 1. A three-dimensional schematic depiction of the deployment of the MoEDAL detectoraround the LHCb VELO region at Point 8 of the LHC.
The main subdetector system comprises a large array (100 m ) of CR39 R (cid:13) [58],Makrofol R (cid:13) [59] and lexan R (cid:13) [60] NTD stacks surrounding the intersection region.In p-p running the only source of Standard Model particles that are highly ionizingenough to leave a track in MoEDAL’s NTDs are spallation products with range thatis in the vast majority of cases much less than the thickness of one sheet of the NTDstack. Even then the ionizing signature will be that of a very low energy electricallycharged stopping particle. This signature is very different to that of a penetratingelectrically or magnetically charged particle that will usually traverse every sheet ina MoEDAL NTD stack, accurately defining a track that points back to the MoEDALintersection region. In the case of heavy ion running one might expect a backgroundfrom high ionizing fragments. However, such heavy-ion fragments are produced inthe far forward direction and do not enter the acceptance of the MoEDAL detector.A unique feature of the MoEDAL detector is the use of paramagnetic trappingvolumes (MMTs) to capture electrically- and magnetically-charged highly-ionizingparticles for subsequent analysis at a remote detector facility. Magnetically-chargedparticles will be monitored at a remote Magnetometer Facility. The search for thedecays of long-lived electrically charged particles that are stopped in the trappingdetectors will subsequently be carried out at a remote underground facility such asSNOLAB.The only non-passive MoEDAL sub-detector system is comprised of an array ofaround ten TimePix pixel devices forming a real-time radiation monitoring systemdevoted to the monitoring of highly-ionizing backgrounds in the MoEDAL cavern. The Nuclear Track Detector system
The main subsystem referred to as the low threshold NTD (LT-NTD) array, thearray originally defined in the TDR [2], is the largest array of plastic NTD stacks ( ∼ ×
25 cm in size, consistsof three sheets of CR39 polymer, three of Makrofol and three of Lexan . A depictionof a MoEDAL TDR NTD stack is shown in Fig. 2. CR39 is the NTD with the lowestdetection threshold, it can detect particles with ionization equivalent to Z/β ∼ Z is electric charge of the impinging particle and β its velocity, expressed asa fraction of the speed of light. A standard minimum-ionizing particle produced inan interaction at the LHC would have a Z/ β (cid:39)
1. The charge resolution of CR39detectors is better than 0 . e [61], where e is the electric charge. Fig. 2. The composition of a MoEDAL LT-NTD stack, the lexan sheets are not shown.
The LTD-NTD array has been enhanced by the High Charge Catcher (HCC)sub-detector with threshold
Z/β (cid:38)
50 comprising three Makrofol sheets in an alu-minium foil envelope. These lightweight low-mass detector stacks can be applieddirectly to the outside of the VELO detector housings and on other accessible sur-faces in the region, for example the front face of the LHCb RICH detector, ratherthan on the walls and ceilings of the VELO cavern. In this way we can increase thegeometrical acceptance for magnetic monopoles to over ∼ Lab. As soon as available a fully automatic state-of-the-art high-throughput opticalscanning-microscopy for high-resolution and large-area surface analysis based onthe AMBIS (Anti Motion-Blurring Imaging System) device will be deployed at theMoEDAL plastic analysis centres. This apparatus is capable of searching quicklylarge areas of NTD material ( ∼
100 cm in 40 minutes) for extremely small fea-tures ( O (10) µ m). In this way the usual scanning process is turned into an imageenhancement and pattern recognition process that can be handled with specializedsoftware. In this way the low Z/β threshold can be maintained.In a multi-sheet stack detector, the position and direction information fromindividual pits can be combined to track the particle back to the interaction region.Also, the actual or effective
Z/β values can be used to determine if the change inionization energy loss is consistent with the scenario under investigation.The signal for a magnetic monopole would be a set of 20 etch pits aligned witha precision of ∼ µ m, pointing towards the intersection point, with etch pitsremaining the same size or decreasing slightly in size, since the monopole energyloss decreases with falling β , making it distinct from an electrically-charged particle. The magnetic monopole trapper detector system
The Magnetic Monopole Trapper (MMT) is the third and newest sub-detector sys-tem to be added to the MoEDAL detector. This detector consists of passive stacksof aluminium trapping volumes placed adjacent to the VELO detector. These stacks- intended to trap magnetic monopoles and highly-ionizing (quasi-)stable massivecharged particles that stop within their volume - will be replaced once a year. Afterremoval the exposed trapping volumes will be sent first to the SQUID facility atETH Zurich to be scanned for trapped magnetic charge. The signal for a magneticmonopole in the MMT trapping detectors at the ETH facility would be a sustainedcurrent resulting from the passage of a monopole though the SQUID detector.A schematic diagram describing the SQUID magnetometer scanning processis shown in Fig. 3. The sensitivity of the SQUID magnetometer housed at ETHZurich, as determined by a “pseudo-monopole” formed from a very long conventionalmagnet, is shown in Fig. 4. The solenoid method is not the only method by whichthe SQUID magnetometer can be calibrated. Further details of this technique canbe found elsewhere [62].After the SQUID scan has been performed, the MMT trapping volumes will besent to an underground laboratory - SNOLAB is currently the favored site - to bemonitored for the decay of trapped very long-lived electrically charged particles.The rate of decay observed can be used to find the particle’s lifetime.The MMT sub-detector has the two attractive advantages of speed and comple-mentarity. It will result in the publication of the first monopole search in 14-TeV pp collisions, and has the potential to procure a robust and independent cross-checkof a discovery as well as a unique measurement of the magnetic properties of amonopole. Fig. 3. A schematic diagram showing how the SQUID apparatus is used. The sample travels insteps completely through the coil. The current in the superconducting coil is read out after eachstep.Fig. 4. A histogram showing the measurements of a number of MoEDAL MMT detector blanks,showing that the monitoring SQUID magnetometer is sensitive to monopoles with charge as lowas one hundredth of a Dirac charge.
The TimePix radiation monitoring system
The fourth and only non-passive sub-detector system is an array of TimePix pixeldevices (NTPX) [63]. It is used to monitor possible highly-ionizing beam-relatedbackgrounds. Each pixel of the innovative TimePix chip contains a preamplifier,a discriminator with hysteresis and 4-bit DAC for threshold adjustment, synchro-nization logic and a 14-bit counter with overflow control. The TimePix chip has anactive area of ∼ segmented into a 256 ×
256 square pixel matrix, where eachpixel is 55 µ on the side.MoEDAL uses TimePix in “Time-over-Threshold” mode, so that each pixel canact as an ADC that can supply an energy measurement. A photograph of a TimePix pixel chip is shown in Fig. 5. The online TimePix radiation monitoring system willbe accessed via the web. Thus, it is not necessary to run shifts even though theTimePix array is a real-time MoEDAL detector system. Fig. 5. A photograph of a Timepix chip with its main features indicated.
Some 5 −
10 TimePix1 silicon pixel imaging devices will be deployed to samplethe radiation levels around the MoEDA/LHCb cavern. Each Timepix detector isessentially a small electronic bubble chamber capable of imaging complete spallationevents in its 300 µ m thick silicon sensitive volume. Data readout and event displayproduced is provided by the “PixelMan” software developed by the CTU-IEAPgroup.
3. Interactions of Electrically- and Magnetically-Charged Particlesin MoEDAL
In this Section we describe the expected interactions of SMPs with electrical and/ormagnetic charge in the MoEDAL detector. In addition, a description is given ofthe theory of electromagnetic energy loss for electrically- and magnetically-chargedparticles. We also consider the physics of monopole trapping. Specific scenarios forhighly-ionizing particles with magnetic and/or electric charge will be discussed insubsequent sections.
Ionization energy loss in matter
A main detection mode for SMPs in MoEDAL is via the measurement of continuousionization energy loss dE/dx . Both electrically and magnetically charged SMPs loseenergy principally through ionization energy loss as they propagate through matter.The theory of electromagnetic energy loss for both electrically and magneticallycharged particles is well established [64]. Ionization energy loss for electrically-charged particles
As an electrically charged particle moves through matter it loses energy either byinteractions with atomic electrons or by collisions with atomic nuclei in the material.The first of these results in the freeing of electrons from the atoms in the material(i.e., ionization) while the second results in the displacement of atoms from thelattice. The energy loss due to the second process is called the Non-Ionizing EnergyLoss (NIEL). Except at very low β , the energy loss ( dE/dx ), due to the ionizationenergy is much larger than the NIEL [68] in most particle detectors.The mean rate of energy loss (or stopping power) for moderately relativisticcharged particles other than electrons is given by the Bethe-Bloch formula [64], dEdx = 4 πN A r e m e c ZA z β (cid:20)
12 ln 2 m e c β γ T max . I e − β − δ ( βγ )2 (cid:21) , (1)where: Z ( A ) is the atomic number (mass) of the medium; z is the charge of theincident particle; m e and r e are the mass and classical radius of the electron, re-spectively; N A is Avogadro’s number; β is the velocity of the incident particle asa fraction of the speed of light ( c ); γ = 1 / (cid:112) − β ; and, I e is the mean ionizationpotential of the medium. The ionization potential can be parameterized by [69], I e ( Z ) = (12 Z + 7) eV for Z ≤
13 and (9 . Z + 58 . Z − . ) eV for Z >
13. Thequantity T max . is the maximum kinetic energy that can be imparted to a free elec-tron in a single collision, and is given, for a particle with mass M , by: T max . = 2 m e c β γ γm e M + (cid:16) m e M (cid:17) . (2)The δ term represents the density effect correction to ionization energy loss. Asthe particle energy increases, its electric field flattens and extends, so that thedistant-collision contribution increases as ln βγ . However, real media become po-larized, diminishing the extension of the field and thereby limiting the relativisticrise at high energy. Thus the δ term is important for massive particles — where T max . ≈ m e c β γ — with βγ >
3. Slight differences in δ occur for different chargesmoving with low velocity. The density effect correction is usually computed usingSternheimer parameterization [70].The Bethe-Bloch formula (1) is based on a first-order Born approximation. How-ever, for lower energy, higher-order corrections are important. These corrections areusually included by adding the “Bloch correction” z L ( β ) inside the square bracketof Eq. (6). An additional correction term, zL β , makes the stopping power for apositive particle somewhat larger than for a negative particle, all other factors beingequal [71]. This is indicated by the short dotted lines labelled µ − in Fig. 6.At low energies, in the so-called Lindhard region [72], where particles are movingwith speed less than around 0 . c , the velocity of the incident particle is comparableto, or less than, the velocity of the outer atomic electrons, and the Bethe-Blochformula is no longer valid. In this region Lindhard has introduced a successful dE/dx for positively-charged muons in copper as a function of βγ = p/M , taken from the Particle Data Group book [64]. The solid curve indicates the total stoppingpower. Data below the break at βγ ≈ µ − . formula for the stopping power that is proportional to the particle’s velocity, β [72]: dEdx = N ξ e πe a Zz ( Z + z ) ββ , (3)where N is the number of atoms per unit volume, ξ ≈ z / , and a is the Bohr radiusof the hydrogen atom. The formula holds for β < z / β , where β = e / (2 (cid:15) hc ) isthe electron velocity in the classical lowest Bohr orbit of the hydrogen atom.The intermediate region, roughly 0 . < β < .
05, described by Anderson andZiegler [73] and defined by the relation:max (cid:20) αz / (1 + αz / ) , (2 Z . + 1)400 (cid:21) ≤ β ≤ αz (1 + αz ) , (4)does not have a satisfactory theoretical description. However, Lewin [69] describeda useful phenomenological polynomial interpolation over the intermediate region,of the form: dEdx = Aβ + Bβ + Cβ + D, (5)where the coefficients A , B , C and D are discussed in Ref. [69]. Ionization energy loss of magnetically-charged particles
A fast ( β > − ) magnetic monopole with a single Dirac charge ( g D ) b has anequivalent electric charge of Z e q = β (137e/2). Thus for a relativistic monopole theenergy loss is around 4 ,
700 times (68 . ) that of a Minimum-Ionizing electrically-charged Particle (MIP). Thus, one would expect a monopole to leave a unique andstriking ionization signature.The ionization energy loss by magnetic monopoles can be described by a formulavery similar to the Bethe-Bloch equation, with the electric charge term replaced bythe electric charge equivalent of the magnetic charge to the monopole. At relativis-tic velocities the energy loss is therefore constant, independent of β . The detailedformula for the stopping power of a magnetic monopole with magnetic charge ng ( n = 1 , , ... ) is given by [74]: dEdx = 4 πe ( ng ) m e c n e (cid:20)
12 ln 2 m e c β γ T max . I m − δ K ( | g | )2 − B ( | g | ) (cid:21) , (6)where n e is the number of electrons per unit volume in the medium, I m is themean ionization potential for magnetic monopoles, which is close in value to I e ,and K ( | g | ) = 0 . , . B ( | g | )(= 0 . , . g =1 g D / g D , respectively [74]. The relationship between I m and I e is given by I m = I e e − D/ , where the power D has been calculated by Sternheimer [75] for variouselements, for example D ( Al ) = 0 . D ( F e ) = 0 .
14 and D ( C ) = 0 .
22. The stoppingpower for a unit Dirac magnetic monopole in aluminium as a function of the velocityof the monopole is shown in Fig. 7 . The above formalism allows accurate estimatesof the stopping power of magnetic monopoles for β ≥ . γ ≤ p/M = βγ , where p and M are the momentum and the mass of themonopole, respectively. The monopole energy loss calculation is implemented as partof a GEANT package for the simulation of monopole trajectories in a detector [77].The inspection of the Bethe-Bloch formulae for electronically and magneticallycharged particles for a singly-charged Dirac monopole and a unit electric chargemoving with velocity β shows that the ratio of their stopping powers is ∼ β .It can be seen from Fig. 7 that as the monopole slows the ionization decreases ascompared to electrically-charged particles where the opposite is true.One of the most successful approaches for calculating the stopping powers of ma-terials has been to treat them approximately as a free (degenerate) gas of electrons- a “Fermi gas”. This is clearly appropriate for interactions with the conductionelectrons of metallic absorbers. For nonmetallic absorbers it represents a reasonableapproximation for heavy atoms ( Z ≥ b The concept of Dirac (magnetic) charge is presented in Section 5.4Fig. 7. Left: The dE/dx for a Dirac monopole in aluminium as a function of the velocity of themonopole, obtained from [74] and adjusted for the electron density in aluminium. Right: The ratioof range to mass for a Dirac monopole in aluminium versus βγ , calculated from the stopping power dE/dx . in Fermi gases: (cid:18) dEdx (cid:19) m = 2 πN e ( ng ) e vm e c v F (cid:20) ln 1 Z min − (cid:21) , (7)where v F is the Fermi velocity, v is the projectile velocity, Z min = (cid:126) / (2 m e v F a ), N e is the density of non-conducting electrons in the medium, and a = 0 . × − cm(roughly the “mean free path” of an electron bound in an atom). This equation isexpected to be valid for non-conductors for 10 − ≤ β ≤ − .For conductors one should add another term that depends on the conductionelectrons. However, Eq. (7) should actually provide a good description of energyloss in a conductor for β ≤ − , with the parameters Z min = (cid:126) / (2 mv F Λ), andΛ ≈ aT m /T , where a is a lattice parameter; T m is the melting point of the metal, T is the temperature and N e is the density of conduction electrons.For velocities β ≤ − magnetic monopoles cannot excite atoms, but they canlose energy in elastic collisions with atoms or nuclei. In the case of monopole-atomelastic scattering this process is dominated by the coupling of the atomic electronmagnetic moments with the magnetic monopole field. An estimate of the energyloss can be achieved by considering the elastic interaction of a monopole and anatom characterized only by its magnetic moment [79]: dEdx ≈ N a E c.m. σ ≈ N a (cid:126) m e , (8)where N a is the number of atoms/cm . The results of a more precise calculation [81]are shown in Fig. 8. The energy is released to the medium in the form of thermal and acoustic energy. Monopole-nucleus elastic scattering is expected to be dominatedby the interaction of the monopole magnetic charge with the magnetic moment ofthe nucleus. Thus we obtain a formula rather like Eq. (8). Fig. 8. The energy losses in MeV/cm of a g = g D monopole in liquid hydrogen as a function of β . Curve a) monopole with β − cannot excite atoms energy loss here i due to elastic monopole-hydrogen atom/nucleus scattering. in the region covered by curve (b) energy loss via the ionizationor excitation of atoms and molecules of the medium (“electronic” energy loss) dominates for β > − . The dE/dx of magnetic monopoles with 10 − < β < − is mainly due to excitations inatoms. Curve c) shows the ionization energy loss. The figure was obtained from Ref. [80]. In a second approach [78] it was assumed that the atoms of the absorbing mate-rial have no magnetic moment and that the interaction is dominated by the trans-verse electric field. In this case, at large impact parameters the atom will respondto an applied electric field only through its induced electric dipole moment. Thisapproach results in the following expression for energy loss: dEdx atomic = 4 πN a g Z r M nuc c ln (cid:18) M nuc vca gZe (cid:19) , (9)where M nuc is the mass of the nucleus, a is the Bohr radius, v is the monopolevelocity as a fraction of the speed of light and Z is the atomic number of themedium. Taking silicon as an example, we see that dE/dx nuc = 1 . / (g / cm )at β = 10 − , which is about 7% of the electronic stopping power. For β = 10 − , dE/dx nuc is only about 1% of the electronic stopping power. Ionization energy loss in plastic Nuclear Track Detectors
A key quantity for assessing NTDs is the Restricted Energy Loss (REL), which isthe energy deposited within ∼
10 nm from the track. For computation of the REL,say for CR39, only energy transfers to atoms above 12 eV are considered, because itis estimated that at least 12 eV is required to break the molecular bonds [82]. The REL is mainly due to the monopole itself with some contribution from short-range δ -rays. At high velocities ( β > .
05) the REL for the monopole tracks are obtainedexcluding the energy transfers that result in δ -ray production and thus in energydeposited far away from the track [83]. The REL for high-velocity monopoles isshown in the (A) region of Fig. 9 [82]. Fig. 9. The restricted energy loss of a magnetic monopole as a function of β in the nuclear trackdetector CR39 ( ρ = I .31 g/cm ). The detection thresholds of two types of CR39 used by MACROexperiment (T1 and T2) are also shown. Notice that the solid curves represent β regions where thecalculations are more reliable, the dashed lines are interpolations. Explanations about the curvesin regions A and B are given in the text. The figure is obtained from Ref. [82]. At lower velocities ( β < − ) there are two contributions to REL. First there isthe contribution due to ionization that can be computed assuming that the mediumis a degenerate electron gas [78]. However, another estimate [84] gives a smaller esti-mate of ionization energy loss. The second contribution to REL for slow monopolesis due to the elastic recoil of atoms. The procedure to compute this contributioncan be found in Ref. [85] and [82]. The elastic recoil is due to the diamagnetic in-teraction between the magnetic monopole and the carbon and oxygen atoms of themedium.The approach of Ref. [85] is used to estimate the atomic elastic recoil contri-bution, which gives rise to a bump in REL around βg/g D , shown in Fig. 9. Theionization contribution dominates at β higher than the value at which the minimumREL occurs. For 10 − < β < − a smooth interpolation has been performed. Asis shown in Fig. 9, monopoles with g > g D can be detected by the CR39 detector for β > × − .The practical threshold of CR39 was determined by direct measurements withheavy ions to be Z/β (cid:38) ∼
25 MeV cm g − .The threshold of Makrofol is approximately ten times higher.3.2.1. Track formation in NTDs
When a particle passes through a NTD, it leaves a trail of damage along its pathcalled the latent track (LT) with diameter of the order of 10 nm [89]. The LT can beenlarged and thus made visible to an optical microscope by chemically etching thedetector. The etchants are highly basic or acid solutions, e.g., aqueous solutions ofNaOH or KOH of different concentrations and temperatures, usually in the range40 → o C. Etching takes place via the dissolution of the disordered region of theLT, which is in a state of higher free energy than the undamaged bulk material.The track etch rate v T is defined as the rate at which the detector material ischemically etched along the LT, whereas the bulk etch rate v B is defined as therate at which the undamaged material of the NTD is etched away. The track etchrate v T depends on the energy loss of the incident particles and on the chemicaletching conditions (concentration, temperature, etc.) whereas v B depends only onthe etching conditions. The reduced etch rate p is defined as p = v T /v B . If v T > v B ( p >
1) etch-pit cones are formed.The formation of etch pit cones for a particle impinging normally on the NTDis depicted in Fig. 10. Etching a layer for a short time yields two etched cones oneach side of the sheet. The primary ionization rate may be determined from thegeometry of the etched cones. For CR39 this technique yields measurements of theelectric charge of heavy nuclei to a precision of 0 . e if one uses several layers ofplastic sheets, placed perpendicular to the incoming ions [90, 91]. Fig. 10. Depiction of the latent track left by the passage of an ionizing particle through a NTDand the subsequent formation of etch-pit cones.
For an electrically-charged particle slowing down appreciably within the NTD stack, the opening angle of the etch-pit cone would become smaller. For a particlestopping inside the detector, if the chemical etching continues beyond the trackrange, the cone end develops into a spherical shape (end of range tracks). For amonopole slowing down appreciably within an NTD stack its ionization would fallrather than rise and thus the opening angle of the etch pits would become largerrather than smaller. For relativistic monopoles at the LHC the energy loss across anNTD stack would usually be essentially constant, yielding a trail of equal diameteretch-pit pairs, assuming that all NTD sheets were etched in the same manner andfor the same time.
4. Bound States Between Monopoles and Matter
The study of the interactions of magnetic monopoles in matter is of critical impor-tance in the understanding of the energy loss of monopoles as well as the formationof bound systems of monopoles and atomic nuclei. The consideration of the forma-tion of bound states between monopoles and matter was necessary for the design ofthe MoEDAL trapping detector subsystem (MMT).
Trapping monopoles
Once the monopoles are produced in a collision at the LHC, they will travel throughthe surrounding material losing energy as described above. In some cases they willlose enough energy to slow down and become trapped in the material, presumablyby binding to a nucleus of an atom forming the material. We assume that thisbinding is due to the interaction between the magnetic charge of the monopole andthe magnetic moment of the nucleus. In the case of dyons the situation is simple,the correct sign of the electric charge will always bind electrically to nuclei. Thus,we consider here only the binding of a monopole to a nucleus.The magnetic moment of a nucleus with charge Ze and mass M = AM p is: µ = Ze M g N S , (10)where S is the spin of the nucleus and g N is the gyromagnetic ratio of the nucleus,and M is the reduced mass of the monopole-nucleus system. If the monopole is heavycompared to the nucleus, which is a good assumption for searches at the LHC, thereduced mass is essentially equal to the mass of the monopole. If the monopole hasa magnetic charge g = n/ e (using the units (cid:126) = c = 1), where n = ± , ± , ... ,the electromagnetic field around the monopole-nucleus system carries an angularmomentum | q | = | nZ | /
2, which can combine with the orbital angular momentum togive the values: l = | q | , | q | + 1 , .... . This in turn can be coupled with the nuclear spin S to give a total angular momentum: j = | q | + 1 − S, | q | + 1 , .... , provided | q | ≥ S c . c If | n | = 1, this is only true for magnetic charge coupled to H ( S = 1 , | q | = 1 / Li ( S = 2 , | q | =3 /
2) and B ( S = 3 , | q | = 5 / We consider first the non-relativistic binding for single nucleons with S =1 / Z = 0) will occur in the lowest angularmomentum state, J = 1 /
2, if | g N | / > / (2 n ). Since g N / − .
91, this condi-tion is satisfied for all n . Defining a “reduced” gyromagnetic ratio of the nucleus, g (cid:48) N = g N ( A/Z ), binding will occur in the special lowest angular momentum state J = l − /
2, if g (cid:48) N / > / l . The proton has a gyromagnetic ratio of 5 . J if and only if: | g (cid:48) N | / > g c = 2 l (cid:12)(cid:12) J + J − l (cid:12)(cid:12) + 2 . (11)In order to calculate the binding energy, one must regulate the potential at r = 0.The results shown in Table 1 [94] assume a hard core. Table 1. Weakly-bound states of nuclei to a magnetic monopole. The angularmomentum quantum number J of the lowest bound state is indicated. A singleDirac charge was assumed in all calculations.Nucleus Spin(S) g N / g (cid:48) N / J E bind
Ref. n H 1/2 2.79 2.79 l -1/2 =0 15.1 keV [92] H 1/2 2.79 2.79 l -1/2 =0 320 keV [96] H 1/2 2.79 2.79 l -1/2 =0 50-1000 keV [95] He 1/2 0.857 1.71 l +1/2 =3/2 13.4 keV [92] Al 5/2 3.63 7.56 l - 5/2 = 4 2.6 MeV [95] Al 5/2 3.63 7.56 l - 5/2 = 4 560 keV [97] Be 1/2 -0.62 -1.46 l +1/2 = 49/2 6.3 keV [92] The more general case for non-relativistic binding for a general S was considered,for example, in Ref [96]. We assume that l ≥ S , the only exceptions being H, Liand B. The binding in the lowest angular momentum state J = l − S is givenby the same criteria as in the spin-1 / J = l − S + 1, occurs if λ ± > / λ ± = (cid:18) S − (cid:19) g (cid:48) N S l − l − ± (cid:115) (1 + l ) + (2 S − − l ) g (cid:48) N S l + 14 l (cid:18) g (cid:48) N S (cid:19) . (12)Spin 1 is a special case where λ − is always negative, while λ + > g (cid:48) N / > g (cid:48) c ,where: g c = 34 l (3 + 16 l + 16 l )9 + 4 l (13)For higher spins S >
1, both λ ± can exceed 1 /
4, if λ + > / g (cid:48) N / > g c − or λ − > / g (cid:48) N / > g c + . For S = 5 / g c ) ∓ = 36 + 28 l ∓ √ l + 64 l l . (14) Thus,
Al will bind in either of these states, or the lowest angular momentumstate, since g (cid:48) N / .
56 and 1 . < g c − < .
67 and 1 . < g c + < . Binding of the monopole-nucleus state to the material matrix
A practical question for a monopole trapping detector is how well the monopole-nucleus state is bound to the material lattice. The decay rate of a such a state hasbeen estimated [94] to be:Γ ∼ n − / s − exp (cid:34) − √ × (cid:18) − Em e (cid:19) / B nB A / (cid:18) m p m e (cid:19) / (cid:35) , (15)where the characteristic field, defined by eB = m e , is 4 × T. If we assume B = 1 . A = 27, − E = 2 . Al), to get a lifetime of at least a10 years, the binding energy would need to be greater than around 1 eV. Accordingto this calculation any state that is bound at the keV level or more will be stablefor around 10 ,
000 years.This calculation suggests that a major disruption of the lattice would be requiredto dislodge the monopole-nucleus state. If monopoles bind strongly to nuclei theywill not be extracted by the fields available in the LHC experiments [94]. However,another estimate [98] suggests that magnetic fields of the order of 10 kG would besufficient to release trapped monopoles. MoEDAL is deployed in a “zero” field regionof the LHCb, with only a small fringe field from the LHCb main dipole magnet,much smaller than the field required to free a trapped monopole, for both casesconsidered above.
5. Magnetic Monopoles and Dyons
As we have seen from the above discussion the MoEDAL detector is designed toexploit the energy loss mechanisms of magnetically charged particles in order tooptimize its potential to discover such revolutionary messengers of new physics. Wewill now discuss the various theoretical scenarios in which magnetic charge wouldbe produced at the LHC. There are several more extensive reviews of magneticmonopoles available in the literature [99–102].In classical electrodynamics, as described by Maxwell’s equations, the existenceof magnetic charge might be expected because it would make the theory moresymmetric. In vacuum, the Maxwell equations are symmetric under a duality trans-formation that mixes the electric and magnetic fields, (cid:126)E + i (cid:126)B → e iφ ( (cid:126)E + i (cid:126)B ) , (16)but this duality symmetry is broken if magnetic charges do not exist in Nature. Thisis because the duality would transform the electric charge density ρ E to magnetic charge density ρ B , ρ E + iρ M → e iφ ( ρ E + iρ M ) . (17)The symmetry of the equations therefore motivates the expectation that both elec-tric and magnetic charges should exist in Nature.Magnetic charges can be incorporated into classical electrodynamics trivially bymodifying the magnetic Gauss’s law to become (cid:126) ∇ · (cid:126)B = ρ M . (18)An isolated magnetic point charge g will then have a magnetic Coulomb field (cid:126)B ( (cid:126)r ) = g π (cid:126)rr . (19)The description of the electromagnetic fields requires the introduction of the vectorpotential (cid:126)A , which is related to the magnetic field (cid:126)B by the relation (cid:126)B = (cid:126) ∇ × (cid:126)A. (20)For any smooth vector potential (cid:126)A , the magnetic field is then automatically source-less, (cid:126) ∇ · (cid:126)B = 0, and this appears to rule out the existence of magnetic charges.However, Dirac showed in 1931 that this conclusion is premature [4]. Because thevector potential (cid:126)A is not an observable quantity, it does not have to be smooth.Dirac found that the magnetic field (19) of a an isolated magnetic charge g can berepresented by the vector potential (cid:126)A ( (cid:126)r ) = g πr (cid:126)r × (cid:126)nr − (cid:126)r · (cid:126)n (21)everywhere except along a line in the direction of the unit vector (cid:126)n . Along this line,which is known as the Dirac string, the magnetic field is singular. However, if onetries to probe the Dirac string with an electrically charged particle with electriccharge q , one finds that it is unobservable if the magnetic charge g satisfies theDirac quantization condition, qg ∈ π Z . (22)where Z is the integer number set. If the electric charges of all particles satisfy thiscondition, meaning that they are quantized in units of 2 π/g , then the Dirac string iscompletely unobservable. In that case the vector potential (21) describes physicallya localized magnetic charge at the origin, surrounded by the magnetic Coulomb field(19), with the only singularity at the origin. The condition (22) implies that theelectric charge has to be quantized, i.e., an integer multiple of the elementary charge q = 2 π/g . This means that not only are magnetic charges allowed by quantummechanics, but their existence also explains the observed quantization of electriccharge.Obviously, the quantization condition (22) also implies that the magnetic chargeis quantized in units of g = 2 π/q , where q is the quantum of electric charge, which in the Standard Model is the charge of the positron, q = e . The quark electriccharges are quantized in units of e/
3, but because they are confined, they are notrelevant for the quantization argument [16]. Note that the minimum magnetic charge g is very large. The strength of the magnetic Coulomb force between two charges g is g /q = 4 π /q ≈ q . The magnetic analogue of the fine structure constant α = q / π ≈ /
137 is α M = g / π = π/α ≈ G is not simply connected, i.e., π ( G ) (cid:54) = 1.This is directly related to the Dirac quantisation condition (22), because electro-magnetism can be described by a compact U (1) gauge group only if electric chargesare quantised. Otherwise the gauge group is the non-compact covering group R ofreal numbers.Schwinger [15] generalized the quantization condition to dyons, particles thatcarry both electric and magnetic charge. In this case, the charges of all particleshave to satisfy the condition q g − q g ∈ π Z . (23)His argument also implies that the minimum charge for a magnetic monopole shouldbe g = 4 π/q , twice the Dirac charge. GUT Monopoles
The discussion in the previous section focussed on static monopoles. Formulating aquantum field theoretic description of dynamical magnetic monopoles is challeng-ing, but there examples of weakly-coupled quantum field theories in which magneticmonopoles appear as non-perturbative solutions. The most important case is the’t Hooft-Polyakov monopole solution [6, 7] in the Georgi-Glashow model, which isan SU (2) gauge field theory with an Higgs field Φ in the adjoint representation.When the Higgs field has a non-zero vacuum expectation value, (cid:104) Φ (cid:105) = v >
0, the SU (2) gauge symmetry breaks spontaneously to U (1), thereby giving rise to elec-trodynamics. In this broken phase the theory has a smooth, spherically symmetric“hedgehog” solution with magnetic charge g = 4 π/q , where q is the electric chargeof the W + boson. The monopole has a non-zero core size r ∼ /qv and a finitemass M ∼ v/q . Therefore it appears as a particle state in the spectrum of the the-ory. Lattice field theory simulations [21] have confirmed the validity of the classicalmass estimate also in the quantum theory at weak coupling. The theory also has dyon solutions with both electric and magnetic charges [8].At the semiclassical level they can have arbitrary electric charge, but quantumeffects force the charges to be quantized according to Eq. (23). In the presence ofCP violation the electric charges are non-integer valued [10]. Dyons are generallyheavier than electrically neutral monopoles and can therefore decay into monopolesand electrons or positrons.Although the Georgi-Glashow model by itself is not a realistic theory of elemen-tary particles, the same solutions also exist in all Grand Unified Theories (GUTs),in which the strong and electroweak forces are unified into a simple gauge group.In the simplest SU (5) GUT [104], with the symmetry breaking pattern SU (5) → SU (3) × SU (2) × U (1) (24)the mass of these monopoles is determined by the GUT scale: M ∼ Λ GUT /α ∼ GeV, and therefore well beyond the reach of the LHC. The lightest monopolesin the theory have a single Dirac charge g = 2 π/e , but they can form doubly-chargedbound states.In some GUTs, it is possible to find ’t Hooft-Polyakov monopole solutions withlower mass. For example, the Pati-Salam model [105] with the symmetry breakingpattern SO (10) → SU (4) × SU (2) × SU (2) → SU (3) × SU (2) × U (1) , (25)has monopole solutions with mass M ∼ GeV [11] and charge g = 4 π/e , twicethe Dirac charge. Family unification models with the symmetry group SU (4) × SU (3) × SU (3) can have multiply-charged monopole solutions with masses as lowas M ∼ GeV [18].Monopole solutions exist also in theories with compactified extra dimen-sions [12, 13]. In this case the U (1) gauge group of electrodynamics corresponds tothe compactified dimension. At the monopole core the size of the extra dimensionshrinks to a point in a smooth way. The natural mass values for these Kaluza-Kleinmonopoles are above the Planck scale, M ∼ M Pl /α ∼ GeV but, again, thereare models in which they are considerably lighter.These examples show that magnetic monopoles can exist consistently in quan-tum field theories, and also make it possible to investigate their properties and be-haviour using normal quantum field theory methods. They are also well-motivatedphysical theories, and therefore they indicate that it is likely that superheavymonopoles of mass M (cid:38) GeV exist. Of course it would be impossible toproduce such monopoles in any conceivable experiment. However, it is perfectlypossible that there is some new unexpected physics between the electroweak andGUT scales, and therefore there can well be lighter magnetic monopoles that arenot related to grand unification or compactified extra dimensions. Monopole-like structures in the electroweak theory
The discovery of a Higgs-like boson in July 2012 by the ATLAS and CMS [106,107] experiments at the Large Hadron Collider (LHC) at CERN has led to thepossibility that the puzzle of the Standard Model spectrum may be completed.More recently, this new particle looks increasingly like a Standard Model (SM)Higgs boson [108–111], reinforcing the electroweak theory of Glashow, Salam andWeinberg as a successful theory. The experimental verification of a monopole-likesolution within the framework of the SM would explain from first principles thequantization of the electric charge, something that the present SM cannot do.5.2.1.
Electroweak Monopole
There has been some discussion in the literature of the possible existence ofmonopoles within the Standard Electroweak Theory. The electroweak symmetrybreaking pattern is SU (2) × U (1) Y → U (1) EM . A topological monopole requiresnontrivial topology of the quotient group SU (2) × U (1) Y /U (1) EM which, becauseof the residual U (1) symmetry would be putatively nontrivial and of the sort whichsupports monopoles. It is therefore possible to repeat Dirac’s argument and writedown the potential (21) describing a static monopole with a non-zero magnetichypercharge. At long distances, the Dirac quantisation condition (22) must be sat-isfied by the electromagnetic charges, and therefore the monopole will also have anon-trivial SU (2) gauge field configuration.However, unlike the model which is used in the discussion of the ’t Hooft-Polyakov monopole where the scalar field was an SU (2) triplet, the standard Higgsfield is an SU (2) doublet and it is not possible to make the usual spherically sym-metric hedgehog monopole configuration from a doublet. To see this in more detail,consider the Lagrangian of the Weinberg-Salam model, L = ( D µ φ ) † D µ φ − λ (cid:16) φ † φ − µ λ (cid:17) − F µν F µν − G µν G µν (26) D µ φ = (cid:16) ∂ µ − i g (cid:126)τ · (cid:126)A µ − i g (cid:48) B µ (cid:17) φ (27) F µν = ∂ µ A aν − ∂ ν A aµ + g (cid:15) abc A bµ A cν , G µν = ∂ µ B ν − ∂ ν B µ (28)where we use the (1 , − , − , −
1) signature of the Minkowski space metric. Theground state of the standard model has a nonzero value for the Higgs field, φ † φ = µ /λ , and the rest of the fields equal to zero. The usual fields, W ± , Z , the Higgsboson and the photon are quanta of fluctuations about this ground state.It has been pointed out, initially by Cho and Maison [14], that there is a singulartopological monopole solution of this model. Their ansatz for a time-independent, spherically symmetric solution is φ ( r, θ, ϕ ) = ρ ( r ) (cid:34) i √ e − iϕ sin θ − i √ cos θ (cid:35) (29) A a = ˆ r a g A ( r ) , A ai ( r, θ, ϕ ) = g ( f ( r ) − (cid:15) aij r j r (30) B = g (cid:48) B ( r ) , B i ( r, θ, ϕ ) = g (cid:48) (1 − cos θ ) ∇ i ϕ (31)The angular dependence of the fields in this anzatz are determined by the require-ment of rotational covariance, that is, the requirement that the solution leads to aspherically symmetric monopole and, moreover, that the solution has a magneticmonopole charge for the degrees of freedom which will become the electromagneticfields. The field (cid:126)B ( r, θ, φ ) has the usual Dirac string at θ = π which is invisible toparticles with appropriately quantized charges.To see that this solution must be a singular solution of the Weinberg-Salamtheory (26), we substitute the ansatz into the energy functional to get the energyof the classical field configuration, E = πg (cid:82) ∞ drr (cid:104) g g (cid:48) + ˙ f + (1 − f ) + g ( r ˙ ρ ) + g f ρ + g r ( A − B ) ρ + λg r (cid:16) ρ − µ λ (cid:17) + g g (cid:48) ( r ˙ B ) + ( r ˙ A ) + f A (cid:21) (32)Here, first of all, we see the energy must diverge. The integral of the first term inthe integrand, which arises from the magnetic term (cid:82) ( (cid:126) ∇ × (cid:126)B ) , is divergent, andall of the other terms are positive semi-definite. The first, divergent term thereforeprovides a lower found on the energy. . The minimum energy configuration is foundby the simplest ansatz there all of the other terms in the energy vanish, that is,where A = B = 0, f = 1 and ρ = µ/ √ λ and where the only nonzero field is B i ( r ) = g (cid:48) (1 − cos θ ) ∇ i ϕ (33)This classical field is very similar to the Dirac monopole. However, as Cho andMaison pointed out [14], due to the way that the electromagnetic charge arisesfrom an SU(2) weight, it must have an even number of units of Dirac monopolecharge in general and two units in this specific case.The divergence of the energy is due to the point-like nature of the monopole. Itshould be resolved by an ultraviolet regularization. One would naively expect thatthis would make the first term in the energy proportional to the ultraviolet cutoff,which would obtain its scale from physics beyond the standard model, and makingthe monopole mass very large. However, there are some suggestions for resolution ofthis singularity which would result in lighter monopoles, with masses in the rangeof multi-TeV.This divergence may be regularised by new physics beyond the Standard Model,which would lead to an effective ultraviolet cutoff Λ (cid:38) E ∼ Λ α , (34) where α is the fine structure constant. Because α (cid:28)
1, this would appear to implythat the mass of a magnetic monopole would have to be significantly higher thanthe energy scale Λ of new physics. This would set a lower limit of several TeV forthe monopole mass. One would also generally expect that the same physics thatcuts off the divergence also predicts other new particles with masses m ∼ Λ whichhave not been seen at the LHC yet.However, comparison with the renormalisation of other particle masses in quan-tum field theory suggests that the estimate (34) may not be relevant. The sameargument, when applied to the electric field of the electron, would suggest that itsmass should have an ultraviolet divergence ∼ e Λ, but a proper quantum field the-ory calculation shows that because of chiral symmetry the actual divergence is onlylogarithmic ∼ e m log Λ /m . Furthermore, the ultraviolet divergence is actually can-celled by the bare mass (or the mass counterterm) of the particle. As a result, thefermion masses in the Standard Model are free parameters, not determined by thetheory. If the same applies to magnetic monopoles, then it means that the physicalmonopole mass may be related to the scale of new physics Λ in a different way, ornot at all, and could be significantly lower. In particular, monopoles may then belight enough to be produced at the LHC.A complete quantum field theory calculation of the monopole mass requires aformulation with dynamical magnetic monopoles, instead of the above treatmentin which the monopole appears as a static, classical object. The Standard Modelitself does not contain magnetic monopoles, but it may be possible to add themas additional elementary degrees of freedom. However, this has turned out to bevery difficult to do in practice, even in the simpler theory of quantum electrody-namics [112], [113], [114]. The formulation requires two vector potentials and is notmanifestly Lorentz invariant, although physical observables are Lorentz invariant ifthe charges satisfy the quantisation condition (23). Even if these problems with theformulation of the theory are overcome, any quantum field theory in which mag-netic monopoles appear as dynamical particles will also suffer from the practicalproblem that their coupling to the electromagnetic field is strong. The loop expan-sion would give a power series in α M , and would therefore not converge, makingperturbation theory inapplicable. The full calculation will therefore require non-perturbative techniques such as lattice field theory simulations.5.2.2. The Cho-Maison Mass Estimate
There is no ’t Hooft-Polyakov monopole within the SM, because of the trivial topol-ogy of the quotient group SU (2) × U (1) Y /U (1) EM after the spontaneous symmetrybreaking of SU (2) × U (1) Y → U EM (1). Such a quotient group space does not possessthe non-trivial second homotopy required for the existence of ’t Hooft-Polyakov-likemonopole solutions.However, Cho and Maison [14] suggested that the SM could be viewed as agauged CP model, with the Higgs doublet field interpreted as the CP field. This would be an extension of our view of the SM. It would bypass the previous argumentof the trivial group-space topology, since the second homotopy group of the gauged CP model is the same as that of the Georgi-Glashow model that contains the ’tHooft-Polyakov monopole.The Cho-Maison monopole can therefore be seen as a hybrid between the ’tHooft-Polyakov and Dirac monopoles. Unlike the Dirac monopole, it would carrymagnetic charge (4 π ) /e because the U (1) EM in the SM has a period of 4 π , not2 π , as it comes from the U (1) subgroup of SU (2). The SU (2) part of the Cho-Maison monopole is finite, like the ‘t Hooft- Polyakov monopole, whereas its U (1)part (corresponding to the U (1) EM gauge field) has a real Dirac monopole-likesingularity at the origin. This singularity is responsible for the fact that its massis indeterminate, whereas the ’t Hooft-Polyakov monopole has a finite total energy,thanks to the EW gauge group being embedded in a simple unified gauge group.Recently, an estimate of the mass of the Electroweak monopole has beenmade [19], based on the assumption that the monopole is a topological soliton. Suchsolitons are topologically non-trivial field configurations that are characterized byfinite total energy. When representing the Cho-Maison monopole as a topologicalsoliton, it is necessary to regularize the solution by means of a cut-off representingphysics beyond the SM that eliminates the short distance singularity due to theAbelian gauge field configuration at the origin. The procedure adopted was to cre-ate an effective theory by embedding the electroweak theory in another microscopicmodel. The authors asserted that such a finite-total-energy soliton must be stableunder a rescaling of its field configuration, according to Derrick’s theorem [115]. Thisimplies that one could consider a simple scale transformation of the coordinates, (cid:126)x → λ (cid:48) (cid:126)x , under which the stable monopole configuration should satisfy certain re-lationships among its constituent quantities pertaining to spatial integrals of thevarious field configurations that enter the solution.However there are some subtle requirements that the cut-off theory has to satisfyin order for such mass estimates to be correct, which we outline now. To this end,we first remark that, in the notation of [19], the total SM contribution to the energy(and hence mass) of the monopole is the sum of four contributions E = K A + K B + K φ + V φ , (35)where K A , K B and K φ stand for the kinetic energies of the non-Abelian gauge field A µ , the Abelian gauge field B µ and the Higgs field φ respectively, while V φ is theHiggs potential energy: K A = 14 (cid:90) d x (cid:126)F ij , K B = 14 (cid:90) d x G ij (36) K φ = (cid:90) d x | D i φ | , V φ = (cid:90) d x V ( φ ) . For the spherically-symmetric Cho-Maison monopole configuration, K A , K φ and V φ are finite, and K B is expressed as an integral which, as mentioned previously, has a short distance ultraviolet (UV) singularity at r = 0, which is regularizedby introducing a short-distance cut off (cid:15) . The scaling properties of the cut-off arecrucial in ensuring that the energy satisfies Derrick’s theorem and is independentof the coordinate scale factor λ (cid:48) . To see this, one needs to calculate explicitly thecontribution K B for the Cho-Maison monopole: one obtains K B = 14 (cid:90) r sin θ dr dθ dϕ G ij = πg (cid:48) (cid:90) ∞ (cid:15) drr = πg (cid:48) (cid:15) . (37)We next introduce the coordinate rescaling (cid:126)r → λ (cid:48) (cid:126)r , under which scalar, vector andtensor quantities scale as φ ( (cid:126)r ) → φ ( λ (cid:48) (cid:126)r ) , B i ( (cid:126)r ) → λ (cid:48) B i ( λ (cid:48) (cid:126)r ) , G ij ( (cid:126)r ) → λ (cid:48) G ij ( λ (cid:48) (cid:126)r ) , (38)We then impose the requirement that the domain of space integration be scale-invariant (which, in view of Derrick’s theorem [115] would also imply that the energydensity, not only the energy, would be invariant in the vicinity of λ (cid:48) (cid:39) (cid:15) → (cid:15)/λ (cid:48) . (39)In this case, K B → ˜ K B = λ (cid:48) (cid:82) ∞ (cid:15)/λ (cid:48) r dr (cid:82) sin θ dθ dφ G ij ( λ (cid:48) (cid:126)r ) , (40)which, by means of a change of variable, leads to˜ K B = λ (cid:48) (cid:82) ∞ (cid:15) r dr (cid:82) sin θ dθ dφ G ij ( (cid:126)r ) = λ (cid:48) K B . (41)The other three contributions K A , K φ , V φ are finite and thus cut-off independent,and therefore are trivially rescaled as K A → ˜ K A = λ (cid:48) K A , K φ → ˜ K φ = ( λ (cid:48) ) − K φ , V φ → ˜ V φ = ( λ (cid:48) ) − V φ , (42)so that the energy (35) is rescaled as E → ˜ E = λ (cid:48) K A + λ (cid:48) K B + ( λ (cid:48) ) − K φ + ( λ (cid:48) ) − V φ . (43)Derrick’s scaling argument [115] consists then in imposing that the energy ˜ E belocally invariant in the vicinity of λ (cid:48) = 1: ∂ ˜ E∂λ (cid:48) (cid:12)(cid:12)(cid:12) λ (cid:48) =1 = 0 , (44)which leads to the relation found in [19] K A + K B = K φ + 3 V φ . (45)This relation allows for the quantity K B to be expressed in terms of the finitequantities K A , K φ , V φ , in a manner independent of its regularization, and leads toan estimate of a few TeV for the monopole mass, following the analysis in Ref. [19].After regularization the initially divergent quantity K B becomes dependent on thecutoff energy itself. Thus, since the K B is expressed in terms of three other finitequantities which are estimated to be of order TeV, then this implies that the cutoff must also be of order TeV. How this regularization can be achieved microscopicallyis being actively investigated.If one accepts the above scaling arguments, the total energy of the Cho-Maisonsoliton depends on quantities that can be calculated using SM data, such as theweak mixing angle, the W -boson mass and the mass of the Higgs-like boson, m H (cid:39)
125 GeV, discovered at the LHC in 2012 [106, 107]. Using these and otherwell-established parameters, the total energy of the EW monopole was estimatedin [19] to be E ∼ . · M W /α em (cid:39) .
85 TeV, where α em is the electromagnetic finestructure constant. Thus, the mass of the monopole depends on the mechanism ofspontaneous symmetry breaking that gives masses to the weak gauge bosons. Thenon-perturbative nature of the monopole is clearly identified by the inverse relation-ship between its mass and the electromagnetic fine structure constant (coupling).We note, however, that this estimate does not include quantum corrections,which lead to renormalization of the couplings of the SM, requiring counterterms inthe Lagrangian to take into account such corrections. The SM is a perturbativelyrenormalizable theory and this can be done, but only order by order in the couplings.However, monopoles are non-perturbative solutions of the theory, where all quantumcorrections must be resummed. Since the complete set of quantum corrections is notknown, their effect on the energy of the EW monopole is also unknown.Other theoretical arguments have been used [19,116] to provide alternative esti-mates of the EW monopole mass. These involve adding higher dimensional operatorsto the SM Lagrangian. Additional operators in the Lagrangian result in additionalterms in the field equations and there are a few scenarios where the new equationshave regular solutions with masses in the 1-10 TeV range. Whether the additionaloperators that are needed for this are allowed by SM phenomenology, particularlythe constraints imposed by precision electroweak measurements, is a question thatis yet to be studied in detail.5.2.3. Singularity resolution within string/brane theory
There is another possibility for singularity resolution which occurs in bottom upstring theory constructions of SM-like gauge theories [117]. These are found by en-gineering configurations of D-branes whose low energy degrees of freedom are thoseof a gauge field theory resembling the standard model. Verlinde has argued that,in the context of these constructions, string compactifications with D-branes mayexhibit regular magnetic monopole solutions [118]. These solutions have the novelaspect that their presence does not rely on broken non-abelian gauge symmetry.Moreover, these stringy monopoles exist on interesting metastable brane configura-tions, such as anti-D3 branes inside a flux compactification or D5-branes wrapping2-cycles that are locally stable but globally trivial. Further to this, Verlinde findsthat, in brane realizations of SM-like gauge theories, the monopoles carry one unitof magnetic hypercharge. He argues that their mass can range from the string scaledown to the multi-TeV regime and give some arguments about how they can be light even in the 1-10 TeV range.Independent of the above detailed arguments on the mass of the EW monopole,there is a simple qualitative argument that is consistent with the above estimate.Roughly speaking, the mass of an EW monopole should receive a contribution fromthe same mechanism that generates the mass of the weak bosons, except that thecoupling is given by the monopole charge. This means that the monopole massshould be of the order of M W /α em (cid:39)
10 TeV, where α em is the electromagneticfine structure constant.Thus, the LHC could be the first collider to produce EW monopoles. However,the monopole-antimonopole pair production rate at LHC is quite uncertain, andcurrently the subject of further study. If the production rate were to exceed thatfor W W production above the threshold energy, the MoEDAL experiment shouldeasily be able to detect the EW monopole, if it is kinematically accessible.5.2.4.
Electroweak strings
In addition to the electroweak monopoles discussed in the previous Section, thereare other defect solutions commonly known as electroweak strings. We recall thata topological defect is classified by the vacuum manifold, denoted by M , andhomotopy groups. Topological monopoles can exist only if the homotopy group π ( M ) (cid:54) = Identity . It has more recently been emphasized that, for certain pa-rameter ranges, a simply-connected M does not necessarily imply the absence ofdefects that are stable when the model has both global and gauge symmetries [17].Within the context of the SM, Nambu [9] realized this a long time ago and made theinteresting suggestion that such electroweak strings should, for energetic reasons,terminate in a (Nambu) monopole and anti-monopole at either end. Certainly, themonopole and antimonopole would tend to annihilate, whilst rotation would ob-struct longitudinal collapse.” An example is the Z -string that carries the flux of the Z boson.Furthermore, Nambu estimated that such dumbbell-like configurations couldhave masses in the TeV range. Given the energy range of the LHC this early sug-gestion can take on new interest. Independently, this suggestion has resurfaced at atheoretical level through primarily the work of Achucarro and Vachaspati [17] whocoined the phrase “semilocal strings” for such non-topological strings. The defectsthey consider are stable, not for topological reasons, but due to the interactions oftheir constituents, the scalar and gauge fields. We consider such defects if they areof finite energy.The Nambu monopole is estimated to have a mass, M N , whose order of magni-tude is given by [9] M N (cid:39) π e sin / θ W (cid:114) m H m W µ, (46)where µ = m W /g , g is the SU (2) gauge coupling, m W is the W boson mass, and m H is the Higgs mass. From the recent experimental results on the Higgs boson mass, we obtain M N (cid:39)
689 GeV. Just like isolated monopoles, the Nambu monopolesatisfies the Dirac quantization condition. The dumbbell structures can rotate andso emit electromagnetic radiation. The lifetime of such dumbbells is greater thanthe non-spinning variety, and might be long enough to be observed at energiesgreater than 7 TeV, but instabilities of the connecting Z − string may decrease thelifetime [119]. Vacuum decay and light ’t Hooft-Polyakov monopoles
When ’t Hooft [6] and Polyakov [7] independently discovered that the SO (3) Georgi-Glashow model [120] inevitably contains monopole solutions, they further realizedthat any model of unification with an electromagnetic U (1) subgroup embedded intoa semi-simple gauge group that is spontaneously broken by the Higgs mechanismpossesses monopole solutions. This mechanism leads, however, to a mass propor-tional to the vector meson mass arising from the spontaneous broken symmetry: ∼ M W /α em , α em being the fine structure constant at the breaking scale, i.e., theGUT scale.Vacuum metastabilities may exist at GUT scales, and appear for particularchoices of the effective potential. The Higgs minimum remains, but a second lowerminimum appears which allows a vacuum decay. This type of modification, seeFig. 11, can lead to a smaller monopole mass. Fig. 11. The curves show the effective potential for (cid:15) = 1 and µ = − . − . − . The energy density is defined as E ( (cid:15), µ ) = M W α em f ( (cid:15), µ ) , (47)where the function f ( (cid:15), µ ) characterizes the dynamics. For convenience we will fix (cid:15) = 1 and study the variation of f with µ for fixed (cid:15) [121]. The qualitative featuresof our analysis extend to any (cid:15) . The result of the calculation for the potential density in Fig. 11 with differentvalues of µ is shown in Fig. 12. It is apparent that the region of interest is around µ ∼ − .
5, and we see that the potential in Fig. 11 has an inflection point at φ/φ = 1 for µ = − .
5. For values of − . < µ < φ/φ = 1 and is bounded for large fields. For µ < − . φ/φ < φ/φ >
1. The solution then is ill-defined, i.e. themonopole solution is absent [121].
Fig. 12. The function f (1 , µ ) for the potential in Fig. 11 as a function of µ . The function has asingularity at µ = − .
5. For this value the minimum transforms into an inflection point.
The region of interest is therefore µ > − .
5, where the potential modificationleads to a reduction of the energy density producing a slightly smaller mass, but mostimportantly, the Higgs minimum remains, and a second lower minimum appearswhich allows a quantum vacuum decay. The original (false) Higgs vacuum decaysinto a new (true) vacuum of lower energy. This decay is by bubble formation and weenvisage a scenario in which small bubbles of true vacuum containing a monopolesurrounded by larger ones of false vacuum, represent a decaying monopole witheffective masses ranging from its GUT mass to zero (see Fig. 13). A new scaleenters the description, the size of the bubble, which can easily compensate for theGUT scale.
Monopolium
In the absence of uncontroversial evidence for the existence of magnetic monopoles,most assume that, if magnetic monopoles do exist, their mass is too great and/ortheir abundance is too small for them to be detected in cosmic rays or at existingaccelerators. However, Dirac proposed an alternate explanation why monopoles havenot been conclusively observed so far [5, 122]. His idea was that monopoles are notseen freely because they are confined by their strong magnetic forces in monopole -anti-monopole bound states called monopolium [123, 124]. f as a function of bubble radius R for (cid:15) = 1 and µ = 0 . Some researchers have proposed that monopolium, due to its bound-state struc-ture, might be easier to detect than free monopoles [125,126], and the possibility thatthe LHC might be able to discover monopolium has been advocated in [125–127].Monopolium is a neutral state, and is therefore difficult to detect directly in a col-lider detector, although its decay into two photons would give a very nice signalfor the ATLAS and CMS detectors [127] that is not visible in the MoEDAL detec-tor. We discuss here possible scenarios in which monopolium could be seen by theMoEDAL experiment.The production of monopolium at LHC, namely: p + p → p ( X ) + p ( X ) + M (48)would be expected to occur predominantly via photon fusion, as shown in Fig. 14,where p represents the proton, γ the photon, X an unknown final state and M themonopolium. This diagram summarizes the three possible processes:i) inelastic p + p → X + X + ( γγ ) → X + X + M ii) semi-elastic p + p → p + X + ( γγ ) → p + X + M iii) elastic p + p → p + p + ( γγ ) → p + p + M .In inelastic scattering, both intermediate photons are radiated from partons(quarks or antiquarks) in the colliding protons. In the semi-elastic scattering caseone intermediate photon is radiated by a quark (or antiquark), as in the inelasticprocess, while the second photon is radiated coherently from the other proton,coupling to the total proton charge and leaving a final-state proton intact. In theelastic scattering case, both intermediate photons are radiated from the interactingprotons leaving both protons intact in the final state. The full γγ calculation includescontributions from these three individual regimes.For the case of monopole interactions at energies higher than their mass thereis no universally accepted effective field theory [112, 128, 129]. We will employ a minimal model of monopole interaction which assumes an effective monopole-photoncoupling that is proportional to gβ for a monopole moving with velocity β [127,130–132]. The elementary subprocess calculated is shown in Fig. 15. Since the Diracquantization condition does not specify the spin of the monopoles, we choose heremonopoles of spin 1 / s -waveradial structure with minimal energy. Fig. 15. Diagrammatic description of the elementary subprocess for monopolium production fromphoton fusion, where V ( r ) represents the interaction binding the monopole-antimonopole pair toform monopolium. The standard expression for the cross section of the elementary subprocess forproducing monopolium of mass M and width Γ M is given by: σ (2 γ → M ) = 4 πE M Γ( E ) Γ M ( E − M ) + M Γ M , (49)where Γ( E ), with E off mass shell, describes the production cross section. In thesmall binding limit the width Γ( E ) is proportional to β and therefore monopoliumcan be very long lived close to threshold [120] [121] since Γ M arises from the softeningof the delta function, δ ( E − M ) and is therefore, in principle, independent of theproduction rate Γ( E ) and can be attributed to the beam width [133, 134].In Fig. 16 we show the total cross section for monopolium production fromphoton fusion under future LHC running conditions, i.e. a center-of-mass energy of
14 TeV, for a monopole mass ( m ) ranging from 500 to 1000 GeV. In the figure thebinding energy is fixed for each mass (2 m/ m = 750 GeV, the binding energy is 100 GeV and thus M = 1400 GeV. Withthis choice the monopolium mass ( M ) ranges from 933 to 1866 GeV. We note thatdetection with present integrated luminosities is possible even for binding energiesbelow 10% of its mass. Fig. 16. Total cross section for monopolium production at LHC with 7 TeV beams for monopolemasses ranging from 500 to 1000 GeV (full curve). The broken curves represent the differentcontributions to the total cross section as described in the text: semielastic (dashed), elastic (shorstdashed) and inelastic (dotted). We have chosen a binding energy ∼ m/
15 and Γ M = 10 GeV. Monopolium in its ground state is a very heavy neutral object, and thus theonly property suitable to be detected is its heavy mass via collisions with thelarge molecules of the detector. This mechanism is not very effective. However,the monopolium ground state has a very large magnetic polarizability d ∼ r M B ∼ ( αE binding ) − B , where r M is the monopolium size. The presence of large magneticfields might provide the monopolium ground state with sufficient magnetic strengthto be able to ionize the detector medium. However, in the vicinity of the MoEDALdetector there are only very weak stray fields from the LHCb dipole magnet.On the other hand, the binding of monopole-antimonopole pairs might occurin excited states. If those states have angular momentum they will be magneticmultipoles that will be strongly-ionizing and thus directly detectable. Moreover,their decay into lower-lying multipole states will show a peculiar structure of thetrajectory in the detector medium (see Fig. 17(a)) which would be easy to isolatefrom other background trajectories. If the lifetime is governed by the the β -schemethe lifetime of these states will be long enough to be detectable by MoEDAL.Finally, if monopolium is weakly bound or produced in a highly-excited boundstate, the presence of electrons and protons in the medium might allow for the for-mations of dyons (see Fig. 17(b)). Dyons are highly-ionizing particles and thereforeMoEDAL will detect a very clear signal (see Fig. 17(c)). M in excited state (b) Dyon production (c) Di-dyon signatureFig. 17. Monopolium may be produced in excited state that might be a magnetic multipole andthus will be highly ionizing. Its cascade decay via (undetected) photon emission will lead to apeculiar trajectory in the medium. (a) The circle encloses the expected observation consisting ofa —probably curved— polyhedric trajectory. In another case study, a monopolium in the mediummight break up into highly-ionizing dyons (b) producing a very clear di-dyon signal (c). Summary of accelerator experiments
If the monopole mass M is less than half of the centre-of-mass energy in a particlecollision, it is kinematically possible to produce a monopole-antimonopole pair.In particular, production of Cho-Maison monopoles with mass 4 − σ , rather than as lower bounds on the mass. Even these bounds depend onassumptions about the kinematic distributions of the produced particles, which isusually assumed to be the same as for the Drell-Yan pair-production process [136].During the last twenty years collider searches for magnetic monopoles particleshave been made with dedicated MODAL [137] and OPAL monopole detector [138] atLEP [139]. The best LEP limits for magnetic monopole pair production, where themonopoles have single Dirac charge, are as follows. The OPAL experiment at LEPgave an upper bound σ < .
05 pb for the mass range 45 GeV < M <
102 GeV [140]in electron-positron collisions. The CDF experiment at the Tevatron [141] yieldedthe limits σ < . < M <
700 GeV in proton-antiproton col-lisions. Rather than identifying the highly ionizing nature of the monopole theH1 experiment at HERA sought monopoles trapped in the HERA beam pipe.Upper limits on the monopole pair production cross section have been set formonopoles with magnetic charges from 1 to 6g D or more and up to a mass of140 GeV [76]. Most recently, ATLAS placed an upper bound σ <
16 - 145 fb formasses 200 GeV < M < principle.Because the monopoles are large non-perturbative objects which carry a largenumber n ∼ /α of quanta, it has been argued [143,144] that their production crosssection would be suppressed by an exponential factor exp( − /α ), and numerical cal-culations for kinks in (1+1)-dimensional scalar theory support this finding [145,146].This would mean that monopoles would practically never be produced in particlecollisions, even if they are kinematically allowed. However, these semiclassical cal-culations are only valid for monopoles at weak coupling and do not apply to othertypes, such as TeV-scale Cho-Maison monopoles.
6. Electrically-Charged Massive (Meta-)Stable Particles inSupersymmetric Scenarios
As has been discussed above, massive slowly moving ( β (cid:46)
5) electrically chargedparticles are potential highly ionizing avatars of new physics. If they are sufficientlylong-lived to travel a distance of at least O (1)m before decaying and their ˆ Z/β (cid:38) . (cid:96) , quarks and squarks ˜ q , the photon and photino γ , gluons and gluinos˜ g [23]. No highly-charged particles are expected in such a theory, but there areseveral scenarios in which supersymmetry may yield massive, long-lived particlesthat could have electric charges ±
1, potentially detectable in MoEDAL if they areproduced with low velocities.In the minimal supersymmetric extension of the Standard Model (MSSM) [24],the gauge couplings g are the same as in the Standard Model, and there are Yukawainteractions λ related to quark and lepton masses. The sensitivities to the productionof different sparticle species vary as functions of the LHC center-of-mass energy inthe manner shown in Fig. 18. We see, for example, that the sensitivity to direct pro-duction of a pair of stop squarks ˜ t extends to 800 GeV with 100 fb − (= 10 pb − )of data at 14 TeV [147].One complication is that in supersymmetric models there must be two Higgsdoublets, one responsible for the masses of charge 2 / − / µ , and unknown ratio of their vac-uum expectation values, called tan β . In addition, there are a multitude of unknownsupersymmetry-breaking parameters, including scalar masses m , gaugino masses m / , trilinear soft couplings A λ , and a bilinear soft coupling B µ . For simplicity, andmotivated by the agreement of rare and flavor-changing processes with StandardModel predictions, it is often assumed that these parameters are universal, i.e. thereis a single m , a single m / , and a single A λ at some high input renormalizationscale. This scenario is called the constrained MSSM (CMSSM) [25–32]. Later we consider variants in which the soft supersymmetry-breaking contributions to theHiggs masses are allowed to be non-universal (the NUHM) [148].The lightest supersymmetric particle (LSP) is stable in many models becauseof conservation of R parity, where R ≡ ( − S − L +3 B , where S is spin, L is leptonnumber, and B is baryon number [149]. It is easy to check that particles have R = +1and sparticles would have R = −
1. Hence, sparticles would be produced in pairs,heavier sparticles would decay into lighter sparticles, and the LSP would be stablebecause it has no allowed decay mode, and hence present in the Universe today asa relic from the Big Bang [150]. The LSP should have no strong or electromagneticinteractions, for otherwise it would bind to conventional matter and be detectablein anomalous heavy nuclei [150]. Possible weakly-interacting neutral scandidatesin the MSSM include the sneutrino, which has been excluded by LEP and directsearches, the lightest neutralino χ (a mixture of spartners of the Z, H and γ ) andthe gravitino, which would be a nightmare for astrophysical detection, but not inconflict with any experimental limits.On the basis of the above discussion, we can identify several scenarios featur-ing metastable charged sparticles that might be detectable in MoEDAL. One suchscenario is that R parity may not be exact [33], in which case the LSP would bean unstable sparticle, and might be charged and/or coloured. In the former case, itmight be detectable directly at the LHC as a massive slowly-moving charged parti-cle. In the latter case, the LSP would bind with light quarks and/or gluons to make colour-singlet states, and any charged state could again be detectable as a massiveslowly-moving charged particle.However, even if R parity is exact, the next-to-lightest sparticle (NLSP) maybe long-lived. This would occur, for example, if the LSP is the gravitino, or ifthe mass difference between the NLSP and the neutralino LSP is small, offeringmore scenarios for long-lived charged sparticles. The experimental signatures of R -violating scenarios are generically similar to those in the R -parity conservingscenarios that we now discuss.In neutralino dark matter scenarios based on the CMSSM the most naturalcandidate for the NLSP is the lighter stau slepton ˜ τ [151], which could be long-livedif m ˜ τ − m χ is small. In gravitino dark matter scenarios with more general optionsfor the pattern of supersymmetry breaking, other options appear quite naturally,including the lighter selectron or smuon, or a sneutrino [152], or the lighter stopsquark ˜ t [153]. Another possibility in models with split supersymmetry would bethe gluino, whose lightest bound state might be charged. In all these cases, the NLSPwould be naturally very long-lived, with a decay interaction of near-gravitationalstrength.In subsequent Sections we discuss each of these scenarios in more detail. Beforedoing so, we make one general comment: it is a general feature of these scenarios thatthere is a range of sparticle lifetimes, typically O (10 ) s, where the bound-state dy-namics and decays of metastable charged sparticles may serve a useful cosmologicalpurpose, in improving the agreement of Big-Bang Nucleosynthesis calculations withmeasurements of the cosmological Li abundance without upsetting agreement withthe measured abundances of the other light elements [154–164]. This may provideadditional motivation for studying in more detail scenarios for metastable chargedsparticles.
Metastable lepton NLSP in the CMSSM with a neutralinoLSP
We first consider the most constrained supersymmetric scenario, namely a stauNLSP in the CMSSM with a neutralino LSP, which is rather a natural possibility.We recall that there are several regions of the CMSSM parameter space that arecompatible with the constraints imposed by unsuccessful searches for sparticles atthe LHC, as well as the discovery of a Higgs boson weighing ∼
126 GeV [106, 107].These include a strip in the focus-point region where the relic density of the LSP isbrought down into the range allowed by astrophysics and cosmology because of itsrelatively large Higgsino component, a region where the relic density is controlled byrapid annihilation through direct-channel heavy Higgs resonances, and a strip wherethe relic LSP density is reduced by coannihilations with near-degenerate staus andother sleptons. It was found in a global analysis that the two latter possibilities arefavored [165, 166].In the coannihilation region of the CMSSM, the lighter ˜ τ is expected to be the lightest slepton [151], and the ˜ τ − ˜ χ mass difference may well be smaller than m τ :indeed, this is required at large LSP masses. In this case, the dominant stau decaysfor m ˜ τ − m ˜ χ >
160 MeV are expected to be into three particles: ˜ χ νπ or ˜ χ νρ .If m ˜ τ − m ˜ χ < . τ lifetime is calculated to be so long, in excess of ∼
100 ns, that it is likely to escape the detector before decaying, and hence wouldbe detectable as a massive, slowly-moving charged particle [167]. The stau lifetimeas a function of m ˜ τ − m ˜ χ for typical supersymmetric model parameters is shownin the left panel of Fig. 19, and the right panel displays a typical pattern of decaybranching ratios [168]. Three-body decays such as ˜ τ → ˜ χ + ν + π are importantif m ˜ τ − m ˜ χ > m π , whereas four-body decays ˜ τ → ˜ χ + ν + ¯ ν + e/µ dominate if m ˜ τ − m ˜ χ < m π . Fig. 19. Left panel: The ˜ τ lifetime calculated for m ˜ τ = 300 GeV and a ˜ τ L − ˜ τ R mixing angle θ τ = π/
3, as a function of ∆ m ≡ m ˜ τ − m ˜ χ over the range 10 MeV < ∆ m <
10 GeV, where thelifetime is between ∼ and ∼ − s [168]. Right panel: The principal ˜ τ branching ratioscalculated for the same model parameters, as functions of ∆ m ≡ m ˜ τ − m ˜ χ for 100 MeV < ∆ m < τ , a (1260), ρ (770), π , µ , and e , respectively, indicated by the labels adjacent to the correspondingcurves. The vertical dashed lines correspond to the τ , a , ρ , π and µ masses, as indicated by thelabels on the top of the panels. Metastable sleptons in gravitino LSP scenarios
The above discussion is for the case of a neutralino LSP. If the gravitino ˜ G is theLSP, the decay rate of a slepton NLSP is given byΓ(˜ (cid:96) → ˜ G(cid:96) ) = 148 π ˜ M m (cid:96) M G (cid:34) − M G m (cid:96) (cid:35) , (50)where ˜ M is the Planck scale. Since ˜ M is much larger than the electroweak scale,the NLSP lifetime is naturally very long, as seen in Fig. 20 [169].There are many possibilities for the NLSP in scenarios with a gravitino LSP,some of which are illustrated in Fig. 21 [152]. This displays a ( µ, m A ) plane in avariant of the MSSM with universal input squark and slepton masses m = 100 GeVand gaugino masses m / = 500 GeV, tan β = 10, A = 0 and non-universal soft m ˜ τ and the gravitino mass m ˜ G [169]. supersymmetry-breaking contributions to the Higgs boson masses (the NUHM).We see different regions of the plane where the NLSP would be the lighter stau(coloured orange), the lighter selectron (yellow), the tau sneutrino (lighter blue) orthe electron sneutrino (darker blue). Metastable stop squark scenarios
There are also scenarios in which the NLSP is the lighter stop squark, ˜ t [153],though these are more tightly constrained, in particular since the LHC has estab-lished stronger lower limits on a metastable ˜ t mass because of its larger productioncross section. Three scenarios can be envisaged for stop decays:(1) Case 1: m ˜ t − m (cid:101) G > m t , i.e., small m (cid:101) G < m ˜ t − m t . In this case, the stop candecay directly into a top quark and a gravitino, and the rate for this dominantdecay isΓ = 1192 π M m (cid:101) G m t (cid:104) (cid:16) m t − m (cid:101) G − m t (cid:17) + 20 sin θ ˜ t cos θ ˜ t m t m (cid:101) G (cid:105) × (cid:104) ( m t + m (cid:101) G − m t ) − m t m (cid:101) G (cid:105) (cid:104) ( m t + m t − m (cid:101) G ) − m t m t (cid:105) / . (51)This decay rate is similar to that for stau decay into tau plus gravitino (50), µ, m A ) plane in the NUHM with a gravitino LSP and universal input squarkand slepton masses m = 100 GeV, gaugino masses m / = 500 GeV, and tan β = 10, A = 0,illustrating different possibilities for the metastable NLSP: the lighter stau (coloured orange),the lighter selectron (yellow), the tau sneutrino (lighter blue) or the electron sneutrino (darkerblue) [152]. Regions favored by the supersymmetric interpretation of the g µ − b → sγ are shaded green. but in this case m t cannot be neglected. Typical values of the ˜ t lifetime in thiscase are displayed in the left panel of Fig. 22.(2) Case 2: m W + m b < m ˜ t − m ˜ G < m t . In this case, the dominant decays are intothe three-body final state ˜ t → ˜ G + W + b . The formulae for the decay rate inthis case are quite complicated, and can be found in Ref. [153]. Typical valuesof the ˜ t lifetime in this case are displayed in the right panel of Fig. 22, wherewe see that they are typically much longer than in Case 1.(3) Case 3: m b + Λ QCD < m ˜ t − m ˜ G < m W + m b . In this case, the dominant decaysare four-body: ˜ t → ˜ G + b + ¯ qq or (cid:96)ν . The decay rate is further suppressedcompared to Case 2, and likely to exceed 10 s, in which case there would beimportant constraints from the CMB data, that have not been explored.The long-lived stop squark would hadronize immediately after production, form-ing a stop ‘mesino’ ˜ t − ¯ q or a stop ‘baryino’ ˜ t − qq , which might be either charged orneutral. As such stop hadrons pass through matter, they would in general changecharge by nuclear interactions, complicating track-finding in a conventional LHCdetector. There is no consensus on the charge of the lightest stop hadron, which θ ˜ t = 0 (solid red line) and π/ might be charged, and hence detectable by MoEDAL. Long-lived gluinos in split supersymmetry
The above discussion has been in the context of the CMSSM and similar scenarioswhere all the supersymmetric partners of Standard Model particles have masses inthe TeV range. Another scenario, suggested following the non-discovery of super-symmetric particles at LEP, is ‘split supersymmetry’, in which the supersymmetricpartners of quarks and leptons are very heavy whilst the supersymmetric partnersof Standard Model bosons are relatively light [170, 171]. In such a case, the gluinocould have a mass in the TeV range and hence be accessible to the LHC, but wouldhave a very long lifetime: τ ≈ (cid:16) m s GeV (cid:17) (cid:18) m ˜ g (cid:19) s . (52)Long-lived gluinos would form long-lived gluino hadrons, including gluino-gluon (gluinoball) combinations, gluino-¯ qq (mesino) combinations and gluino- qqq (baryino) combinations. The heavier gluino hadrons would be expected to decayinto the lightest species, which would be metastable, with a lifetime given by (52),and it is possible that this metastable gluino hadron could be charged.In the same way as stop hadrons, gluino hadrons may flip charge through con-ventional strong interactions as they pass through matter, and it is possible thatone may pass through most of a conventional LHC tracking detector undetectedin a neutral state before converting into a metastable charged state that could bedetected by MoEDAL. Supersymmetric scenarios with R -parity violation The supersymmetric scenarios discussed in the previous Sections are all in frame-works where R = ( − S − L +3 B is conserved. However, this may not be true ingeneral: there is no exact local symmetry associated with either L or B , and henceno fundamental reason why they should be conserved. Indeed, they are violatedin simple models for neutrino masses and grand unified theories, although in thesecases they are often violated in such a way that the particular combination appear-ing in R is conserved. In general, however, one could consider various ways in which L and/or B could be violated in such a way that R is violated, as represented bythe following superpotential terms [33]: W RV = λ (cid:48)(cid:48) ijk ¯ U i ¯ D j ¯ D k + λ (cid:48) ijk L i Q j ¯ D k + λ ijk L i L j ¯ E k + µ i L i H, (53)where Q i , ¯ U i , ¯ D i , L i and ¯ E i denote chiral superfields corresponding to quark dou-blets, antiquarks, lepton doublets and antileptons, respectively, with i, j, k gener-ation indices. The simultaneous presence of terms of the first and third type in(53), namely λ and λ (cid:48)(cid:48) , is severely restricted by lower limits on the proton lifetime,but other combinations are less restricted. The trilinear couplings in (53) generatesparticle decays such as ˜ q → ¯ q ¯ q or q(cid:96) , or ˜ (cid:96) → (cid:96)(cid:96) , whereas the bilinear couplings in(53) generate Higgs-slepton mixing and thereby also ˜ q → q(cid:96) and ˜ (cid:96) → (cid:96)(cid:96) decays. Fora nominal sparticle mass ∼ λ, λ (cid:48) , λ (cid:48)(cid:48) < − . As already mentioned, there is no strong reasonwhy any of these couplings should vanish, but equally there is no strong reason toexpect any non-zero couplings within this range.If λ ijk (cid:54) = 0, the prospective experimental signature would be similar to thestau NLSP case that was discussed earlier. On the other hand, if λ (cid:48) or λ (cid:48)(cid:48) (cid:54) = 0, theprospective experimental signature would be similar to the stop NLSP case that wasalso discussed earlier, yielding the possibility of charge-changing interactions whilepassing through matter. This could yield a metastable charged particle, createdwhilst passing through the material surrounding the intersection point, that wouldbe detected by MoEDAL. Heavy sleptons from Gauge Mediated SupersymmetryBreaking scenarios
In the Gauge Mediated Supersymmetry Breaking (GMSB) scenario [172–177] su-persymmetry is broken at a low scale, within a few orders of magnitude of the weakscale and the Standard Model gauge interactions serve as ‘messengers’ of super-symmetry breaking, giving rise to a high degree of degeneracy among squarks andsleptons. GMSB offers the the possibility of solving the flavor problem. Moreover,since the relevant dynamics occur at an energy scale much smaller than the Planckmass, GMSB models require no input from quantum gravity.In gauge-mediated theories the supersymmetric mass spectrum is determined interms of relatively few parameters. The most important parameter is Λ =
F/M , where M is the mass scale of the messenger fields, F the order of the mass-squaredsplittings inside the messenger supermultiplets and Λ sets the scale of supersym-metry breaking in the observable sector. The supersymmetric particle masses aretypically a one-loop factor smaller than Λ. Supersymmetric particle masses dependonly logarithmically on M . This scale can vary roughly between several tens of TeVand 10 GeV. The lower bound on M is determined by experimental results; theupper bound from the argument that contributions should be small enough not toreintroduce the flavor problem.In GMSB models the NLSP can be the lightest neutralino χ , the lightest stau˜ τ or, in a very small corner of parameter space, the lightest sneutrino. There is alsothe possibility of having co-NLSPs. This occurs when the mass difference betweenNLSP and co-NLSP is small enough to suppress the ordinary supersymmetric decayand when F is adequately low to allow for a sizeable decay rate into gravitinos.Candidates for co-NLSP include χ (with s ˜ τ NLSP), ˜ τ (with χ NLSP).From the NLSP decay rate [178] the average distance travelled by an NLSP withmass m and produced with energy E is: L = 1 κ γ (cid:18) m (cid:19) (cid:32) (cid:112) F/k (cid:33) (cid:114) E m − × − cm (54)where κ γ is 1 for the stau. Mainly depending on the unknown value of (cid:112) F/k , theNLSP can either decay within microscopic distances or decay well outside the solarsystem.For larger √ F , for √ F (cid:39) GeV, the NLSP lifetime is longer and the colliderphenomenology can resemble the well-known missing-energy supersymmetric signa-tures (for a neutralino NLSP) or can lead to a long-lived heavy charged particle (fora stau NLSP). This signature is quite novel, with a stable charged massive travers-ing the detector, leaving an anomalous ionization track. If the particle is sufficientlyslow it will be detected by MoEDAL.
Metastable charginos
In certain regions of parameter space, charginos — the superpartners of W -bosonsand/or charged Higgs bosons — can have lifetimes of order centimeters to meters.As such they may leave tracks inside MoEDAL and the other LHC detectors. Forinstance, this occurs when the LSP is the neutral wino i.e. the superpartner of theneutral W -boson. Such LSPs arise, for example, in ‘anomaly mediated supersym-metry breaking’ (AMSB) [179–181] and the G -MSSM model which derives fromstring/ M theory [182, 183].The neutral wino is part of an SU (2) triplet whose other two members are twocharginos: ˜ χ +1 and ˜ χ − . In the limit of exact SU (2) -symmetry all three winos aredegenerate in mass . This mass degeneracy can thus only be broken by the Higgssector. Often, the mass splitting is suppressed by couplings and one-loop effects, which are relatively small, typically leading to splittings of order one or two pionmasses (see Ref. [184] and references therein).The near degeneracy between ˜ χ +1 and ˜ χ leads to a striking prediction: that ˜ χ +1 can easily travel distances which range from centimetres to meters before decayinginto ˜ χ plus additional, low mass and momentum states which will either be apositron and neutrino pair or a charged pion. If, in addition, R-parity is violated,other decay modes may be significant.For ∆ M ˜ χ (cid:46) M π , ˜ χ +1 can easily travel a meter or more. If it does so the charginocan be distinguished as a heavy ionizing track (e.g., if βγ < .
85 the track will causean ionization at least twice that of a minimum ionizing particle (MIP)). This typeof long, heavily ionizing track signal will be detected by MoEDAL as long as itsionization is at least five times that of a MIP.We now discuss different production mechanisms for these charginos at the LHC.One such mechanism is for charged winos to arise in the decay products of gluinos.In many models with wino LSP, gluinos typically have masses which range from afew to ten times that of the wino due to renormalization group effects from highscales to the LHC scale. When the gluino mass is of order a few TeV or less, theycan be pair produced at the LHC and their subsequent decay products can ofteninclude ˜ χ +1 and/or ˜ χ − [185, 186]. This is typically simple when squark and sleptonmasses are out of the LHC reach as might be suggested by the measured value ofthe Higgs boson mass.Independently of the gluino channel, charged and neutral winos can be pro-duced through electroweak processes in the supersymmetric analogue of W -bosonpair production and W - Z -boson production at the LHC. Often, direct productionof ( ˜ χ +1 , ˜ χ − ) pairs and/or ( ˜ χ +1 , ˜ χ ) pairs can be the dominant production modeof supersymmetric particles with a larger cross section than gluino pair produc-tion. These channels are particularly interesting because MoEDAL has a distinctadvantage over ATLAS and CMS. Consider, for instance, the production of ( ˜ χ +1 ,˜ χ ) pairs. ˜ χ +1 decays to ˜ χ plus, say, a very soft pion. The pion is so soft that itwill never leave the magnetic field of the ATLAS or CMS inner detector leaving atrack which will be impossible to distinguish from other products of pp collision.Hence, effectively, the final state consists of two ˜ χ ’s which leave the detector with-out depositing any energy. Such events will not trigger ATLAS or CMS and so theobservation of such events requires associated production of additional high p T -jetsand/or charged leptons, thereby reducing the sensitivity. In MoEDAL by contrast,the mere presence of the chargino with sufficient ionization is enough to provide asignal.Another relevant class of models is Gaugino Anomaly Mediation [187]. Thisis a scenario of supersymmetry breaking suggested by the phenomenology of fluxcompactified type IIB string theory. The main element of this scenario is that thegaugino masses are of the anomaly-mediated SUSY breaking form, while scalar andtrilinear soft SUSY breaking terms are highly suppressed.Renormalization group effects give rise to an experimentally viable sparticle mass spectrum, while at the same time avoiding charged LSPs. SUSY-induced flavor andCP-violating processes are also suppressed since scalar and trilinear soft terms arehighly suppressed. Under these premises the lightest SUSY particle is the neutralwino, while the heaviest is the gluino.As far as LHC phenomenology is concerned in this scenario, there should bea strong multi-jet plus missing energy E missT signal from squark pair production.Also, a double mass edge from the opposite-sign/same flavor dilepton invariantmass distribution should be visible. Importantly, short - yet visible - highly ionizingtracks from quasi-stable charginos, which should provide a smoking-gun signaturefor Gaugino Anomaly Mediation, that would be detectable by MoEDAL.Charginos which are predominantly the superpartners of charged Higgs bosonscan also have suitably long lifetimes and these have been studied in Ref. [188]. The Fat Higgs model
The Fat Higgs [34] is a particular, interesting solution to the “supersymmetric littlehierarchy problem” [189]. It proposes an alternative to the standard MSSM pictureof electroweak symmetry breaking (EWSB) and results in a heavier ‘light’ CP-even Higgs than can be realized in that standard scenario, thus naturally evadingthe LEP-II bounds. A new variant of the Fat Higgs Model [190] has been produced,where the Higgs fields remain elementary, alleviating the supersymmetric fine-tuningproblem while maintaining unification in a natural way.A latest incarnation of the supersymmetric Fat Higgs model has been introducedin which the MSSM Higgs bosons and the top quark are composite [191]. Theunderlying theory is a confining SU (3) gauge theory with the MSSM gauge groupsrealized as gauged sub-groups of the chiral flavor symmetries. This motivates therequirement for a large top mass and SM-like Higgs of mass greater than that of the Z -boson in a natural way as the residual of the strong dynamics responsible for thecomposite fields. This solves the fine-tuning problem associated with these couplingspresent in the original Fat Higgs and ‘New Fat Higgs’ models, respectively.The model also has a number of additional chiral multiplets. The colored quarksinglets q and q have masses of order of the compositeness scale ( λ ) whereas thecolor neutral particles are expected to have masses of order 200 GeV. We expectthe lightest of these to be the singlet χ fields, with the slightly heavier charged( ± ) fields ( ψ ) to be be slightly heavier. The scalar components are expected to beslightly heavier than their fermionic partners due to SUSY-breaking contributionsto the scalar masses.The dynamically generated super-potential has a symmetry which has all of theexotic particles coupling in pairs. Since all of the exotic states must decay through q whose mass is of order a PeV, the exotics are typically very long lived and havecomplicated multi-particle final states. In the case of ψ this results in electricallycharged fermions and their scalar partners which are collider stable appearing asmassive charged objects. It is expected that the LHC will cover the entire parameter space [192]. XYons from 5D SUSY breaking
In a recently proposed 5D model [35] a general framework is presented for super-symmetric theories that do not suffer from fine tuning in electroweak symmetrybreaking. Supersymmetry is dynamically broken at a scale Λ ∼ (10 − SU (5) symmetry, whose SU (3) × SU (2) × U (1)subgroup is identified as the standard model gauge group. This SU (5) symmetryis dynamically broken at the scale Λ, leading to TeV scale exotic scalars with thequantum numbers of GUT XY bosons appear, the so-called XYons.If a condition analogous to R parity holds in the DSB, the Xyons, that havemulti-TeV mass, are long lived. Their precise quantum numbers depend on thedetails of the DSB; in general they are both colored and charged. In the simplest SU (5) case they lie in a colour triplet isospin doublet with electric charges Q = − / , − /
3, but also SO (10) assignments are possible, for example an additionaldoublet with Q = 1 / , − /
3, could easily be possible.The xyonic fermionic mesons are: ˜ T ≡ φ ↑ ¯ d , ˜ T − ≡ φ ↑ ¯ u, ˜ T (cid:48)− ≡ φ ↓ ¯( d ) and˜ T (cid:48)−− ≡ φ ↓ ¯ u . In the case of SU (5) XYons, the masses of these XYonic mesons(XYmesons) split due to the mass difference between φ ↑ and φ ↓ — XYmesonscontaining φ ↓ are heavier than those containing φ ↑ by about 600 MeV. This impliesthat ˜ T (cid:48)− ( ˜ T (cid:48)−− ) decays into ˜ T ( ˜ T − ) and a charged pion with the lifetime of abouta picosecond.The mass splitting between ˜ T and ˜ T − (and ˜ T (cid:48)− and ˜ T (cid:48)−− ) is of order a fewMeV, which comes from isospin breaking effects due to electromagnetic interactionsand the u − d mass difference. Because the two effects work in the opposite direction,it is not clear which of ˜ T and ˜ T − is lighter. The decay of the heavier into the lighterstate is through weak interactions with lifetime is of order 10 − to 10 seconds, sothat both ˜ T and ˜ T − are essentially stable for collider purposes. The multi-TeVmass of the charged XYmeson means that it is likely that will it be slow moving ahighly ionizing enough at the LHC to be detectable by MoEDAL.There are also bosonic baryons formed by XYons and the standard model quarks.The lightest states of these xyonic baryons (xybaryons) will come either from a (2 , U S ≡ φ ↑ [ u, d ] , ˜ U − S ≡ φ ↓ [ u, d ] , (55)or a (2 ,
3) vector multiplet˜ U + V ≡ φ ↑ uu, ˜ U V ≡ φ ↑ { ud } , ˜ U − V ≡ φ ↑ dd (56)˜ U (cid:48) V ≡ φ ↓ uu, ˜ U (cid:48)− V ≡ φ ↓ { ud } , ˜ U (cid:48)−− V ≡ φ ↓ dd (57)where {} and [] denote summarization and antisymmetrization, respectively. In the model described here [35] only the lighter of baryons ˜ U S and ˜ U + V , ˜ U V and ˜ U − V are collider stable particle(s) at colliders. The stability of these lighterXYbaryons is ensured by baryon number conservation. The charged baryons againwith multi-TeV masses leave highly-ionizing tracks so that they can be detectedrelatively easily by MoEDAL.There are also be other signals that can be used to detect XYons. When anti-XYmesons or XYbaryons traverse a detector they can exchange isospin and chargewith the background material through hadronic interactions, and so make transi-tions between neutral and charged states. This leaves a distinct signature of inter-mittent highly ionizing tracks which are detectable using MoEDAL. Current LHC limits on sparticles
SUSY searches in collider experiments involving promptly-decaying sparticles typ-ically focus on events with high transverse missing energy, arising from (weaklyinteracting) LSPs, in conjunction with no or few leptons ( e , µ ), many jets and/or b -jets, τ -leptons and photons. In the absence of deviations from SM predictions,lower bounds on sparticle masses have been set by ATLAS [193] and CMS [194] inseveral SUSY scenarios using pp collision data at √ s = 7 − g ˜ g , ˜ g ˜ q and ˜ q ˜ q is expected to be abundant at the LHC,followed by cascade decay into lighter sparticles that finally leads to the LSP. In theCMSSM case, the 95% confidence limit (CL) on squark mass reaches 1750 GeV andon gluino mass is 1400 GeV if the results of various analyses are employed [195].Naturalness considerations suggest that the third-generation sfermions (˜ t , ˜ b and ˜ τ ) are the lightest colored sparticles. In gluino-mediated ˜ t production, gluinoswith masses 560–1300 GeV have been ruled out for a massless LSP by CMS [196].For a heavy gluino, ˜ t ˜ t production yields ( m ˜ t , m ˜ χ ) limits that depend of masshierarchy and decay branching ratios. The stringent bounds reach the 680 GeV(250 GeV) in stop (neutralino) mass at 95% CL as set by ATLAS [195].If all squarks and gluinos are above the TeV scale, weak gauginos and sleptonswith masses of few hundred GeV may be the only sparticles accessible at the LHC.Charginos with masses up to 740 GeV are excluded by CMS for a massless LSP inthe chargino-pair production with an intermediate slepton/sneutrino [194].Both ATLAS and CMS experiments have also probed prompt R -parity violatingSUSY through various channels, either by exclusively searching for specific decaychains, or by inclusively searching for multilepton events. Of more interest to theMoEDAL physics program are searches for unstable long-lived LSPs. Such an analy-sis looking for a multi-track displaced vertex (DV) that contains a high-momentummuon at a distance between millimeters and tens of centimeters from the pp inter-action point has been performed by ATLAS [197]. The results are interpreted inthe context of an R -parity breaking SUSY scenario, where such a final state occursin the decay ˜ χ → µq ¯ q (cid:48) , allowed by the non-zero RPV coupling λ (cid:48) ij . The limits arereported as a function of the neutralino lifetime and for a range of neutralino masses and velocities, which are the factors with greatest impact on the limit. Indicativelysquark masses of up to 700 GeV have been ruled out for ˜ χ LSP decay lengths from1 mm to 1 m if squark-pair production and 50% branching fraction for the LSPdecay is assumed.ATLAS has searched for ˜ χ ± decays into a neutralino and a soft (undetectable)pion, experimentally being observable as ‘disappearing tracks’. Such particles woulddecay inside the inner detector volume and would be identified by well-reconstructedtracks in the inner-tracker layers, but with low numbers of hits in the outer-trackerlayers. Constraints on the chargino mass, the mean lifetime and the mass splittingare set, which are valid for most scenarios in which the LSP is a nearly pure neutralwino. In the AMSB models, a chargino having a mass below 270 GeV is excludedat 95% CL [198].Both experiments have searched for stable leptons, which being charged andpenetrating, are expected to interact as if they were heavy muons. A recent analysisby ATLAS [199] is based on a measurement of the mass of slepton candidates, asestimated from their velocity and momentum based on their interactions in theinner detector, the calorimeters and the muon spectrometer. The null results areinterpreted in the context of GMSB models where the ˜ τ is the NLSP. Long-lived˜ τ in the GMSB model considered are excluded at 95% CL at masses below 402–347 GeV, for tan β = 550. Exclusion limits on the ˜ τ mass up to 342 (300) GeVare set in the hypothesis that ˜ τ are produced directly or via other slepton (˜ e , ˜ µ )pair production, assuming a mass splitting between the light slepton and stau of1 (90) GeV. In decoupled scenarios, where ˜ τ pair production is the only SUSYsignature, exclusion limits up to 267 GeV are set on the ˜ τ mass.A more general search for heavy stable charged particles has been carried outrecently by CMS [200] involving the momentum, energy deposition, and time-of-flight of signal candidates. Leptons with an electric charge between e/ e , aswell as bound states that can undergo charge exchange with the detector material,such as R-hadrons, have been considered utilizing long time-of-flight to the outermuon system and anomalously high (or low) energy deposition in the inner tracker.The lower limits on gluino masses range between 1233 and 1322 GeV dependingon fraction of ˜ gg production and the interaction scheme. For stop production, thecorresponding limits range between 818 and 935 GeV. Drell-Yan like signals with | Q | = e/ , e/ , e, e, e, e, e, e, e, e are excluded with masses below 200, 480,574, 685, 752, 793, 796, 781, 757, and 715 GeV, respectively.A fraction of the R-hadrons that may produced at the LHC could lose all oftheir momentum, mainly from ionization energy loss, and come to rest within thedetector volume, only to decay to a ˜ χ and hadronic jets at some later time. In thelatest analysis performed by ATLAS with data at √ s = 7 and 8 TeV, candidatedecay events are triggered in selected empty LHC bunch crossings in order to remove pp collision backgrounds [201]. In the absence of an excess of events, limits are seton gluino, stop, and sbottom masses for different decays, lifetimes, and neutralinomasses. With a neutralino of mass 100 GeV, the analysis excludes gluinos with mass below 832 GeV, for a gluino lifetime between 10 s and 1000 s in the genericR-hadron model with equal branching ratios for decays to qq ˜ χ and g ˜ χ . Underthe same assumptions for the neutralino mass and squark lifetime, top squarks andbottom squarks in the Regge R-hadron model are excluded with masses below 379and 344 GeV, respectively.
7. Scenarios with Extra Dimensions
Over the past two decades, new models based on compactified extra spatial di-mensions (ED) have been proposed, which could explain the large gap between theelectroweak (EW) and the Planck scale of M EW /M P L ≈ − . The four main LHCsearch scenarios discussed in this arena are the Arkani-Hamed-Dimopoulos-Dvali(ADD) model of large extra dimensions [36–38], the Randall-Sundrum (RS) modelof warped extra dimensions [39], TeV − -sized extra dimensions [40–42], and theUniversal Extra Dimensions (UED) model [43]. Extra dimensions and microscopic black holes
The ADD model [36–38], foresees the existence of n spatial flat extra dimensions,which are accessible only to gravity. The other fields, on the contrary, are localizedon a three-dimensional brane. The extra dimensions are compactified on a toruswhose size R is related to the fundamental mass scale M D by the expression: M P L = M nD R n (58)needed to restore at large distances the correct value of the Newton gravitationalconstant. Using the above equation for M D of the order of 1 TeV, R can be, de-pending on n , as large as a tenth of a millimetre, motivating the name “large extradimensions” for this framework. In this model the weakness of gravity is due to thefact it spreads into the large bulk of the extra dimensions away from the brane andthe hierarchy is removed.The compactification of the the extra dimensions gives rise to a tower of massiveKaluza-Klein (KK) states with a mass gap ∆ m ∼ /R . The KK gravitons can beproduced, at sizeable rates, in high-energy particle collisions, and since they areweakly coupled to matter (the couplings are of gravitational strength) they escapethe detector, resulting in missing energy. Even if the detailed aspect of the theoryat energies above M D is not known, the graviton emission rates can be calculatedin a effective theory which holds for energies below M D [202].Searches at the LHC for evidence in favour of this model can be performed bydetecting an excess of events with a single energetic jet or a single energetic photonrecoiling against the graviton (missing E T + jet or missing E T + γ ) compared to theexpected rate of these events from Standard Model processes, mainly from jet + Z → νν and jet + W → lν . The presence of ADD extra dimensions can be detected atthe LHC also by investigating the contribution of virtual KK graviton exchangeto Drell-Yan processes, in particular di-lepton or di-photon production. Virtual graviton exchange produces deviations from the Standard Model expectations inthe high invariant mass ( m ll > η νµ , which dependson the position along the extra dimension: ds = e − k | y | dx µ dy ν n µν . (59)This “warp factor” reformulates the hierarchy problem. The sole fundamental scaleis of the order of M P L , and the TeV scale Λ is generated on the Standard Modelbrane by the warp factor: Λ = M P L e − kπr c (60)where kπr c ∼ −
12 and the value of k is of the order of M P L .In this model the gravitons are coupled to the Standard Model fields and theydecay into fermions or bosons. Two parameters determine the model, which can bechosen as the mass m G of the first excited KK graviton and, the coupling c = k/M P L that determines the width of the resonances. The clear signature of the RS gravitonsat the LHC is the presence of resonances in the invariant mass spectrum of di-leptons, m ll , or di-photons m γγ , with an angular distribution characteristic of spin2. The contribution of the standard Drell-Yan processes to the m ll spectrum fallscontinuously and becomes very low at high m ll ∼ Long-lived microscopic black holes
In a regime of the RS model in which the brane cannot be neglected there are veryfew physical solutions to the higher-dimensional black hole problem [216, 217]. Aclass of RS solutions have been found in which the solution is a Reissner-Nordstrommetric with the electric charge replaced by a tidal charge [218]. If the effects of thistidal-charge term are negligible, the solution becomes an effective four-dimensionalsolution and the effects of low-scale gravity are unlikely to be observed. If theextra term is significant, the effects of low-scale gravity may be observable if thefundamental scale of gravity is low enough.The decays of tidal-charged black holes have been studied in the context ofthe microcanonical picture [211, 219, 220]. The microcanonical corrections may besignificant when the object reaches the Planck size and the classical black holedescription fails. The microcanonical corrections to the canonical decay treatmentare larger in the RS scenario for Planck-sized objects, and in certain cases they maylive long enough to be considered long-lived or even quasi-stable. This possibility isdiscussed in [211, 219–221].At the LHC black holes are typically formed from the interaction of valencequarks as those carry the largest available partonic momenta. Thus, the largestcross-section will be for black holes with a charge of ∼ β (cid:46) Microscopic black hole remnants
The final fate of a black hole is still an open question. The last stages of the evapo-ration process are closely connected to the information-loss puzzle [222–224]. Whenone tries to avoid the information-loss problem there are two possibilities. Either theinformation is regained during the decay by some mechanism, or a stable black holeremnant is formed that retains the information. An important argument against theexistence of remnants is that, since no evident quantum number prevents it, blackholes should radiate away completely. On the other hand, it has been argued thatthe generalized uncertainty principle [225, 226] may prevent the total evaporationof a black hole, not by symmetry but by dynamics, as a minimum size and massare approached. Other arguments for black-hole remnants are given in [227–233].The prospect of microscopic black hole production at the LHC has been discussedwithin the framework of models with large extra dimensions by Arkani-Hamed,Dimopoulos and Dvali in [36–38].To compute the production details, the cross-section for black hole productionmay be approximated by the classical geometric cross-section: σ ( BH ) ≈ πR H ,where R H is the horizon radius of the black hole. This expression contains only thefundamental Planck scale as a coupling constant. This cross-section is a subject ofongoing research [234, 235], but the classical limit may be used up to energies of at √ s = 14 TeVcalculated with the PYTHIA event generator and the
CHARYBDIS program. least ∼ f [236–239], where M f is true fundamental of gravity. It has also beenshown that the naive classical result remains valid in string theory [240].Black holes produced at the LHC are expected to decay with an average mul-tiplicity of ≈ ± PYTHIA event generator and the
CHARYBDIS program [210]. In this study it wasassumed that the effective temperature of the black hole drops towards zero fora finite remnant mass, M R . This mass of the remnant is a few time M f and aparameter of the model. Even though the temperature-mass relation is not clearfrom the present status of theoretical studies, such a drop of the temperature canbe implemented into the simulation. The value of M R does not noticeably affectthe investigated charge distribution, as it results from the very general statisticaldistribution of the charge of the emitted particles.Thus, independent of the underlying quantum-gravitational assumption leading to the remnant formation, the authors found that about 30% of the remnants carryzero electric charge, whereas ∼
40% would be singly-charged black holes, and theremaining ∼
30% of remnants would be multiply-charged. (We note, however, thatanother study finds a much smaller percentage of charged black holes [242]). Thedistribution of the remnant charges obtained is shown in Fig. 23. The black holeremnants considered here are heavy, with masses of a TeV or more. A significantfraction of the black-hole remnants produced would have a Z/ β of greater than5, sufficient to register in the CR39 NTDs forming the LT-NTD sub-detector ofMoEDAL.Another study [243] noted that, if the Planck scale is of the order of a TeV,non-commutative geometry-inspired black holes could become accessible to experi-ments. One of the main consequences of the model is the existence of a black-holeremnant whose mass increases with a decrease in the mass scale associated withnon-commutativity and a decrease in the number of dimensions. The experimentalsignatures differ from previous studies of black holes and remnants at the LHCin that the mass of the remnant could be well above the Planck scale, and in afew percent of the time the remnant is singly-charged. The large multi-TeV massand charge of the non-commutative geometry-inspired black hole make it also acandidate for detection by MoEDAL. Long-lived Kaluza-Klein particles from Universal ExtraDimensions
Nowadays there are many models that contain extra dimensions, but the UniversalExtra Dimensions (UED) model [43] is the model closest to the original paradigmof Kaluza and Klein [244, 245]. In this model, SM fields propagate into an extradimension that is compactified, in the simplest case onto an S /Z orbifolded cylin-der. This orbifolding endows the momentum modes in the higher dimensions witha property known as Kaluza-Klein (KK) parity, an additional quantum numbermeans that only pair-production is possible.At tree level the only difference between the mass of the KK modes of the SMparticles is their lower-dimensional mass, but radiative corrections spoil this andgenerally lead to a specific spectrum [246]. The S /Z compactification mentionedabove together with minimal extra assumptions is referred to as minimal UED(mUED) scenario, and the entire mass spectrum of the KK modes in this casedepends only upon the Higgs mass, the compatification scale R − and the cut-off Λwhere the higher-dimensional (non-renormalizable) theory breaks down, requiringan ultraviolet completion. The dependance of the KK mass spectrum upon theprecise value of Λ is weak, and it is normally taken to be some multiple of R − oforder 20 or so.Now the Higgs mass has been observed to be m H ∼
125 GeV. Unlike the de-pendence on the cut-off Λ, the mass spectrum depends sensitively on this value, sothe parameter space is now quite tightly constrained and for all but the very largest compactifications the first KK mode of the hypercharge gauge boson is the lightestparticle [246, 247]. In some sense this is a good thing, as it means that the theorypossesses a dark matter candidate which is not charged [248], but at the same timeit means that in these very simple models there would be no charged particles ob-servable at large distances from the LHC interaction region for MoEDAL to detect.Charged fermionic KK modes can of course be created at the LHC, but the masssplitting between the lightest KK mode and the next-to-lightest KK mode wouldbe such that the decay rate of particles charged under the SM gauge group wouldbe very rapid and occur very close to the interaction point [247].If the lightest KK particle were charged, it would be a problem if we were toassume a normal cosmology with some relatively high reheat temperature, as theUniverse would be full of stable charged particles, something we know is not thecase because we have not detected any (for example in the same searches as thosefor anomalous R -hadrons in sea water [249, 250].There is a slight complication here, due to the fact that there should also bea KK graviton associated with the compact space that does not suffer radiativecorrections, and therefore has a mass of R − . For compactification scales below 800GeV, the KK graviton can be the lightest KK particle. This in principle opens thedoor for the lightest gauge particle in the UED model to be charged, with decayto the graviton taking a very long time due to the the gravitational coupling [247].There would be the usual problems with the non-observance of γ -rays by the Fermisatellite or the Compton Gamma-Ray Observatory, but these in principle couldbe circumvented by invoking a highly non-standard cosmology just before nucle-osynthesis, with a low reheat temperature. In this situation, charged KK particlescould be observed by MoEDAL. However, this would never take place in the mUEDmodel, as in that case the lightest KK excitation of a SM particle is not chargedfor a 125 GeV Higgs.However, there are non-minimal versions of UED which contain additionalboundary terms located at the fixed points of the orbifold. In these models thereare regions of the parameter space where the charged component of the Higgs canbe the lightest KK particle, and hence of interest to MoEDAL [251]. D-matter
Modern versions of string theory incorporate higher-dimensional “domain-wall”- likemembrane (“brane”) structures in space-time. Fundamental open strings - whichrepresent elementary-particle excitations above the vacuum - have their ends at-tached to membranes embedded in higher-spatial dimensional “bulk” spaces. Onthe other hand, only gravity and closed string modes (such as radions) are freeto propagate in the bulk space between branes. These brane structures are calledD-branes because the attachment of the ends of the open strings is described (in aworld-sheet picture) by Dirichlet world-sheet boundary conditions.However, once we accept the concept of higher-dimensional space-times with domain-world structures, it is also natural to consider cases where the bulk is“punctured” by lower-dimensional D-brane defects, which are either point-like orhave their longitudinal dimensions compactified [44–47]. From a low-energy ob-server’s point of view, living on a brane Universe with three spatial longitudinal,uncompactified dimensions, such structures would effectively appear to be point-like“D-particles”.Unlike the space-filling background D-brane worlds, the effectively point-like D-particles - obtained from Dp-branes with all their dimensions compactified - havedynamical degrees of freedom. Thus, in contrast to the background D-branes, D-particles can be treated as quantum excitations above the vacuum [44, 48] that arecollectively referred to as D-matter . D-matter states are non-perturbative stringyobjects with masses of order m D ∼ M s /g s , where g s is the string coupling. However, g s cannot be arbitrarily small since, to reproduce the observed gauge and gravita-tional couplings, g s is typically of order one. Hence, the D-matter states could belight enough to be phenomenologically relevant at the LHC.7.3.1. D-particles with magnetic charge
The stability of a D-brane is due to the charge it carries. Depending on their type,D-branes could carry integral or torsion ( discrete ) charges. The lightest D-particle(LDP) is stable, because it is the lightest state carrying its particular charge. There-fore, just as in the case of the lightest supersymmetric particle (LSP) the LDPs arepossible candidates for cold dark matter [48]. D-particles, like all other D-branes,are solitonic non-perturbative objects in the string/brane theory. As discussed inthe relevant literature [48], there are similarities and differences between D-particlesand magnetic monopoles, which are common in string models, with non-trivial cos-mological implications [44, 49, 252].An important difference between the D-matter states and other non-perturbativeobjects, such as magnetic monopoles, is that they could have perturbative couplingsshown in Table 2. Magnetic monopoles are characterized by magnetic charges,e.g., µ n ∼ n/g YM ( n ∈ Z ) where g YM is the Yang-Mills (gauge) coupling of thespontaneously-broken gauge theory that accommodates ‘t Hooft-Polyakov monopolestates. The interactions of the D-matter are proportional to g YM ∼ √ g s , where g s = O (1) is the string coupling and are thus perturbative, with no magnetic chargein general.Nevertheless, in the modern context of brane-inspired gauge theories, one canconstruct brane states that have properties similar to a magnetic monopole. Thus,they can have magnetic charges. In this case, they would manifest themselves inMoEDAL in a manner similar to magnetically-charged monopoles. For instance,one may consider a D1 brane with its ends attached to two coincident D3 branes.Such a state corresponds to a magnetic monopole in the SU(2) gauge theory thatlives on the D3-brane world-volume. Such a construction is S-dual to the case of anopen fundamental string with its ends attached to the two D3 branes (corresponding g YM denotes the Yang-Mills gauge coupling, < φ > denotesthe vacuum expectation value of the scalar field φ of the monopole configuration, λ is itscoupling constant, and M X is the symmetry breaking scale. The size of a D-matter par-ticle depends on the probe, since D-branes can probe smaller distances than fundamentalstrings. From ref. [48].’t Hooft-Polyakov Monopole D-MatterMass (cid:104) φ (cid:105) g YM ∼ M X g YM M s g s ∼ M s g YM(size) − λ (cid:104) φ (cid:105) g αs M s g YM (cid:104) φ (cid:105) α = (cid:26) − / ∝ µ m = ng YM where n ∈ Z ∝ g YM to g s → /g s ).Perturbative, non magnetically-charged LDPs are weakly-interacting, and sothey could be candidates for dark matter, depending on the string scale [48]. Ingeneral, brane defects have spin structures, so D-matter states could be bosonicor fermionic, corresponding to the bosonic or fermionic zero modes of D-branes,respectively.7.3.2. Electrically-charged D-particles
Non-magnetically-charged D-matter could be produced at colliders and also giverise to interesting signatures of direct relevance to the MoEDAL experiment. Forinstance, the excited states of D-matter (D (cid:63) ), which formally can be obtained fromthe LDP by attaching fundamental open strings, can be electrically-charged, pro-vided one end of the open string is attached to the D3 brane Universe. Such chargedstates, are supermassive - compared to the other states of the SM, which are repre-sented by open strings with their ends attached to the brane world with mass givenby: M (cid:63) = M D + n M s (61)where n ∈ Z + is the resonance level, and M D ∼ M s /g s is the LDP mass. Forcomparison, we give the masses of the towers corresponding to conventional stringresonances, Kaluza-Klein (KK) states and winding modes [48]: M resonances = g s M s + nM s , M = g s M s + n M C ,M = g s M s + n M s M c , (62)where M c = R − is the compactification scale. We thus observe that the varioustowers of new particle excitations have distinct patterns, and for low string scales M s of order of a TeV, they can all have distinct signatures at colliders. For typicalstring couplings of phenomenological relevance, e.g. g s ∼ .
6, and M s = O (1) TeV,we have that the first few massive levels may be accessible to the LHC.Depending on the details of the microscopic model considered, and the way theSM is embedded, such massive charged states can be relatively long-lived, therebyplaying a role analogous to the possible long-lived charged particles in low-energysupersymmetric models, and could likewise be detectable in the MoEDAL detector.The coupling of D-matter to SM excitations can be understood as follows. Asalready mentioned, in the brane world set-up, the SM fields are open-string exci-tations with both endpoints of the open strings attached to the same D p (cid:48) -brane.These open string states are denoted by C p (cid:48) p (cid:48) . There are also open strings thatstretch between the propagating D-matter state and the background D p (cid:48) -brane,and we denote these states by C p (cid:48) .As illustrated in Fig. 24, the C p (cid:48) states couple to the SM fields in the C p (cid:48) p (cid:48) sector. Hence there is an effective coupling of D-matter to Standard Model fields,e.g., gauge bosons, via the interactions between perturbative open-string states. TheD-matter states are charged under the gauge groups localized on the D p (cid:48) -branes.Therefore, they couple with matter fields on the branes through gauge interactions. Fig. 24. Interactions between D-matter via perturbative string states, which describe SM exci-tations. The enveloping rectangle denotes a D p (cid:48) brane with p (cid:48) uncompactified longitudinal dimen-sions. The C p (cid:48) denotes open strings stretched between the D-particles (D0-branes) and the D p (cid:48) brane. Finally, the C p (cid:48) p (cid:48) denote open string excitations with their ends attached on the D p (cid:48) braneworld (Picture taken from ref. [48]).0 Such trilinear couplings between D − D pairs and SM gauge bosons imply theproduction of D-matter in SM particle collisions, such as the quark-antiquark pro-cess indicated in Fig. 25, which is a typical process used in dark matter searches atthe LHC. In a low-energy, string-inspired, effective field-theory action, the leading (a) Signal (b) DM production(c) Z → νν background (d) W → (cid:96) i nv ν backgroundFig. 25. (a) Feynman diagrams at the parton level for the production of D-particles by, say, qqcollisions in a generic D-matter low-energy model. This is only an example [49]. There are manyother processes for the production of D-matter from SM boson decays or gauge boson fusion, whichwe do not consider in our qualitative discussion here. (b) Production of conventional dark-matterparticle-antiparticle ( χ ¯ χ ) in effective field theories, assuming that dark matter, which may co-existwith D-matter, couples to quarks via higher-dimensional contact interactions [253, 254]. (c), (d)The dominant background processes within the Standard Model framework. interactions of the D-particles with Standard Model matter are provided by termswith the generic structure (omitting Lorentz derivative or Dirac-matrix structuresfor brevity) [48]: ∝ g D D D (Gauge Bosons) . (63)The symbol ∝ in front of each type of interaction is included to denote form factorsthat arise from tree-level string amplitude calculations [48]. As a result of (63),for instance, one may have the graphs of Fig. 25(a), arising from quark/antiquarkscattering.D-matter/antimatter pairs can be produced [49] by the decay of intermediateoff-shell Z -bosons, which is in agreement with (63). The D-matter pairs producedin a hadron collider will traverse the detector and exit undetected, as they areonly weakly interacting, giving rise to large transverse missing energy, E missT . Hencemono- X analyses, targeting DM-pair production plus an initial-state-radiation jet,photon or gauge boson, such as the one shown in Fig. 25(b), would be of highlyrelevant investigative tool. The dominant SM background in such searches involves the decay of a Z toa neutrino pair and of W + to a lost (“invisible” (cid:96) inv ) lepton and a neutrino, asdepicted in Figs. 25(c) and 25(d), respectively. Such searches have been performedby the ATLAS and CMS experiments of the LHC at centre-of-mass energies of 7 and8 TeV giving null results. For example, the null results found using, e.g., the ATLASdetector in searches for missing energy + jets, impose, in the context of our model, abound on the dark matter mass m χ and the D-particle coupling g . With the LHCdata at √ s = 8 TeV and 20 fb − integrated luminosity, the current lower boundson the DM mass set by ATLAS using a mono- W/Z analysis is O (1 TeV) [255],improving significantly earlier bounds [254]. The full LHC potential ( ∼
300 fb − at √ s = 14 TeV) will strengthen greatly the constraints on the parameters of TeV-scaleD-particles. On the other hand, as mentioned previously, excited states of such aLDP, of mass M (cid:63) D , involving stretched strings between the D-particle and the braneworld, can be charged and thus highly-ionising. Thus, they are of relevance to theMoEDAL detector searches, provided the string scale is sufficiently low.
8. Highly-Ionizing Particles in Other Scenarios
We now turn to a brief overview of exotic possibilities for (meta-)stable massiveparticle (SMP) states in scenarios for physics beyond the SM (BSM) other thanthose that arise in supersymmetric or extra-dimensional scenarios. We cannot becomplete - the model space is far too large - nor do we give a detailed discussion ofeach scenario, but we hope to illustrate the spectrum of ideas that are relevant tothe MoEDAL experiment, and where possible point the reader to relevant literaturewhere further information can be found.
Long-lived heavy quarks
A number of models that predict new heavy particles beyond the top quark arestill consistent with current experimental measurements. For example, vector-likequarks - those whose different chiral components transform identically under theelectroweak gauge group - are a common feature of BSM scenarios [256], includingextra-dimensional models, grand unified models and little Higgs models. However,those models involving a fourth sequential family of quarks are now disfavoured bythe recent results on the the Higgs boson [257].Non-chiral quarks can also decouple in the heavy-mass limit, leading to SM-likesignals. In models where the mixings of these states with the light SM fermions aresuppressed, the Higgs production rates would not be easily distinguishable from theSM expectations [258]. These new quarks could be long-lived enough to be effec-tively stable as far as collider detectors are concerned. The compact nature of theMoEDAL detector would allow particles, with lifetimes of the order of nanoseconds,to be detected as effectively “stable” highly ionizing particles.It is important to recall that particles with nanosecond lifetimes or more wouldhadronize, allowing for a rich spectrum of new heavy and exotic bound states. Such pseudo-stable, or stable, massive particles are hypothesized in many new physicsmodels, either due to the fact that the decays are suppressed by kinematics or smallcouplings [22] or because of new conserved quantum number such as R -parity insupersymmetric models. Table 3. Vector-like multiplets allowed to mix with the SM quarks through Yukawa cou-plings. The electric charge is the sum of the third component of isospin T and of thehyper- charge Y . Q q T / B − / (cid:18) X / T / (cid:19) (cid:18) T / B − / (cid:19) (cid:18) B − / Y − / (cid:19) X / T / B − / T / B − / Y − / T Y Such new states can only mix with the SM quarks through a limited number ofgauge-invariant couplings. Classifying them into SU(2) L multiplets, their Yukawaterms only allow for seven distinct possibilities, i.e., the two singlets, the threedoublets and the two triplets displayed in Table 3, whose notation is adapted fromRef. [259].The production of new heavy quarks, either chiral or vector-like, is usually as-sumed to proceed at the LHC dominantly through gluon fusion, gg → QQ . Butelectroweak single production can also provide an alternative mechanism, as it isnot a affected by the large phase-space suppression of pair-production. For exam-ple, new heavy quarks can be produced singly in favour-changing processes via theelectroweak interaction through, q ( i q ) j → V ∗ → q k Q , where V = W, Z [260–262].Single electroweak production is also a promising discovery channel for new heavyquark searches with m Q ∼ .The partial decay width for a new sequential heavy quark Q decaying on-shellto a light quark q through a charged current, assuming m Q (cid:29) m q , can be writtenas: Γ( Q → qW ) ≈ . | κ Qg | m Q m W (64)where κ Qq signifies the generic Q-g quark coupling, equal to the Cabibbo-Kobayashi-Maskawa (CKM) matrix element for a new sequential family of quarks.The classification given in Table 4 summarizes the long-lived quark possibilitiescorresponding to the small mixing scenarios considered here. Scenario (a) definesthe short-lived scenario with no experimental differences compared to the directsearches carried out in the general purpose LHC detectors. The second scenario (b)arises for intermediate decay lengths ranging between a few microns and centimetredistances. Possible exceptions are as follows. In the case of new heavy multipletswith sizeable mass splittings, as allowed in extra generation models and possibleextensions [262–265], if m Q (cid:46) m Q + m V , the heaviest quark Q can be short-livedand decay semi-weakly to Q V ( ∗ ) , while the lightest partner is likely stable if all its decay modes suffer severe suppression. On the other hand If m Q (cid:39) m Q , allheavy-to-heavy transitions are suppressed and both quarks could be long-lived. Table 4. Possible decay signatures for newlong-lived quarks with masses m Q ∼ | κ Qq | (cid:38) − (cid:38) − (cid:38) − (cid:38) − Γ( GeV ) | (cid:38) − (cid:38) − (cid:38) − (cid:38) − τ ( s ) (cid:46) − (cid:38) − (cid:46) − (cid:38) − Scenario (c) of Table 4 describes long-lived particles with decay lengths largerthan standard LHC detector dimensions. If all heavy quark couplings with SMfermions are below the 10 − level, the stable case becomes a relevant scenario,perhaps in conjunction with events with displaced vertices. if all Q − q quark cou-plings to the SM families are less than around 10 − , such new heavy fermions couldhadronize. As a result, annihilation decays and hadronic transitions between theformed bound states would dominate.While QQ quarkonium resonances would be impossible to observe in MoEDAL,the possibilities for “open-favour” hadrons Qq , ( Qq ) and Qqq ( Qqq ) with q beinga light SM quark, provide a wide spectrum of new heavy mesons and baryons thatcould be sought at the LHC. Such states can form by capturing a light quark partnerand transforming as they pass through the detector into various slow-moving heavystates. Table 5 lists these states assuming that they hadronize with u , d and s quarks. Table 5. Possible mesons and baryons involving Q = X / , T / , B − / and Y − / vector-likequarks. The states in bold font are hadrons whose yields are expected to be substantial at theLHC, as predicted in [266] for penetration depths between 0 and 3 meters. Only the neutral andpositively-charged hadrons are displayed.Chrg Mesons BaryonsQ=0 T¯u , ¯Tu , B¯d , ¯Bd , B ¯ s, ¯ Bs T dd, T ds, T ss,
Bud , Bud, Bus, Bus, Y uu, Y uu
Q=1
X¯u , T¯d , T ¯ s, ¯Bu , ¯Yd , ¯ Y s Xdd, Xds, Xss,
Tud , T us, Buu, Bdd, Bds, Bss, Y ud, Y us
Q=2
X¯d , X ¯ s, ¯Yu Xud , Xus, T uu, Y dd, Y ds, Y ss Q=3 -
Xuu
Interestingly, the interactions of such open-flavour mesons with the materialwould be similar to those of R -hadrons. As they move through and interact withthe detector material, most of the new states convert into baryons, allowing for Quu, Qud and
Qdd states, as new heavy mesons are kinematically favoured to in-crease their baryon number by emitting one or more pions [266].Interestingly, new mesons that convert at the beginning of the scattering chain could generate intermittent tracks, disappearing and reappearing, signalling possi-ble baryonic or electric charge exchange. Indeed, Q ¯ q and ¯ Qq bound states traversinga medium composed of light quarks likely flip their electric charge, frequently in-terchanging their parton constituents with those of the material nuclei.The pseudo-stable hadrons described here would lead to observable tracks dueto the high ionization energy losses, allowing for signatures similar to slow-movingmuons with high transverse momentum. Searches for pseudo-stable charged parti-cles, with a highly-ionizing signature therefore provide a promising strategy to ruleout or confirm the possibilities for novel exotic quarks with long lifetimes. Suchsignatures are accessible to the MoEDAL detector.Limits derived from ATLAS and CMS searches [267], can be placed on searchesfor heavy and long-lived quarks. For example, ATLAS results [268] for tW finalstates rules out cross-sections of σBR ( Q → tW ) > <τ < × − s (3 mm < cτ <
10 cm), corresponding to an excluded heavy quarkmass of m Q <
650 GeV.The detection of an SMP in the multipurpose LHC detectors requires the heavystate to propagate through the full tracking detector. The reinterpretation [262]of the CMS search [269], assuming similar behaviour as for scalar long-lived topquarks, excludes cross-sections of σ > − s ( cτ >
30 m). The mass limit m Q <
800 GeV/c is still valid for lifetimes τ > − s ( cτ > Massive (pseudo-)stable particles from vector-like confinement
A plausible extension of of the SM is obtained by adding new fermions in vector-like representations of the SM gauge groups, with a mass scale within the reach ofthe LHC. One can easily imagine such fermions as remnants of physics at a higherenergy scale. The advantage of, say, a new vector-like fermion is that it can havemass without coupling to electroweak symmetry breaking and affecting the precisionelectroweak observables. Such new fermions may also interact via new gauge forces,which may be weakly or strongly coupled.In the case where these new fermions also feel a new strong gauge force, inaddition to SM gauge forces, that confines at TeV energies, the phenomenologyis drastically different from that of the Standard Model. Vector-like confinementaugments the SM at the TeV scale in the same manner that QCD augments QEDat the GeV scale. A new confining gauge interaction (hypercolour) and new vector- like fermions (hyperquarks) are added to the SM.Hyperquarks are assumed to be light compared to the hypercolor confinementscale, in a way that is analogous to the u, d and s quarks, which are light comparedto the QCD confinement scale. The hyperquarks, once pair-produced, rapidly formbound states due to hypercolor confinement, allowing for both resonant and pair-production of hypermesons at the LHC, in a way that is analogous to the resonantand pair-production of mesons and pions at a low-energy e + - e − collider.There are many possible models of vector-like confinement. However, the pres-ence of a spin-1 bound state ˜ ρ - analogous to the QCD ρ meson - and a pseu-doscalar bound state ˜ π - analogous to the QCD pion - are completely general. Thescenario of vectorlike confinement is discussed in detail elsewhere [50]. The spin-1resonances decay predominantly into a pair of pseudoscalar bound states, just asthe ρ → π + π − . The resonant ˜ ρ production followed by ˜ ρ → ˜ π + ˜ π − is the signatureprocess of vector-like confinement. Fig. 26. On the left we show the diagram for the production of a ˜ π pair via a ˜ ρ resonance. Onthe right we show the diagram for Drell-Yan production of a ˜ π pair. A generic phenomenological feature in vector-like confinement models is theexistence of charged and/or colored massive pseudoscalars, or hyperpions, that arestable on collider time scales [51]. If coloured, such hyperpions will hadronize withquarks and gluons, thereby forming a massive stable hadron, like an R -hadron,which will carry a net electric charge some fraction of the time. Charged long-livedcolour-neutral pseudoscalars and “R-hadrons” can be pair produced via a Drell-Yan process as well as the decay of a spin-1 resonance, as shown in Fig. 26 (left), orthrough an s -channel gluon, as in Fig. 26 (right) [51]. In both cases the producedparticles can be stable on collider distance and time scales. In many vector-likeconfinement scenarios these massive stable particles are sufficiently slow-moving( β (cid:46) Fourth-generation fermions
An intriguing way to address the big hierarchy problem of the Standard Model is tointroduce a a new fourth family of leptons. Although models that involve a fourthsequential quark are now disfavoured by recent results on the Higgs boson [257].A natural method to accomplish such a scenario is to have the Higgs itself bea composite of these new fermions. This setup was investigated [271] using as a template minimal walking technicolor [272] with a general heavy neutrino massstructure with and without mixing with the SM families. By imposing an exactly-conserved ε -lepton number the mixing between the fourth-generation ε neutrino andthe three light neutrinos can be forbidden. On the other hand, the possibility thatthe new heavy leptons mix with the Standard Model leptons can also be allowed.It is certainly possible that the neutrino will be the heavier than the chargedleptons. In this case, the charged lepton can only decay through mixing with lightergenerations, and might thus be extremely long-lived. Collider signatures of long-lived charged leptons could either be displaced vertices or, if the charged leptondecays outside the detector, a muonlike signal. In the event that the heavy leptonis slow-moving it will be highly-ionizing and thus can be detected by the MoEDALexperiment. ‘Terafermions’ from a ‘sinister’ extension of the StandardModel In a model introduced by Glashow and Cohen [273] based on the gauge groupSU(3) × SU(2) × SU(2) (cid:48) × U(1), the quarks and leptons of the Standard Modelare accompanied by an equal number of “terafermions”. An unconventional CPoperation called CP (cid:48) , maps ordinary fermions into the conventional CP conjugatesof their tera-equivalents, and vice versa. This ‘sinister’ (i.e., ‘left-left symmetric’)model is akin to certain ‘left-right symmetric’ models for which an unconventionalspace-reflection operation P (cid:48) , rather than CP (cid:48) , links ordinary and exotic fermions.The model also involves heavy versions of the weak intermediaries: W (cid:48) and Z (cid:48) bosons. Soft CP (cid:48) breaking within a simple Higgs sector (comprised of a SU(2) dou-blet and a SU(2) (cid:48) doublet) leads to large and experimentally allowed masses for theterafermions, and for the W (cid:48) and Z (cid:48) . This model resolves two of the problems of theSM: the mass hierarchy and the strong CP problem. A natural seesaw mechanismallows the observed neutrinos to have very small Dirac masses. This extension of theSM predicts the existence of novel heavy stable quarks and leptons that, throughthe formation of electromagnetically-bound states (“terahelium”), yield candidatesfor dark matter.In this model the tera-electron is the least massive charged terafermion. Theother charged teraleptons are unstable, decaying rapidly via W (cid:48) exchange. Thelightest teraquark, U , is stable with an estimated mass of a few TeV. The heavierteraquark , D , is unstable, decaying for example via D → U + E − + ν (cid:48) e . Althoughthe electric charge of the U quark is only 2/3, the slow-moving massive U particlecould have sufficient ionization to be detectable by MoEDAL. A massive particle from a simple extension to the SM
The SM is based on the gauge group SU(3) × SU(2) × U(1), which has quarks thattransform non-trivially under all the three factor groups SU(3), SU(2) and U(1).On the other hand, leptons transform non-trivially under only two of these groups, namely SU(2) and U(1). However, it is possible to have a fermion that transformsnontrivially under U(1) [274]. It is an electrically-charged fermion that does not haveweak decays or strong interactions. If in addition it is stable, it will be of interest toMoEDAL. Absolute stability in the case of a singly-charged particle is not possibleif the Standard Model Higgs doublet exists, unless a discrete symmetry is imposed.However, in the scenarios described in Ref. [274] there is no need of the discretesymmetry. Conservation of the U(1) hyper- charge itself forbids the Higgs couplingof as well as the off-diagonal mass terms connecting with the right-handed chargedleptons. Thus, a doubly charged particle is automatically stable and potentiallydetectable by MoEDAL. Fractionally charged massive particles
Fig. 27. Currently-allowed windows for FCHAMPs, consistent with the relic density, accelerator,and Z width constraints, for which | Q L − n | ≤ . n = 0 , ,
2, from Ref. [275]. The FCHAMPmass, m L ≡ GeV.
A final topic we discuss briefly Fractionally Charged Massive Particles(FCHAMPS). Such particles exist in extensions of the SM that can be obtainedin the low-energy limit of superstring theories. The lightest FCHAMP would bestable, and any of them produced during the Early Universe would be present to-day. In [275], the thermal production, annihilation and, survival of an FCHAMP, a lepton with electroweak, i.e., with non-trivial hypercharge U (1) Y , but no stronginteractions, of mass m and charge Q L (in units of the electron charge) have beenexplored, taking into account standard cosmological constraints coming from pri-mordial nucleosynthesis and cosmic microwave background radiation. In addition,the invisible width of the Z -boson of the Standard Model can be used to pro-vide constraints on the FCHAMP charge-mass relation. The surviving FCHAMPabundance on Earth is orders of magnitude higher than the limits from terrestrialsearches for fractionally-charged particles, closing the window on FCHAMPs with Q L ≥ .
01. However, as Q L approaches an integer ( | Q L − n | ≤ . e makes FCHAMPs candidates for detection by theMoEDAL detector.
9. Scenarios with Doubly-Charged Massive Stable Particles
Doubly-charged particles appear in many BSM scenarios. As examples, doubly-charged scalar states, often dubbed doubly-charged Higgs fields, appear in left-rightsymmetric models [105, 276–278] and in see-saw models for neutrino masses withHiggs triplets [279–293]. Doubly-charged fermions can appear in extra-dimensionalmodels including new physics models inspired by string theories [294], and as thesupersymmetric partners of the doubly-charged scalar fields in supersymmetric ex-tensions of left-right symmetric models [295–298]. Finally, models of new physicswith an extended gauge group often include doubly-charged vector bosons [299–303].It is also possible to consider vector states with double electric charge independentlyof any gauge-group structure, as in models with non-commutative geometry or incomposite or technicolor theories [304–311].A general effective Lagrangian analysis of production and decay rates of dou-bly charged exotic particles (scalars, fermions and vectors) at the LHC indicatespromising channels and distinct signatures and shows how to distinguish amongparticles with different spins and SU (2) L representations [312]. We consider suchnew physics scenarios with potentially massive long-lived doubly-charged particlesin more detail below. Such particles would give rise to highly-ionizing particles thatcould be detected by the MoEDAL detector. XY gauginos and warped extra dimension models
Models that address supersymmetric grand unification in warped extra dimensionswith “GUT parity” [313–316] were introduced to alleviate the problems of the con-ventional supersymmetric desert picture. In these models the combination of extradimensions and effective TeV-scale supersymmetric grand unification results in KKtowers, not only of the SM gauge and Higgs fields, but also of their supersymmet-ric GUT partners, including XY bosons of Grand Unification as well as coloured Higgs multiplets. A parity can be chosen such that the MSSM particles are evenand their GUT partners odd, hence the lightest “GUT-odd” particle (LGP) is sta-ble or long-lived if this quantum number is conserved or approximately conserved,respectively.In an early model involving gauge coupling unification of the four-dimensionalMSSM [313] we have a scenario where the LGP is a light isospin-up (-down) colour-triplet XY gaugino, with electric charge -1/3 (-4/3). Since the XY gauginos arecoloured, they hadronize by picking up an up or down quark, making neutral orcharged mesons T ≡ ˜ X ↑ ¯ d , T − ≡ ˜ X ↑ ¯ u , T (cid:48)− ≡ ˜ X ↓ ¯ d and T −− ≡ ˜ X ↓ ¯ u ,where ˜ X ↑ and ˜ X ↓ are the isospin up and down components of the XY gauginodoublets, respectively. Among these mesons, the lightest one is either T or T − ,and the heavier states can decay through beta processes. However, the decay is slowenough that all the meson states are effectively stable on collider distance and timescales, and the singly- and doubly-charged mesons, which have TeV-scale masses,will easily be seen because they leave highly-ionizing tracks capable of being detectedby the MoEDAL detector. In more recent five-dimensional models [314–316] manypossibilities for highly-ionizing particle production are open. Doubly-charged leptons in the framework of walkingtechnicolor models
Technicolor models were originally rejected due to some serious shortcomings, for ex-ample their predictions of large Flavour-Changing Neutral Currents (FCNCs) [317].Also early technocolour models led to a plethora of technimesons [318], for whichthere was no evidence. However, extended technicolor models where the technicoloursector has a “walking” behaviour - that is the slow running of the technicolour gaugecoupling over an extended range - do not have a FCNC problem. Indeed, the latestwalking technicolour models [311, 319–321] provide a good description of particlephysics phenomena. The discovery in 2012 by ATLAS and CMS of a Higgs-like bo-son with mass approximately 126 GeV [106, 107] was not generically predicted bywalking technicolour models, but can be accommodated by them.The minimal walking technicolor model [311, 319–321] has two techniquarks, U(up) and D (down), that transform under the adjoint representation of an SU(2)technicolor gauge group. The global symmetry of the model is a SU(4) that breaksspontaneously to an SO(4), and the chiral condensate of the techniquarks breaks theelectroweak symmetry. There are nine Goldstone bosons emerging from the symme-try breaking, three of which are eaten by the W and Z bosons. The remaining sixGoldstone bosons are U U , U D , DD composites and their corresponding antiparti-cles. The effective theory of the minimal walking technicolor model presented herehas been described in detail elsewhere [311]The six Goldstone bosons carry technibaryon number since they are made of twotechniquarks or two anti-techniquarks. If no processes violate technibaryon number,the lightest technibaryon will be stable. The electric charges of the U U , U D , and DD boson are given in general by n + 1 , n , and n − n is anarbitrary real number.The model requires in addition the existence of a fourth family of leptons, (cid:18) ν (cid:48) e (cid:48) L (cid:19) ( ν (cid:48) R , e (cid:48) R ) , (65)i.e., a new ‘neutrino’ ν (cid:48) and a new ‘electron’ e (cid:48) . Their hypercharges are are ( − y ) / − (3 y − / , − (3 y + 1) / y = 1, the Goldstone bosons U U , U D , and DD have electric charges 2, 1, and 0, respectively. Using the conven-tion Q = T + Y , the electric charges of the new lepton ν (cid:48) and e (cid:48) are -1 and -2,respectively.Thus two types of of stable doubly-charged particles can exist in the frameworkof Minimal Walking Technicolour, the technibaryon U U ++ and the technilepton e (cid:48) ++ . The masses of these particles are expected to exceed 100 GeV. The MoEDALdetector has a low enough threshold to detect doubly-charged techniparticles withvelocities smaller than around 0.4c. Doubly-charged Higgs bosons in the L-R symmetric model
The electroweak gauge symmetry of the SM is broken by the Higgs mechanism,which imparts masses to the W and Z bosons, the mediators of the weak forces.A number of models mentioned above include additional symmetries and extendthe SM Higgs sector by introducing doubly-charged Higgs bosons. We considerhere in more detail one good example of such a model, the L-R Symmetric Model[105, 276–278].One major puzzle of the SM is the fact that weak interaction couplings arestrictly left-handed. In order to remedy this apparent arbitrariness of Nature, onecan extend the gauge group of the SM to include a right-handed sector. The sim-plest realization is a Left-Right Symmetric Model (LRSM) [105,276] that postulatesa right-handed version of the weak interaction, whose gauge symmetry is sponta-neously broken at high mass scale, leading to the parity-violating SM. This modelaccommodates naturally recent data on neutrino oscillations [322] and the existenceof small neutrino masses [323]. The model generally requires Higgs triplets contain-ing doubly-charged Higgs bosons ( H ±± ) ∆ ++ R and ∆ ++ L , which could be light inthe minimal supersymmetric left-right model [324–326].Single production of a doubly-charged Higgs boson at the LHC is possible viavector boson fusion, or via the fusion of a singly-charged Higgs boson with eithera W ± or another singly-charged Higgs boson. The amplitudes of the W L W L and W R W R vector boson fusion processes are proportional to v L,R , the vacuum expec-tation values of the neutral members of the scalar triplets of the LRSM . For thecase of ∆ ++ R production, the vector boson fusion process dominates. For the produc-tion process W + W + → ∆ ++ L , the suppression due to the small value of the v L issomewhat compensated by the fact that the incoming quarks radiate a lower-massvector gauge boson. Pair production of doubly-charged Higgs bosons is also possible via a Drell-Yanprocess, with γ , Z or Z R exchanged in the s-channel, but at a high kinematic pricesince substantial energy is required to produce two heavy particles. In the case of∆ ++ L , double production may nevertheless be the only possibility if v L is very smallor vanishing.The decay of a doubly-charged Higgs boson can proceed via several channels.Dilepton decay provides a clean signature, kinematically enhanced, but the branch-ing ratios depend on the unknown Yukawa couplings. Present bounds [327, 328]on the diagonal couplings h ee,µµ,ττ to charged leptons are consistent with val-ues O (1) if the mass scale of the triplet is large. For the ∆ ++ L , this may be thedominant mode if v L is very small. One would then have the golden signature q ¯ q → γ ∗ /Z ∗ /Z (cid:48)∗ → ∆ ++ L ∆ −− L → l .In the case of very small Yukawa couplings H ll (cid:46) − , the doubly-charged Higgsboson could be quasi-stable. In this case slowly moving pseudo-stable Higgs bosonscould be detected in the MoEDAL NTDs. For example with CR39, one could detectdoubly-charged Higgs particles moving with speeds less than around β (cid:39) . Doubly Charged Higgsinos in the L-R supersymmetric model
If the LR symmetric model is extended to include supersymmetry, the emergingmodel cures some of the outstanding problems of MSSM. It disallows explicit R-parity violation [329], provides a natural mechanism for generation neutrino massesusing Higgs triplet fields that transform as the adjoint representation of the SU (2) R group. It also provides a solution to the strong and electroweak CP problem inMSSM [330, 331].The left-right supersymmetric models predict the existence of the fermionic part-ners of the doubly charged Higgs bosons, the doubly charged higgsinos. If the scalefor left-right symmetry breaking is chosen so that the light neutrinos have theexperimentally expected masses, the doubly charged higgsinos can be light. Suchparticles could be produced in abundance and thus give definite signs of left-rightsymmetry at future colliders like the LHC and at the linear collider. These particleswill be distinguished by certain characteristic signatures in regard to their leptonand jet spectra in the final state. In particular, they give rise to a distinguishing4 (cid:96) + E missT [295–298]. As with doubly charged Higs bosons, doubly charged Higgsi-nos can be long-lived enough to traverse the MoEDAL and be detected in its NTDsystem. Doubly-charged leptons in the framework of almostcommutative geometry
The novel mathematical theory of almost-commutative (AC) geometry [332] hasbeen invoked in an attempt to to unify gauge models with gravity. The AC-model[333–335], which is based on almost-commutative geometry, extends the fermioncontent of the SM by two heavy particles with opposite electromagnetic and weak Z -boson charges. Having no other SM gauge charges, these particles (AC-fermions)behave as heavy stable leptons with charges -2e and +2e, called here A and C ,respectively.The AC-fermions are sterile relative to the SU(2) electroweak interaction, anddo not contribute to SM parameters. The masses of AC-fermions originate fromthe non-commutative geometry of the internal space, which is less than the Planckscale, and are not related to the Higgs mechanism. The mass scale of the A andC fermions is fixed on cosmological grounds. It was assumed in [336, 337] that themasses of the A and C leptons are greater than 100 GeV.In the absence of AC-fermion mixing with light fermions, AC-fermions can beabsolutely stable. Such absolute stability follows from a new U(1) interaction ofelectromagnetic type and strict conservation of the additional U(1) gauge charge,which is called Y-charge and is carried only by AC-leptons. A heavy doubly-chargedlepton with speed β ∼ <
10. Highly-Ionizing Multi-Particle Excitations
An intriguing class of highly-ionizing electrically-charged particles is that of multi-particle excitations. We discuss three examples of such exotic states - Q-balls,strangelets and quirks.
Q-balls
In theories where scalar fields carry a conserved global quantum number Q , therecan exist non-topological solitons that are stabilized by global charge conservation.They act like homogenous balls of matter, with Q playing the role of the quantumnumber. Coleman called this type of matter Q-balls [52]The conditions for the existence of absolutely stable Q-balls may be satisfiedin supersymmetric theories with low-energy supersymmetry breaking [53]. The roleof conserved quantum number is played in this case by the baryon number, or bylepton number for sleptonic Q-balls.These Q-balls can be considered as coherent states of squarks, sleptons andHiggs fields. Under certain assumptions about the internal self-interactions of theseparticles and fields, the Q-balls could be absolutely stable [338,339]. SupersymmetricQ-balls fall into two classes: supersymmetric electrically-neutral solitons (SENS) andsupersymmetric electrically-charged solitons (SECS).Low-charge, Q-balls - called Q-beads - have been hypothesized [340], whichare also extended objects whose size is large in comparison to their de Brogliewavelength. These could be produced at a collider, although the probability ofproducing them is probably exponentially reduced by the size of the Q-bead. Butthe question of the potential observability of Q-beads is by no means clear and needsfurther consideration. If Q-beads can be created in a collider, their signatures couldbe spectacular. For example, a soliton with both B (cid:54) = 0 and L (cid:54) = 0 would interact as a massive leptoquark. Such objects would register in the passive detector systemof the MoEDAL experiment. Strangelets
Strangelets are hypothetical baryonic objects consisting of approximately equalnumbers of u, d and s quarks, which may be stable or metastable. The reason forthis stability is that the Fermi energy for a large enough system with a fixed numberof u and d quarks is higher than the corresponding system of u, d and s quarks dueto the Pauli Principle [341,342]. Calculations with the MIT bag model confirm thatstrangelets could be stable [343, 344].The use of ultra-relativistic heavy ion collisions - for instance at the LHC - isthe only known way of creating a QGP for laboratory studies and the goal has beenfor several years to create and detect the QGP. More generally the motivation forthese experiments is to study the thermodynamics of strongly interacting matter.Strangelets could be produced as cooled remnants of a quark-gluon plasma (QGP)through the strangeness distillation mechanism proposed in [345, 346]. Thus thedetection of strangelets could be a signal for the formation of a QGP. The basicidea in the distillation mechanism is that ¯ s quarks produced in the interaction bindwith the u and d quarks from the initial-state nuclei, forming K + and K mesons.When these mesons evaporate from the system, they carry away anti-strangenessand entropy. The remaining baryon-rich system is strongly enhanced with s quarks,which could favour the formation of strangelets.Coalescence models [347, 348] provide another production mechanism forstrangelets, whereby hypernuclei produced in heavy-ion interactions could decay tostrangelets. However, it should be pointed out that the good agreement of measure-ments of particle production at RHIC with simple thermodynamic models severelyconstrains the production of strangelets in heavy-ion collisions at the LHC [349].The cross-sections and lifetimes of strangelets have recently been calculatedusing the MIT bag model [350]. The estimated lifetimes range from 10 − - 10 − sfor short-lived ones to 10 − - 10 − s for long-lived ones. According to this model,charged strangelets are expected to have a high negative charge and to be rathermassive. For example, interesting candidates for longlived strangelets are lying in avalley of stability which starts at the quark alpha (6u6d6s) and continues by addingone unit of negative charge, i.e. (A, Z) = (8,-2),(9,-3), (10,-4), (11,-5), etc. However,scenarios that include the production of negatively charged strangelets at the LHCbeen been strongly criticized [349]. Alternatively, the possibility that (meta-)stablestrangelets with small positive charge could exist has been discussed in a numberof references [351–353]. Massive, multiply charged strangelets could be sufficientlyionizing to reach the detection threshold of MoEDAL. Quirks
Quirks are particles appearing [354, 355] in extensions of the SM that includeheavy particles that are charged under both the SM Group and additional non-Abelian asymptotically-free gauge groups (“infracolour” (IC)), which may havemasses reachable at the LHC. Quirks are analogous to the quarks of QCD, butthe confining gauge group is specifically not the colour SU(3) of QCD. The ICgroup may be of SU(N) type, and the quirks are assumed to be in its fundamentalrepresentation. The new group is assumed to become strong (confining) at a scaleΛ (cid:28) m Q . Thus, in contrast to the familiar QCD scale, the confining scale of thenew group is much lower than the fermion mass, hence the name infracolour. Thephenomenologically interesting range of the quirk mass, m Q , is100 GeV ≤ m Q ≤ O (10) TeV . Thus, such models are of relevance to LHC physics, including the MoEDAL exper-iment. The confinement scale Λ can be as low as 100 eV [355].
Fig. 28. Loop diagrams that contribute to the coupling of the Infracolour (IC) gluons (helicalstructures) to the SM gauge bosons (wavy lines) or fermions (continuous external lines). Quirksare represented as internal-loop continuous lines.
Since the SM is uncharged under the infracolour sector, couplings of SM matterto the infracolour sector can arise only through quirk-loop processes of the formdepicted in Fig. 28. The leading coupling is provided by the diagram of Fig. 28(a),which leads to terms in the effective Lagrangian that mix the field strengths of theIC and SM gauge groups, of the form d : L eff ∼ g g (cid:48) π m Q F µν F (cid:48) ρσ , (66)where g and g (cid:48) denote the SM and IC gauge couplings respectively. The operator(66) mediates the decay of an IC gluon into photons and/or ordinary colour gluons d The reader should notice that the two-loop processes of Fig. 28(b), which couple the IC glu-ons to the fermionic SM sector suffer, in addition to the loop suppression, an additional helicitysuppression, as compared to the diagram of Fig, 28(a), and are therefore non-leading contributions.5 with a life-time that depends crucially on the magnitude of the confining scale Λ.It can be shown that [355] for Λ ≥
50 GeV the IC glueball can decay within aparticle detector, while its life-time becomes longer than the age of the Universe forΛ ≤
50 MeV.
Fig. 29. Quirk-Antiquirk pairs are connected by IC flux strings which have the shape of tubes:(a) tube for quirk-antiquirk separation r (cid:28) Λ − , (b) tube for quirk-antiquirk separation r (cid:29) Λ − .(c) the breaking of strings is exponentially suppressed, requiring energy 2 m Q (cid:29) Λ. When quirks are pair-produced at the LHC they are bound together by a fluxtube but, unlike QCD, there is no kinematical possibility of the pair hadronizinginto jets, as the tension of the flux-tube is too low compared with the Quirk mass( cf. fig. 29). The quirk-antiquirk pair stays connected by the IC string like a “rubberband” that can stretch up to macroscopic lengths, depending on the magnitude ofthe confining scale Λ. One would expect the size of the confining flux tube to be [355] L ∼ m Q Λ ∼ (cid:16) m Q TeV (cid:17) (cid:18)
Λ100eV (cid:19) (67)where m Q is the mass of the quirks at the end of the confining fluxtubes. Tech-nically speaking, for an energy E ∼ π Λ and area A , string breaking is exponen-tially suppressed, since the relevant life-time τ for a string of length L ∼ m Q /σ ,with the string tension σ ∼ E A , can be estimated to be (by analogy with the Schwinger mechanism of pair creation of charged particles by a weak external elec-tric field [355]): τ ∼ π m Q e m Q / Λ , and in general m Q (cid:29) Λ. This is already longerthan the age of the Universe for m Q ≥
100 GeV and Λ /m Q ≤ . m is in the phenomenologically interesting rangeof 100 GeV to a few TeV, and that the new gauge group gets strong at a scale Λ < m and thus the breaking of strings is exponentially suppressed, quirk production resultsin strings that are long compared to Λ − . The existence of these long stable stringswould lead to highly exotic events at the LHC. For 100 eV (cid:46) Λ (cid:46) keV the stringsare macroscopic. In this case one would observe events with two separated quirktracks with measurable curvature toward each other due to the string interaction,as shown in Fig. 30 [355]. Fig. 30. Anomalous tracks from quirks with macroscopic strings
The difficulty in detecting quirks with macroscopic strings is that the triggersand track reconstruction algorithms of conventional LHC detectors are designedfor conventional tracks, and will likely miss these events altogether. However, theMoEDAL detector does not suffer from these drawbacks. Indeed, the signature inthe NTDs for two massive quirks separated by a macroscopically string would bequite spectacular.For 10 keV (cid:46) Λ (cid:46) MeV and m Q ∼ reducing matter interactions to a negligible rate within the pipe. The decay lengthof coloured quirks within the beam pipe has been estimated to be [355]: cτ ∼ cm (cid:18) Λ100 keV (cid:19) − (cid:16) m Q T eV (cid:17) , (68)while for uncoloured quirks: cτ ∼ cm (cid:18) Λ M eV (cid:19) − (cid:16) m Q T eV (cid:17) , (69)one can see that heavier quirks with small Λ ( ∼
10 KeV) would have lifetimessufficient to exit the beam-pipe. However the efficiency of the mechanism of energyloss considered [355] is uncertain, particularly for the infracolor energy loss. Thedecay lengths may be significantly longer than these estimates. Once the quirkbound state reaches the beam pipe, interactions with matter efficiently randomizethe angular momentum and prevent annihilation.Thus, the quirk bound state could appear as collider stable highly-ionizing par-ticle. In MoEDAL the latent tracks resulting from the passage of a highly ionizingparticles are only of the order of 10nm in diameter, with resulting etch pits around5-10 µ m in diameter. Thus, even in the case of “mesoscopic” strings MoEDAL maystill be able to resolve the “di-quirk” nature of the event. If not, MoEDAL will beable to detect the quirk state as a highly-ionizing, doubly-charged track.If the strings are microscopic, with length of the order of an Angstrom, cor-responding to M eV (cid:46) Λ (cid:46) m Q /f ew , the quirks annihilate promptly within thedetector. For coloured quirks, this can lead to hadronic fireball events with ∼ hadrons each with energy of the order of a GeV, a spectacular signature that how-ever is not detectable by MoEDAL.
11. Stopped Stable and Metastable Particles
As we have seen, massive stable and metastable particles are common in manymodels of new physics at the TeV scale. The discovery of new long-lived particles atthe LHC would provide fundamentally significant insights into the nature of darkmatter, the presence of new symmetries of nature or extra dimensions and manyother BSM scenarios.If such particles are charged and/or coloured, a reasonable fraction of thoseproduced at the LHC will stop in the LHC detectors and the surrounding material,and give observable out-of-time decays. This is particularly true of very-highly-ionizing particles that lose energy quickly in matter. Many such scenarios havebeen discussed in the preceding text.Particle metastability due to high-scale physics is well motivated. Also, as hasbeen discussed above a new physics particle may also be long-lived because ofits small couplings, as in R -violating supersymmetry [33], or TeV-scale seesawmodels [356]. A particle may also be long-lived due to kinematics, e.g., if theMassive Metastable Charge Particle (MMCP) is nearly degenerate with the final state into which it decays. There have been searches for slow-moving MMCP’s atLEP [357–359], the Tevatron [360, 361], and the LHC [362–365] that place boundson their production.While much can be learned by studying the production and propagation of par-ticles at the LHC, there is interesting physics that can only be accessed by studyingtheir decays. These measurements can reveal the properties of the decaying TeV-sector particles. For example, the Lorentz structure of the decay and the branchingfractions to different SM particles can constrain the high-scale physics giving riseto the decay.It is often the case that MMCPs will be stopped in the collider detectors them-selves. However, observing decays within the detector is experimentally challengingbecause the designs of the standard LHC detectors were optimized to measure par-ticles emanating from a central interaction point; moving near to the speed of light( β (cid:38)
12. Detecting Highly-Ionizing Particles at the LHC
The sub-detectors of general-purpose experiments are designed to detect minimum-ionizing particles moving near to the speed of light. Effects arising from the particleslow velocity and the high density of the energy deposition, such as electronics sat-uration, light quenching in scintillators and adjacent hits from delta electrons, areextremely challenging to deal with. Indeed, in some cases it may be impossible tomake an accurate measurement of the effective charge of the particle. For example,the resulting dead time as a result of electronics saturation may be of the orderof the bunch crossing time. An example of this is provided by the effect of highly-ionizing particles on the CMS silicon strip tracker that was studied in [374, 375]. Inaddition, highly-ionizing particles will be absorbed very quickly within the mass ofthe standard collider detector. Indeed, extremely-ionizing particles may be absorbedbefore they penetrate far into the inner tracking detectorsIn order for stable or long lived massive particles to be detected in generalpurpose collider detectors they need to be detected and triggered on in a sub-detector system, or group of sub-detector systems, and be associated to the correctbunch crossing. This detection and triggering must happen within ∆t ns - where ∆tis the time between bunch crossings (nominally 25ns at the LHC with E cm =14 TeV)- after the default arrival time of a particle travelling at the speed of light [376,377].Later arrival would require detection and triggering within the next crossing timewindow. The typically large size of the general purpose collider detectors (the centralATLAS and CMS muon chambers extend to 10 and 7 m, respectively) results inthis being an important source of inefficiency in detecting SMPs. For example, it isonly possible to reconstruct the track of a slowly-moving long lived massive particlein the ATLAS central muon chambers within the correct bunch crossing window if β >
0. 5 [376].But even if a long-lived massive particle travels through the sub-detector systemswithin the timing window in which it was created, additional problems may arise dueits relatively slow speed. Naturally, the time sampling and reconstruction softwareof collider detectors is optimized assuming all particles are travelling near to thespeed of light. Thus, it is quite possible that the quality of the read-out signal orreconstructed track or cluster will be degraded for a collider stable slow moving masslong-lived particle , especially for sub-systems far away from the interaction point.However, if one relies on detector simulations it seems to be possible to trigger andmeasure slowly-moving particles at, for example, ATLAS and CMS [376, 378, 379].Of course, this is an area which must continue to be studied as the simulationprograms are further developed and the detectors better understood.The response of each of the general-purpose experiments’ subdetectors to highly-ionizing particles cannot be calibrated directly in situ, and consequently signal ef-ficiency determination relies heavily on simulations. This point is exemplified byan ATLAS search for which the dominant source of uncertainty arises from themodelling of the effect of electron-ion recombination in the liquid-argon calorime- ter in the case of a high energy loss [380]. Last, but not least, the extremely highbackground from Standard Model particles at, say, the High Luminosity LHC in adetector with non-optimal granularity can give rise to backgrounds from, for exam-ple, multi-particle occupancy. Fig. 31. A comparison of the sensitivity of various LHC detectors for highly-ionizing particles.
The MoEDAL-LHC detector is designed to optimize the search for highly-ionizing particles and magnetic charge in a way that is complementary to the reachof the general-purpose LHC detectors, and largely overcomes the experimental diffi-culties for general purpose collider detectors mentioned above. The MoEDAL NTDdetector system is light, thin - around ∼ . Thus, little material is added to the relatively small amount ofexisting material comprising the LHCb vertex detector (VELO) around LHC in-tersection Point IP8. The measurement of the passage of highly-ionizing particles- with Z/ β (cid:38) We estimate that in standard collider detectors between 10 and 100 highly-ionizing particles will need to be registered before a discovery can be claimed. Acomparison of the sensitivity of MoEDAL to highly-Ionizing particles with thatof the other LHC detectors - assuming that ATLAS and CMS need to detect aconservative minimum of 100 events to claim discovery whereas MoEDAL only one- is shown in Fig. 31. This figure is based on an initial study of the detection ofhighly-ionizing particles at the LHC [381].
13. Summary and Conclusions
The primary motivation for the MoEDAL experiment is to look for fundamentalmagnetic monopoles. The discovery of such a particle would revolutionize our under-standing of electrodynamics, electroweak theory, the Standard Model and scenariosfor grand unification. Following the pioneering proposal by Dirac, it was realized by’t Hooft and Polyakov that monopoles appear in generic unified theories. In partic-ular, they may well appear close to the electroweak scale and hence be accessibleat the LHC. Importantly, such a discovery would prove insights into the topologyof the underlying theory at that electroweak scale.As we have also seen, there are many scenarios for new physics in which new,long-lived singly-charged particles may appear. Those produced with low velocitieswould be highly-ionizing and therefore also detectable by the MoEDAL experiment.There are also scenarios predicting the existence of (meta-)stable particles withmultiple electric charges, which would be even more highly-ionizing. We have alsodiscussed in this report several more exotic scenarios for new physics at the LHCthat might be detectable with MoEDAL.The MoEDAL detector is dedicated to the search for the highly ionizing mes-sengers of new physics. It is designed to be clearly superior to the existing LHCdetectors in this challenging arena. Importantly, MoEDAL extends the discoveryreach of the LHC in a complementary way.MoEDAL’s contribution is invaluable even in those scenarios where we can ex-pect a considerable overlap between the physics reach of MoEDAL and the otherLHC experiments. Indeed, MoEDAL is a totally different kind of LHC detector withvery different, systematics and sensitivity. Also, any new particle detected by theMoEDAL would provide a permanent record and in some cases the particle itselfwould be captured. Such considerations would be crucial in the verification and un-derstanding of any revolutionary discovery of beyond the Standard Model physicsat the LHC.We conclude that the MoEDAL experiment, dedicated to the detection of newphysics, would reveal unprecedented insights into such fundamental questions as:does magnetic charge exist; are there new symmetries of nature; are there extradimensions; what is the nature of dark matter; and, how did the universe unfurlat the earliest times. In short, MoEDAL has a revolutionary physics potential thatwill significantly enhance the discovery horizon of the LHC. NOTES
Acknowledgements
We thank the editors of International Journal of Modern Physics A for the invi-tation to write this review. It is a pleasure to thank David Milstead for valuablediscussions. This work was partially supported by: the London Centre for Terauni-verse Studies (LCTS), using funding from the European Research Council via theAdvanced Investigator Grant 267352, the Science and Technology Facilities Coun-cil (STFC, UK), a Natural Science and Engineering Research Council of Canadaproject grant; the V-P Research of the University of Alberta; the Provost of theUniversity of Alberta; and, UEFISCDI (Romania).
Notes Defined to be a convolution of the efficiency and acceptance The concept of Dirac (magnetic) charge is presented in Section 5. If | n | = 1, this is only true for magnetic charge coupled to H ( S = 1 , | q | = 1 / Li ( S =2 , | q | = 3 /
2) and B ( S = 3 , | q | = 5 / The reader should notice that the two-loop processes of Fig. 28(b), which couple the ICgluons to the fermionic SM sector suffer, in addition to the loop suppression, an additional helicitysuppression, as compared to the diagram of Fig, 28(a), and are therefore non-leading contributions.
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