The history of LHCb
TThe history of LHCb
I. Belyaev , G. Carboni , N. Harnew , C. Matteuzzi and F. Teubert NRC Kurchatov Institute/ITEP, Moscow, INFN and Universit`a di Roma Tor Vergata, University of Oxford, INFN and Universit`a Milano-Bicocca, CERN, Geneva
Abstract
In this paper we describe the history of the LHCb experiment over the last threedecades, and its remarkable successes and achievements. LHCb was conceivedprimarily as a b -physics experiment, dedicated to CP violation studies and measure-ments of very rare b decays, however the tremendous potential for c -physics was alsoclear. At first data taking, the versatility of the experiment as a general-purposedetector in the forward region also became evident, with measurements achievablesuch as electroweak physics, jets and new particle searches in open states. Thesewere facilitated by the excellent capability of the detector to identify muons and toreconstruct decay vertices close to the primary pp interaction region.By the end of the LHC Run 2 in 2018, before the accelerator paused for its secondlong shut down, LHCb had measured the CKM quark mixing matrix elements and CP violation parameters to world-leading precision in the heavy-quark systems.The experiment had also measured many rare decays of b and c quark mesons andbaryons to below their Standard Model expectations, some down to branching ratiosof order 10 − . In addition, world knowledge of b and c spectroscopy had improvedsignificantly through discoveries of many new resonances already anticipated in thequark model, and also adding new exotic four and five quark states.The paper describes the evolution of the LHCb detector, from conception to itsoperation at the present time. The authors’ subjective summary of the experiment’simportant contributions is then presented, demonstrating the wide domain ofsuccessful physics measurements that have been achieved over the years. To appear in EPJH a r X i v : . [ phy s i c s . h i s t - ph ] J a n ontents b physics at the end of the XXth century . . . . . . . . . . . . . . . . . . 11.2 Towards the LHC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 CP violation 20 β . . . . . . . . . . . . . . . . . 243.3.2 Measurements of the CKM angle α . . . . . . . . . . . . . . . . . 253.3.3 Measurements of the CKM angle γ . . . . . . . . . . . . . . . . . 253.3.4 The sides of the triangle . . . . . . . . . . . . . . . . . . . . . . . 273.4 Other CP violation measurements . . . . . . . . . . . . . . . . . . . . . . 293.4.1 B s weak mixing phase φ s in B s → J/ψφ . . . . . . . . . . . . . . 293.4.2 CP violation in charm . . . . . . . . . . . . . . . . . . . . . . . . 303.4.3 CP violation in beauty baryons . . . . . . . . . . . . . . . . . . . 303.4.4 CP violation in charmless 3-body B ± decays . . . . . . . . . . . . 30 B → µ + µ − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 B → K ∗ µ + µ − . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.3 Lepton Universality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 J/ψJ/ψ mass spectrum . . . . . . . . . . . . . . . . . . 575.8 Light hadron spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . 58ii
Measurements not originally planned in LHCb 59 W and Z . . . . . . . . . . . . . . . . . . . . . 596.2 Jets in LHCb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596.3 Dark Photons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 646.4 Nuclear Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 iii Introduction
LHCb is an experiment at the CERN LHC, dedicated to the study of heavy flavourswith large statistics. The resulting high precision makes possible the observation of tinydeviations from the predictions of the Standard Model (SM) in CP violation and rarephenomena, variations which could hint at New Physics (NP) processes. LHCb startedtaking data in 2010. The so-called Run 1 commenced at an initial centre of mass energy of √ s = 7 TeV which was then increased to √ s = 8 TeV, collecting an integrated luminosityof 3 .
23 fb − until the end of 2012. After a two-year shutdown, LHC operation continuedfrom 2015 to 2018 (Run 2), when the experiment took data at √ s = 13 TeV, recordingan integrated luminosity of ∼ − . Throughout the running periods, LHCb collectedand analysed an unprecedented number of b decays, and also enlarged its scope to includecharm physics, W and Z measurements, jets and nuclear collisions.In this paper the motivation for the LHCb experiment is described, recalling how itsdesign was developed and evolved. The experiment’s major achievements in terms ofphysics results are then summarised. Finally we discuss the plans for the future upgrade,in the period when the Super-KEKB collider will also operate.The layout of this paper is as follows. The Introduction (Sect. 1) describes thestatus of the b physics programme at the time when the LHCb detector was conceived,and provides an evolution of its design. In Sect. 2 the basic elements of the detectorare described, optimised for the requirements of heavy-flavour physics measurements,together with a description of the triggers. The measurements which were originally themajor aims of the experiment, i.e. the CKM matrix measurements and CP violationand very rare decays of the b -quark, are reviewed in Sects. 3 and 4, respectively. InSect. 5, a summary of the wide-ranging results in b - and c - spectroscopy is presented.A review is given of the many non planned physics areas in Sect. 6, such as resultson jets, electro-weak (EW) physics, and searches for new particles not associated withheavy flavours. In all these domains, LHCb proves to be an extremely versatile detector,providing complementary measurements to those of the LHC General Purpose Detectors(GPDs). The paper concludes in Sect. 8 with a short description of the upgrade plans,which will ensure LHCb operation beyond 2030.The paper presents the authors’ subjective summary of LHCb’s many major physicsresults, however the review inevitably omits a substantial number of important mea-surements. To this end, additional information can be found in the paper’s exhaustivebibliography. b physics at the end of the XXth century In 1970 Glashow, Iliopoulos and Maiani postulated the existence of a fourth quark, charm , necessary to explain the smallness of K oscillations in the framework of theStandard Model of Weak Interactions [1]. The so-called Glashow-Iliopoulos-Maiani (GIM)mechanism generalized Cabibbo’s idea of rotated weak currents to the quark model withtwo doublets, introducing a 2 × J/ψ [2, 3], soon identified as a cc bound state, and followed by the discovery of opencharm. In 1973 Kobayashi and Maskawa [4] proposed a third heavy-quark doublet inorder to describe CP violation in the framework of the SM, thus generalizing the Cabibbo1atrix to the 3 × Υ in 1975, followed by the charged and neutral B -mesons in 1983 [5] proved the validityof their idea and held the prospect of understanding quantitatively CP violation.The level of CP violation in b quark decays was expected to be orders of magnitudelarger than in the neutral K system, but unfortunately the relevant decay channels hadonly tiny branching fractions, so the lack of intense “ b -quark sources” slowed the progressof beauty physics: in particular, in 1986 the PDG only listed five decay modes of B and B ± . However in 1987 a new impetus came from the discovery at ARGUS of B − B oscillations [6]. It was clear that the forthcoming LEP machine, designed for an entirelydifferent purpose, and the symmetrical CESR collider, could not yield an exhaustive answerto all the questions related to the CKM hypothesis, despite their valuable contributionsto many facets of b -physics [7, 8]. When in 1989 P. Oddone proposed an asymmetric e + e − collider [9] operating at the Υ (4 S ) energy with a luminosity above 10 cm − s − , anintense period of accelerator studies ensued. This gave birth to the PEP-II and KEKB B Factories, which were approved in 1994, and started operating in 1998, soon reaching andpassing their design luminosity.Around this time, proponents pursued the idea of exploiting hadron beams to attackthe problem of detecting CP violation in the b sector. The idea behind this was thatthe large hadronic b production cross-section plus the high-intensity hadron beams atthe already existing and planned proton accelerators would produce a large number of bb pairs, sufficient to gather evidence for CP violation at least in the so-called “goldenchannel” B → J/ψK . To achieve an adequate background rejection, the experimentaldifficulties were formidable because of the small ratio of the b cross-section to the totalhadronic cross-section at the √ s values available in fixed-target and collider experiments.In 1985, the fixed-target WA75 hybrid experiment at the CERN SPS [10] observed inemulsions the first partially reconstructed bb pair produced by an extracted pion beamof 350 GeV/c, confirming that the production cross-section at such low energies wasvery small. To circumvent this problem, simple experiments were proposed [11] for theCERN SPS and for the planned UNK machine [12] at Serpukhov, with a brute-forceapproach based on a high-intensity extracted beam and a minimalist detector designed toreconstruct the B → J/ψK decay and to provide flavour tagging (Fig. 1.1). There wasno time-dependent analysis of the decay since the beam-dump character of the experimentsmade the use of a micro vertex detector impossible. There were exploratory fixed-targetexperiments, at CERN (WA92) [13] and at Fermilab (E653, E672, E771, E789) [14], whichtried to observe and measure beauty events, albeit without (or very limited) success.In 1989 P. Schlein proposed a dedicated Beauty experiment exploiting the large b cross-section expected at the CERN SPS proton-antiproton collider ( √ s = 630 GeV) [15].The authors of the proposal (P238) remarked that the bulk of bb production occurredat very small angles with respect to the beams, therefore making a compact experimentpractical. The heart of the detector was a Silicon Microvertex Detector operating veryclose to the beam (1.5 mm) coupled to a fast readout and track-reconstruction electronics.The Microvertex Detector provided the trigger by requiring that accepted events had to beinconsistent with a single vertex. P238 was not approved but the CERN R&D Committee,established to support new detector developments in view of the LHC, approved in 1991 atest of the Microvertex Detector [16] in the SPS Collider. This proved very successful [17]and paved the way towards the future COBEX experimental proposal.At the time when the e + e − colliders were approved, the HERA-B experiment had been2 igure 1.1: A sketch of a proposed beam-dump style experiment designed to detect B → J/ψK decays. The K would traverse the conical slit before decaying [11]. conceived at DESY [18]. Approved in 1994, HERA-B exploited the 920 GeV HERA protonbeam on a fixed target made of metallic wires, placed inside Roman Pots in the vacuumpipe, and immersed in the beam halo. HERA-B was approved to take data in 1998, oneyear before PEP-II and KEKB. The sophisticated apparatus consisted of a single-armspectrometer, including a RICH, a large microvertex silicon detector, a high-resolutiontracker, plus an electromagnetic calorimeter. HERA-B was designed primarily for thedetection of the B → J/ψK decay and its trigger was based on J/ψ reconstruction atthe first level.At √ s = 40 GeV, the bb cross-section is about 10 − of the total hadronic cross-section,hence HERA-B had to achieve a background rejection around 10 − for the B → J/ψK decay. Data taking conditions were similar to those of the current LHCb experiment (a40 MHz interaction rate), as were the requirements of radiation resistance. HERA-Bstarted data taking in 2000 but it soon emerged that the detector did not have sufficientrejection power against background and the track reconstruction was not as efficient asexpected. The large number of detector stations and their total thickness in terms ofradiation lengths made secondary interactions an important issue for event reconstruction.Eventually HERA-B could not observe b events efficiently, but taught several valuablelessons for any future experiment working in a crowded hadron-collision environment.These were a need of a robust and efficient tracking and a flexible trigger systems ableto adapt to harsher environments than may have been expected, as well as the need todesign the thinnest and lightest detector (in terms of radiation and interaction lengths). Over the same period, the planned LHC and SSC machines, with their large energies,promised spectacular increases of the bb cross-section, thus making the task of backgroundrejection much simpler. This was particularly true for operation in collider mode, buteven in fixed-target mode ( √ s ≈ O (130) GeV) the b cross-section was expected to be3 respectable 1 µ b at the LHC and 2 µ b at the SSC [19]. The large cross-section andcorresponding good background rejection would facilitate a hadron B Factory, competitiveand complementary with e + e − colliders, which could focus primarily on the measurementof CP violation and also allow the study of the spectrum of all b particles. Given theintrinsically “democratic” nature of hadronic production, the new hadron machines wouldalso give access to large samples of B s and of b baryons, something not possible at e + e − colliders operating at the Υ resonances.Two schools of thought soon emerged: one pursuing a fixed-target (FT) strategy andthe other based on a collider mode. The more favourable ratio of the bb to the totalhadronic cross-section, about two orders of magnitude larger in collider mode, gave this acompetitive advantage.There was, however, a strong reason in favour of the FT concept: a collider B experiment could not operate at the design luminosity of the machine (10 − cm s − )because of the significant number of overlapping interactions (pile-up) with multiplevertices. This would have required dedicated low-luminosity running, creating a potentialconflict with the major experiments and considerably reducing the data-taking time. Laterit was ascertained that the individual experiment luminosities could be tuned over a broadrange with an appropriate design of beam optics in the interaction regions, hence thiswould become a moot point, but at the time it was a serious one.Moreover, for the advocates of the FT approach, the advantage of the larger cross-section in collider mode was partially offset by the higher event multiplicity and by theshorter flight path of beauty particles. In addition, while the p T of the b decay productswould to a good approximation be the same in the two modes, the p T of the other collisionproducts would be smaller in FT mode, thus making the trigger simpler. Active silicontargets were also possible with an extracted beam, where the track of a charged b -hadronwould be directly measured.Finally, bb production kinematics is forward peaked in the centre-of-mass (CM) system,but the Lorentz boost of the centre-of-mass in the FT mode ( βγ >
60) concentrates theevent at smaller angles than in collider mode. It was therefore possible, in principle,to build a more compact detector, achieving larger angular acceptance at lower cost.There was also the possibility of recycling components (in particular dipole magnets)from existing detectors. The cost was an important consideration, since a dedicated B experiment at the LHC (or SSC) was generally considered to have secondary importancewith respect to the general-purpose experiments.The anticipated demise of the SSC led three groups to study and propose dedicated b experiments at the LHC. The three Letters of Intent (LoI) were presented in 1993.COBEX [20], an acronym for Collider Beauty Experiment, with P. Schlein as spokesperson,was a collider experiment with a backward-forward geometry. The other two proposals,Gajet [21] (spokesperson T. Nakada) and LHB [22] (spokesperson G. Carboni) were fixedtarget experiments, the first, as the name suggests, using a gas jet target, the latterexploiting an extracted beam. Since no traditional beam extraction was foreseen for theLHC, LHB (Large Hadron Beautyfactory) used a parasitic extraction technique, based onchanneling in a bent silicon crystal placed close to one of the circulating beams (Fig. 1.2).A dedicated R&D experiment, RD22, approved by the CERN DRDC [23] to test thefeasibility of this idea at the SPS, demonstrated that high-efficiency beam extraction(larger than 10%) was possible [24]. The three proposed experiments were presented intheir final form in 1994 at the Beauty’94 Conference [25]. It should also be noted that,4 (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0) Distance from Crossing Point (m) V e r t i ca l D i s p l ace m e n t ( m ) (cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)(cid:0)
20 mrad
Enlarged aperture D1Crystal0.7 mrad Q3 Warm Septum magnet3.4 mrad D1Optional Cold Bends15 mrad
Figure 1.2: Proposed LHC beam extraction scheme based on crystal channeling. The channeledbeam, deflected by 0.7 mrad in a bent silicon crystal, was guided towards the beam transporttunnel by several conventional magnets. The cost of the extracted beam was a non-negligiblefraction of the detector cost. by then, CDF had already contributed important b -physics results, offering a glimpse ofwhat would later prove to be the extraordinary success of b -physics at hadronic machines.Following the submission of the LoIs, the LHC Committee (LHCC) considered theproposals in June 1994. One of its concerns was the small size of the three collaborations:the total number of physicists involved was barely one hundred. In addition the Committeeremarked that beam extraction by channeling could not be guaranteed at that stage, be-cause accelerator experts feared possible interference with normal LHC operation. Finallythe following recommendation was issued: “The collider model approach has the greaterpotential in view of the very high rate of b production, the much better signal/backgroundratio and the possibility of exploring other physics in the forward direction at 14 TeV”. The LHCC encouraged the three collaborations to join together and design a new ex-periment, incorporating attributes of each, and operating in collider mode. The LHCCnoted that its ambitious request was justified by the fact that, at the startup of the LHC,the experiment would not be an exploratory one, since CP violation would already havebeen observed “at HERA-B, FNAL or B Factories”. The LHCC also issued guidelinesrequiring a number of issues to be addressed and solved. The three experiments combinedinto the new LHC-B Collaboration (then named), which published its Letter of Intent in1995 [26].The new experiment derived several of its characteristics from the parent proposals:notably the concept of a silicon vertex detector in retractable pots, the calorimeter design,and the high p T first-level trigger.In the transition to LHC-B, a number of proponents from the former three collabo-rations decided not to continue. This unfortunately included P. Schlein and his UCLAcolleagues who had pushed very strongly for the collider-mode idea with COBEX, and whohad been a driving force up to that point. The LHCC decision sent a strong signal to thehigh-energy physics community: that CERN were prepared to give their strong support toone dedicated B experiment. This encouraged many physicists from institutions aroundthe world to join the new collaboration over the subsequent years. T. Nakada, who was5n instigator of the Gajet proposal, was elected LHC-B spokesperson. The 1995 Letterof Intent of LHC-B established the basis for the new detector design, which was refinedin the following years, until its approval in 1998. By that time, the name had changedfrom LHC-B to simply LHCb. Fig. 1.3 shows the detector as it appeared in the Letter ofIntent. Figure 1.3: The LHC-B detector as it was proposed in 1995. All the basic components shownwould be part of the final detector, albeit with many refinements and optimisations that will bedescribed in the following Section.
Soon afterwards, a competing B -physics experiment, BTeV [27], was proposed to runat the Fermilab Tevatron, incorporating a single magnet, a double arm spectrometer anda vertex trigger at the first level, in order to recover the reduced b production cross section.Following the decision to shut down the Tevatron, BTeV was not approved, howeverseveral of the experiment’s innovative ideas were carried through to the future LHCbexperiment. 6 The LHCb Detector
The basic mechanism for heavy-quark production at the LHC is via gluon-gluon fusion.The angular distribution of cc or bb pairs is peaked at small angles with respect to thebeam-line, with high correlation between the constituents of the pair. This allows thedetection with good acceptance of the resulting hadrons in a rather limited solid angle.QCD calculations give cross-section values of σ cc (cid:39) . σ bb (cid:39) . single arm spectrometer.The LoI design inherited important features from the three ancestor experiments andfrom the contemporary HERA-B, which had rate and radiation issues similar to thoseexpected at the LHC. In contrast to the latter experiment, LHC-B had in addition ahadron calorimeter and a second (upstream) RICH with two radiators. Initially it wasthought that an efficient tracking system in a harsh environment would require a largenumber of tracking stations, so, paralleling HERA-B, LHC-B had twelve tracking stationsin the large-angle region. This number was reduced to ten in the Technical Proposalpresented in 1998 [28], which by then had changed its name to LHCb.The disappointing performance of HERA-B was largely ascribed to the large amount ofmaterial in the detector, which prompted the LHCb collaboration to perform a thoroughreview of the apparatus, with the aim to reduce material without sacrificing performance.A Technical Design Report submitted in 2003 presented the LHCb “Reoptimized” Detec-tor [29]. This is the basis on which the experiment was eventually built and is describedin the following subsections. The LHCb detector [30] is a forward spectrometer, shown in Fig. 2.1, and is installedat Intersection Point 8 of the LHC. A modification to the LHC optics, shifting theinteraction point by about 11 m from the centre, allowed maximum use of the cavernspace. This results in a detector length of approximately 20 m, and with maximumtransverse dimensions about 6 × . The angular acceptance ranges from approximately10 mrad to 300 mrad (Fig. 2.2) in the horizontal magnetic-bending plane, and from10 mrad to 250 mrad in the vertical plane (Fig. 2.1). With this geometry the detector isable to reconstruct approximately 20% of all bb pairs produced.To measure the momenta of charged particles, a dipole magnet producing a verticalmagnetic field is used. It is a warm magnet providing an integrated field of 4 Tm, withsaddle-shaped coils in a window-frame yoke, and with sloping poles in order to matchthe required detector acceptance. The design of the magnet allows for a level of fringefield inside the upstream Ring Imaging Cherenkov detector (RICH 1, see Sec. 2.4) of lessthan 2 mT whilst providing a residual field in the regions between the upstream trackingstations.The tracking system consists of a silicon VErtex LOcator detector (VELO) [31],7urrounding the interaction region, and four planar tracking stations, the TT trackerupstream of the dipole magnet and three tracking stations T1-T3 downstream of themagnet [32, 33]. The T1-T3 stations consist of an Inner Tracker (IT), located at thecentre of the stations and surrounding the beam-pipe, and an Outer Tracker (OT) forthe outer regions. A minimum momentum of around 1.5 GeV/ c is required for a track toreach the downstream stations [34]. M1 M3M2 M4 M5RICH 2 HCALECALSPD/ PSMagnet z5my5m 10m 15m 20mTT T1T2T3Ver t exLocat or RICH 1
Figure 2.1: The LHCb detector: side viewFigure 2.2: The LHCb detector: top view (cid:39) c using aerogel (in Run 1 only) and C F radiators, whilst the downstream detector, RICH 2, covers the high momentum rangefrom 15 GeV/ c up to and beyond 100 GeV/ c using a CF radiator.Two calorimeters, one electromagnetic (ECAL) and the other hadronic (HCAL),supplemented by a Preshower Detector (SPD/PS) [35], provide identification of electrons,photons and hadrons and a measurement of their energy. This measurement is used atthe trigger level to select candidates on the basis of their transverse energy. Muons play acrucial role in many of LHCb’s measurements because of the cleanliness of the signature.Their identification is achieved by five muon stations (M1 – M5), interspersed with ironfilters. The muon system also supplies measurements of muon transverse momenta for thetrigger. The role of the VELO is to measure the impact parameters of all tracks relative to theprimary vertex (PV), to reconstruct the production points and decay vertices of hadronscontaining b - and c -quarks and to allow precision measurements of their mean lifetimes.The subdetector accepts particles with pseudorapidities in the range 1 . < η < . | z | < . µ m thickness,one with strips in the radial, r coordinate, the other in the polar, φ coordinate. Thiscylindrical geometry allows a fast track- and vertex-reconstruction to be made at thesecond stage of trigger. The strip segmentation is such to limit the highest occupancy ofthe strips to less than 1.1 %.The VELO is positioned, with an accuracy better than 4 µ m, at the closest distancepossible from the beam, about 7 mm during data taking, The sensors operate withina so-called Roman pot configuration, located inside a secondary vacuum of less than2 · − mbar pressure, separated from the primary LHC vacuum. The sensors areretracted during beam injection and are then quickly moved in for physics operation whenthe LHC beams are stable.The vessel containing the silicon discs and the front-end electronics (RF-box) hasaluminium walls of 300 µ m thickness to minimize multiple scattering. The averagematerial budget of the detector for tracks in the LHCb acceptance is 0.22 X . In order tominimize radiation damage and to dissipate the produced heat, a cooling system keepsthe temperature range between -10 to 0 ◦ C.Fig. 2.3 summarizes the VELO performance in terms of impact parameter and decaytime resolution [31]. 9 -1 c [GeV T p m ] m r e s o l u ti on [ x I P T p = 11.6 + 23.4/ s T p = 11.6 + 22.6/ s Simulation,
LHCb VELO ] c [GeV/ p r e s o l u ti on [f s ] LHCb
Figure 2.3: Left: Projected impact parameter resolution as a function of 1 /p T . Right: Decaytime resolution (points) as a function of momentum for B s → J/ψφ decays. The superimposedhistogram shows the distribution of momentum for the decay.
Following the VELO, the tracking system is composed of the TT station, located betweenRICH 1 and the magnet, and three stations (T1,T2,T3) downstream of the magnet. TheTT is composed of four stations grouped in pairs, called TTa and TTb, spaced by 30 cm.Each station consists of silicon microstrip planar modules covering a rectangular area of150 cm ×
130 cm (width times height), covering the LHCb acceptance of 300 mrad inthe horizontal plane and 250 mrad in the vertical. The strips of the first and the fourthstations are vertical and measure the bending x coordinate, whilst the second and thirdplanes have stereo angles of ± ◦ , respectively.Tracking stations T1 - T3 each consist of an inner part (IT) surrounding the beampipe, and an outer part (OT) beyond. Each IT station consists of four overlapping siliconlayers, two rotated by a stereo angle of ± y (vertical) axis.Each layer is made up of four independent modules placed around the beam pipe, coveringabout a 120 ×
40 cm area, as shown in Fig. 2.4. Figure 2.4: The LHCb inner detector, (left) a vertically-aligned layer, (right) a stereo layer. µ m per hit, withstrip pitches of about 200 µ m. The hit occupancies vary between 1.9% for the innersectors to 0.2% for the outermost modules. To minimize radiation damage, the sensorsoperate at 5 ◦ C temperature.The OT is a drift detector [32] consisting of straw tubes with internal diameters of 4.9mm, each filled with an Ar/CO gas mixture in a ratio 70 − µ m spatial resolution with 17% maximum strawoccupancy. Each of the three stations is made of four modules, shown schematically inFig. 2.5. A picture of the assembled OD is shown in Fig. 2.6. In the first and third modulesthe straw tubes are aligned to the vertical axis while the third and fourth modules havestereo angles of ± . × . m , covering the fullLHCb acceptance.The overall tracking efficiency for “long” tracks (i.e. those tracks measured in all thetracking detectors including the VELO) is greater than 96 % for 5 < p <
200 GeV/ c . Themomentum resolution dp/p is 0.5% at low momentum, increasing to 1.1% at 240 GeV/ c .The mass resolution is 14 . c for the J/ψ resonance.
Figure 2.5: Schematic views of the LHCb outer detector.
The role of the RICH system [36] is to provide π/K/p discrimination for LHCb, which isessential for most CP -violation studies, background rejection and flavour tagging. Themomentum range which contains 90% of kaons, pions and protons from B meson decayis between 2 and 150 GeV/ c and, to achieve this separation, two Cherenkov detectors,RICH 1 and RICH 2, are employed.The RICH 1 detector differentiates particles with low and intermediate momenta, from1 to ∼
60 GeV/ c . It is located close to the interaction region, upstream of the magnet, andcovers the acceptance from ±
25 mrad to ±
300 mrad (horizontal plane) and to ±
250 mrad(vertical plane). RICH 1 initially contained two different radiator materials: an aerogel11 igure 2.6: The LHCb Outer Detector in place on the beam line. Well visible is the beam pipe. layer 5 cm thick with refractive index n = 1 .
03 and a C F gas layer of length 85 cm withrefractive index n = 1 . π/K discrimination fromabout 1 up to 10 GeV/ c , however it was removed for Run 2 due to occupancy problems.The C F radiator extends the positive π/K identification from about 10 GeV/ c to60 GeV/c, however π/K discrimination below 10 GeV/ c is still possible by operating theRICH in kaon veto mode.RICH 2 has a smaller angular acceptance of ±
15 mrad to ±
120 mrad (horizontal plane)and to ±
100 mrad (vertical plane) and covers the region where high momentum particlesare most abundant. It is located downstream of the magnet, between T3 and the firstmuon station M1. RICH 2 uses a CF gas radiator with refractive index n = 1 . The calorimeter system identifies hadrons, electrons and photons, and also measurestheir energies and positions for the Level-0 trigger. The system is composed of foursub-detectors: the scintillator Pad Detector (SPD), the PreShower detector (PS), theElectromagnetic Calorimeter (ECAL), and the Hadron Calorimeter (HCAL). The SPDand PS are located just upstream of the ECAL. The ECAL, PS and SPD are segmented12 omentum (GeV/c) ( m r a d ) C Θ π µ π K n=1.03n=1.0014n=1.0005
Momentum (GeV/c)Momentum (GeV/c)
10 10 C h e r e n k o v A ng l e ( m r a d ) µ (cid:391)(cid:1) Figure 2.7: (Left) Values of Cherenkov angle as a function of momentum for different particlesfor the three RICH radiators of refractive index n . (Right) Measured Cherenkov angles in LHCbdata [36]. into three sections in the xy plane, with active pads growing from the inner to the outerregions. The HCAL is similarly divided in two sections. The corresponding granularitiesare outlined in Fig. 2.8. Outer section : Inner section : 121.2 mm cells 2688 channels 40.4 mm cells 1536 channels Middle section : 60.6 mm cells 1792 channels
Outer section : Inner section : 262.6 mm cells 608 channels 131.3 mm cells 860 channels
Figure 2.8: The (left) LHCb electromagnetic calorimeter and (right) hadronic calorimeter. Thebottom left regions indicate the areas occupied by the beam-pipe.
The SPD and PS are used at the trigger level and offline, in association with theECAL, to indicate the presence of electrons, photons and neutral pions. The detectorshave two plastic scintillator layers separated by a 15 mm thick lead plate where electronsand photons can radiate; the downstream scintillator then samples the radiated energy.The light from the scintillators is sent to photomultipliers by wavelength-shifter (WLS)optical fibers.The ECAL employs the
Shashlik technology, where independent modules, constructedfrom scintillating tiles and lead plates, are alternated (see Fig. 2.9). The ECAL has136 layers of such modules consisting of 2 mm of lead followed by 4 mm of scintillatormaterial. The ECAL also uses WLS optical fibers to guide the light from the detectorto photomultipliers, placed on the back face of each module. The energy resolutionachieved [35] is σ ( E ) E = 10% √ E ⊕
1% (2.1)where E is the electron energy expressed in GeV.The HCAL is also a sampling calorimeter. It is constituted of iron absorber withscintillating tiles as the active material. The innovative feature of this sampling structureis the orientation of the scintillating material: the tiles run parallel to the beam axis. Inthe lateral direction, tiles are spaced with 1 cm iron, while longitudinally the length ofthe tiles and iron spacers correspond to the hadron interaction length λ I (cid:39)
20 cm in steel.Light is collected by WLS optical fibres running along the detector towards the back sidewhere the photomultiplier tubes are located (see Fig. 2.9).
Figure 2.9: A schematic showing the layout and segmentation of the LHCb ECAL and HCALcalorimeters.
The HCAL is used to measure the hadronic shower transverse energy for the Level-0trigger and to improve the high momentum electron/hadron separation. The energyresolution achieved is σ ( E ) E = (69 ± √ E ⊕ (9 ± E is the hadron energy in GeV. The Muon System consists of five stations, M1-M5, of rectangular shape. The completesystem is made up by 1368 Multi Wire Proportional Chambers supplemented by 12 TripleGEM Chambers in the inner region of the first station, to cope with the very high particlerate. The chambers employ a variety of readouts, optimized for a precise p T measurementfor the trigger. The complete system has an acceptance in the bending plane from 20 mrad14o 306 mrad, and in the non-bending plane from 16 mrad to 258 mrad. This results in atotal acceptance of about 20% for muons from semileptonic inclusive b decays.The M1 station is located in front of the calorimeters and is used in order to improvethe p t measurement for the trigger. The geometry of the five stations is projective; all thetransverse dimensions scale as the distance from the interaction point. Stations M2-M5are placed downstream of the calorimeters and are interleaved with 80 cm thick ironabsorbers. The total absorption thickness, calorimeters included, is about 20 interactionlengths. In this way the minimum momentum for muons crossing the five stations is about6 GeV/ c .Each muon station is designed to achieve an efficiency above 99% in a 20 ns timewindow with a noise rate below 1 kHz per physical channel, as described in [37]. To reachsuch an efficiency, four chamber layers per station are used in M2-M5 (two layers in M1).The time resolution is achieved by a fast gas mixture Ar/CO /CF in the ratio 40:55:5. Aratio 45:15:40 is employed in the Triple GEM chambers. Even with the relatively large bb cross-section at LHC energies, only approximately 1%of visible pp interactions result in a bb event. Moreover, only about 15% of those eventswill produce at least one b -hadron with all decay products passing within the acceptanceof the spectrometer. The branching fractions of decays used to study CP violation aretypically less than 10 − . Further reductions are unavoidable in the offline selection, wherestringent cuts must be applied to enhance signal over background. Therefore the purposeof the LHCb trigger is to achieve the highest efficiency for the events later selected in theoffline analysis while rejecting drastically most of the uninteresting background events.To achieve this goal, the trigger uses information from all LHCb sub-detectors.The trigger is organised in two different levels: the Level-0 (L0) trigger based oncustom electronic boards, and the High-Level Trigger (HLT), implemented in a computerfarm. Level-0 uses the information from the calorimeter and muon systems, performinga selection in order to reduce the event rate from 40 MHz to below 1 MHz, which isthe maximum frequency allowed to read out the entire detector. The HLT is a softwareapplication running on a processor farm that further reduces the rate of events in the kHzrange for storage (see Fig. 2.10).The HLT has significantly evolved over time from the original design in the LHCbTechnical Proposal (TP) [38] in 1998, to the trigger design in the Technical Design Report(TDR) [39] in 2003, to the Run 1 (2010-2012) actual implementation [40] and finally to theadditional features introduced during Run 2 (2015-2018) [41]. In the TP it was assumedthat a first HLT trigger level (L1) would reduce the 1 MHz input rate to a 40 kHz outputrate with a variable latency of less than 256 µ s, using coarse information from the vertexdetector to reconstruct vertices and tracks with no momentum information (the VELO r- φ geometry was designed for this purpose). A second HLT trigger level (L2) was fashionedto extrapolate VELO tracks into the magnetic field to the tracking stations downstream ofthe magnet and reduce the output rate to 5 kHz with an average latency of 10 ms. Finallya third level (L3) would implement the full event reconstruction and a set of exclusiveselections to bring down the rate to 200 Hz.By the time of the trigger TDR in 2003, it became clear that the LHC was not going tostart before the end of the decade when much more powerful processing units would become15vailable. In addition a series of test-beam and detailed simulation studies convinced thecollaboration of the need to have momentum information at the first stage of the HLT.Therefore a new tracking station just upstream of the magnet was introduced (the TTstation). In addition, a shield which had been protecting RICH1 from stray magnetic fieldswas removed to allow for a rough estimation for the momentum of tracks reconstructedbetween the VELO and TT stations. The software trigger then had two levels: Level-1able to reduce the output rate to 40 kHz using L0, VELO and TT information with anaverage latency of 1 ms, and HLT to reduce the output rate to 200 Hz with a combinationof inclusive and exclusive selections. Between the time of the trigger TDR and the firstphysics run (Run 1), the interest in having a more performing HLT for charm physics( cc with a factor 20 larger production cross section than bb ) and a much more robustsystem, convinced the collaboration to push for much more inclusive selections in the finaltrigger stage and a much larger trigger output rate (3-5 kHz). This implied a completeredefinition of the offline data processing model.Furthermore, it had been assumed that the LHC would operate with a 25 ns bunchseparation, limiting the number of overlapping events to a mean number of µ (cid:39) . × cm − s − . When, from 2011, a separation of50 ns was adopted for early LHC operation, the experiment decided to run at µ ≈ . O (110 kHz). Thedecrease in requests for offline reconstruction also helped to mitigate the pressure on theoffline computing model. The L0 trigger is divided into three independent components: the L0-Calorimeter trigger,the L0-Muon trigger and the L0-PileUp trigger. The latter is used to reject multiplevisible interactions in a bunch crossing by means of the “ad hoc”
Pile-Up System detectorhoused in the VELO. The first two components are briefly described below.The L0-Calorimeter part of the trigger obtains informations from the SPD, PS, ECALand HCAL subdetectors and computes the transverse energy deposited by incident particles: E T = E cos θ , where E is the energy of the particle and θ is the polar angle given bythe cell hit in the detector. Together with energy information, the total number of hits inthe SPD (SPD multiplicity) is also determined in order to veto large multiplicity events16 igure 2.10: Trigger overview in Run 1 (left) and Run 2 (right) that would take too large a fraction of the available processing time in the HLT. Fromthe calorimeter information, three types of candidates are built and selected according tospecific E T criteria: i) Hadron candidate (L0Hadron); ii) Photon candidate (L0Photon);and iii) Electron candidate (L0Electron).The L0-Muon part of the trigger requires a muon candidate to have a hit in all fivemuon stations. The L0 muon processor boards select the two highest p T muon tracks ineach quadrant of the muon system with a maximum of eight candidates. The trigger setsa single threshold either on the largest muon p T (L0 muon trigger) or on the product ofthe largest and the 2nd largest (L0 dimuon trigger). Events with SPD multiplicity > Data from L0 are sent to the Event Filter computer Farm (EFF) which runs the HLTalgorithms. The HLT is a software application whose 29500 instances run on the EFF.Each instance is made up of independently operating trigger lines; each line consists ofselection parameters for a specific class of events.The HLT is divided into two stages. The first stage (HLT1) processes the full L0 rateand uses partial event reconstruction to reduce the rate to about 110 kHz. The secondstage (HLT2) reduces the rate to about 12.5 kHz, performimg a more complete eventreconstruction [41]. 17
LT1 reconstructs the trajectories of charged particles traversing the full LHCbtracking system which have a p T larger than 500 MeV. The hits in the VELO arecombined to form straight-line tracks loosely pointing towards the beam line. Next, atleast three hits in the TT are required in a small region around a straight-line extrapolationfrom the VELO. The TT is located in the fringe field of the LHCb dipole magnet, whichallows the momentum to be determined with a relative resolution of about 20%, and thisestimate is used to reject low p T tracks. Tracks are then extrapolated to the T-stationsdownstream of the magnet. The search window in the IT and OT is defined by themaximum possible deflection of charged particles with p T larger than 500 MeV. The searchis also restricted to one side of the straight-line extrapolation by the charge estimate ofthe track. Subsequently, all tracks are fitted with a Kalman filter to obtain the optimalparameter estimate using a simplified geometry description of the LHCb detector. Theset of fitted VELO tracks is re-used to determine the positions of the PVs.Tight timing constraints in HLT1 mean that most particle-identification algorithmscannot be executed. The exception is muon identification due to its clean signature. Hitsin the muon stations are searched for in momentum-dependent regions of interest aroundthe track extrapolations. Tracks with p < p T , and a line which selects a displaced two-track vertex with high p T . Both linesstart by selecting good quality tracks that are inconsistent with originating from the PV.The single-track trigger then selects events based on a hyperbolic requirement in the 2Dplane of the track displacement and p T . The two-track displaced vertex trigger selectsevents based on a multivariate discriminant whose input variables are the vertex-fit quality,the vertex displacement, the scalar sum of the p T of the two tracks and the displacementof the tracks making up the vertex. The two-track line is more efficient at low p T , whereasthe single track line performs better at high p T , such that in combination they providehigh efficiency over the full p T range.The HLT1 muon lines select muonic decays of b and c hadrons, as well muons originatingfrom decays of W and Z bosons. There are four main lines: one line that selects a singledisplaced muon with high p T , a second single muon line that selects very high p T muonswithout displacement for electroweak physics, a third line that selects a dimuon paircompatible with originating from a decay of a charmonium or bottonium resonance orfrom Drell-Yan production, and a fourth line that selects displaced dimuons with norequirement on the dimuon mass. During Run 2, typically about 80 kHz were allocatedto the inclusive HLT1 lines, while about 20 kHz to the muon lines. The rest of the HLT1output is dedicated to special low multiplicity triggers and calibration trigger lines. HLT2 can perform the full event reconstruction since the output of HLT1 is buffered.The full event reconstruction consists of three major steps: the track reconstruction ofcharged particles, the reconstruction of neutral particles and particle identification. TheHLT2 track reconstruction exploits the full information from the tracking sub-detectors,performing additional steps of the pattern recognition which are not possible in HLT1.Tracks with a p T larger than 80 MeV are reconstructed in HLT2, without the requirementto have hits in the TT station. This is to avoid inefficiencies due to the TT acceptance,which is crucial for part of the charm and kaon physics programme. In addition, tracks18roduced by long-lived resonances that decay outside the VELO are reconstructed usingT-station segments that are extrapolated backwards through the magnetic field andcombined with hits in the TT. Similarly, the most precise neutral cluster reconstructionalgorithms are executed. Finally, in addition to the muon identification available in HLT1,HLT2 exploits the full particle identification from the RICH detectors and calorimetersystem.The HLT2 inclusive b -hadron trigger lines look for a two-, three-, or four-track vertexwith sizeable p T , significant displacement from the PV, and a topology compatible withthe decay of a b -hadron, using a multivariate discriminant. Whenever one or more tracksare identified as muons, the requirements on the discriminant are relaxed to increase theefficiency. As in the case of HLT1, several muon lines are used to select muonic decays of b and c hadrons and of W and Z bosons. However in HLT2, the muon reconstruction isidentical to the offline procedure, having access to exactly the same information. DuringRun 2, typically about 3 kHz of the trigger rate is from the inclusive b -hadron triggerwhile the muon lines take about 1 kHz. A large fraction of the trigger bandwidth (2-4 kHz)is allocated to exclusive selection of charm decays, where a reduced amount of informationis saved per event. The rest of the trigger bandwidth is due to other special triggers andcalibration trigger lines. 19 LHCb contributions to CKM measurements and CP violation The violation of the combined operation of charge conjugation and parity, CP , was firstobserved in 1964 in decays of neutral kaons [43]. The BaBar [44] and Belle [45] B Factoryexperiments and the CDF experiment [46] established CP violation in the decays of neutral B mesons. LHCb now extends measurements to much greater precision, and also probesthe B s system, which is vital to explore the full range of CP violation measurements.In the Standard Model, the Cabibbo-Kobayashi-Maskawa (CKM) unitary matrix [4,47],V CKM , describes the electroweak coupling strength V ij of the W boson to quarks i and j :V CKM = V ud V us V ub V cd V cs V cb V td V ts V tb . (3.1) CP is violated in the Standard Model if any element of the CKM matrix is complex.The parametrisation of the CKM matrix due to Wolfenstein [48] is given byV CKM = − λ − λ λ Aλ ( ρ − iη ) − λ + A λ [1 − ρ + iη )] 1 − λ − λ (1 + 4 A ) Aλ Aλ [1 − (1 − λ )( ρ + iη )] − Aλ + Aλ [1 − ρ + iη )] 1 − A λ (3.2)for the four Standard Model parameters ( λ, A, ρ, η ). The expansion parameter, λ , equal tothe sine of the Cabibbo angle, has a value | V us | = 0 .
22 [49], and in Equ. 3.2 the expansionis given for terms up to order λ .The unitarity of the CKM matrix leads to six orthogonality conditions between anypair of columns or any pairs of rows of the matrix. The orthogonality means the sixconditions can be represented as six triangles in the complex plane. The interestingrelations for CP violation are those given by: V ud V ∗ ub + V cd V ∗ cb + V td V ∗ tb = 0 : the unitarity triangle , (3.3) V us V ∗ ub + V cs V ∗ cb + V ts V ∗ tb = 0 : the B s triangle , and (3.4) V cd V ∗ ud + V cb V ∗ ub + V cs V ∗ us = 0 : the charm triangle . (3.5)The unitarity triangle has sides with lengths that are the same order in λ , namely O ( λ ),which implies large CP asymmetries in B and B ± decays. The B s triangle has two sidesof O ( λ ) and the third of O ( λ ). Hence CP violation in B s mixing is significantly smallerthan in the B system. Moreover, the charm triangle has two sides of O ( λ ) and the thirdof O ( λ ), hence CP violation in the charm system is expected to be extremely small. Notethat all three triangles have equal area [50].To study CP violation, the B − physics experiments measure the complex phases ofthe CKM elements and measure the lengths of the sides of the triangles to check for aself-consistent picture. CP violation is predicted in many (often very rare) B hadrondecays, hence LHCb utilises large samples of B , B s , B c mesons and B − baryons. Newphysics can be discovered and studied when new particles appear in, for example, virtual20 igure 3.1: The knowledge of the unitarity triangle as of autumn 2009 [52]. loop processes of rare B decays, leading to observable deviations from Standard Modelexpectations, both in branching ratios and CP observables. Hence the LHCb strategy isto determine with high precision the CKM elements and to compare measurements of thesame parameters, especially those where one is sensitive to new physics and the other toStandard Model processes. The first generation B Factory experiments to study CP violation in the B − system,BaBar and Belle, made huge in-roads into testing the Standard Model description of CP violation; the status was summarised extensively at the Beauty 2009 Conference [51].CDF and D0 extended these studies at the Tevatron, and make first explorations in the B s sector. Fig. 3.1 shows the status of the unitarity triangle measurements compiled bythe CKM-Fitter Group [52] in 2009, when the B Factories had been running for aroundten years. Here graphical results are displayed in the ρ − η plane and the best fit to theapex of the triangle (Equ. 3.3) to the 95% confidence level is shown. The fit to the CKMparametrisations include measurements of the sides of the triangle through measurementsof the CKM elements and the angles, information from rare K and B meson decays, and B s − B s mixing.Before 2009, when the LHC turned on, the B Factory experiments, CDF and, to alesser degree D0, measured the parameters of the unitarity triangle with varying degreesof precision: • The quantity sin 2 β was measured in all channels, including the “gold plated” channel21 → J/ψK S , to a precision of around ∼ • The sides | V td /V ts | and | V ub /V cb | were known from B s − B s mixing and from b → u decays, respectively each to ∼ B s mixing phase ( φ s )was unmeasured; • The angle α was measured in the channels B → ππ , ρπ and ρρ with a statisticalprecision of ∼ ◦ ; • There was a statistics-limited measurement in B → DK modes of the angle γ toaround 20 − ◦ . A measurement of γ from B s modes such as B s → D + s K − hadbeen completely unexplored. • The parameter ε K , measured in kaon decays, provided a very loose constraint onthe triangle vertex; • The B s sector had been largely unexplored by the first generation experiments, ashad b − baryons. Running at the Υ(4 S ), the B Factories produced predominantly B u,d meson pairs, however Belle record a significant sample of Υ(5 S ) data, allowingsome interesting measurements of B s pairs. At the LHC, B , B ± , B s , B c and b − baryons are produced in approximately in the ratios ∼
40 : 40 : 10 : 0 . • The B Factories were statistics limited for very rare processes with branching ratios (cid:46) × − , such as b → s flavour-changing neutral current (FCNC) transitions,e.g. b → sγ and b → sl + l − . Super-rare transitions such as B ( s,d ) → µ + µ − were alsounobserved.In contrast, Fig. 3.2 shows the status of the unitarity triangle measurements today[52]. Figure 3.2: The current knowledge of the unitarity triangle (as of Summer 2019) [52]. igure 3.3: The box diagrams representing mixing between B q and B q mesons. Since flavour is not conserved in the weak interaction, mixing between B q and B q mesons(where q = d or s ) is possible via the box diagrams shown in Fig. 3.3. The probabilityfor finding a B q (or a B q ), given the initial state was a B q (or a B q ) at time ∆ t afterproduction, is given by: P mix (∆ t ) = exp − ∆ tτ B (1 − cos(∆ m q ∆ t )) . (3.6)Here ∆ m q is the mass difference m H − m L , where m H,L are the masses of the heavy andlight mass eigenstates and τ B is the B lifetime. At the LHC, the two neutral B mesonsproduced can oscillate independently at any time after production.Any CP measurement from a time-dependent analysis of neutral B decays needs thedetermination of the B flavour ( b or b ) at production. This requires b − quark “tagging”,and several algorithms have been developed by LHCb involving the combination ofso-called opposite side [53] and same side taggers [54]. • B mixing: B oscillations are measured in the channel B → D − µ + ν µ X and thecharge conjugate modes. The oscillation measurements rely on tagging, and areshown for 3 fb − of data in Fig. 3.4 (left). The LHCb ∆ m d measurement, which isthe world’s best, is ∆ m d = (505 . ± . ± .
0) ns − [55]. • B s mixing: B s − B s oscillations were first observed by CDF [56]. B s oscillationsare measured at LHCb in the mode B s → D − s π + and its charge conjugate state. Theoscillations are shown for 1 fb − of data in Fig. 3.4 (right). The plot shows the proper-time distribution of B s → D − s π + candidates, in five different B s decay channels, thathave been flavour-tagged as not having oscillated. The LHCb ∆ m s measurement,which is again the world’s best, is ∆ m s = (17 . ± . ± . − [57]. • Charm meson mixing: D − D mixing was established in a single experiment in 2013 by LHCb in D → K + π − decays, although it was confirmed earlier by combining several B Factoryresults. The D mixing parameters were measured in LHCb in a decay-time-dependent fit to the ratio N D → K + π − N D → K − π + . The time-dependent fit is shown in Fig.3.4(lower) for 1 fb − of data. The no-mixing scenario is excluded at 9 . σ [58].23 igure 3.4: Proper-time distribution of (left) B − B oscillations in B → D − µ + ν µ X decays,(right) B s − B s oscillations in B s → D − s π + decays, and (lower) D − D oscillations in D → K + π − decays. All distributions rely on flavour tagging, and the curves correspond to the fittedoscillations. The LHCb experiment performs a high-statistics study of CP violation with unprecedentedprecision in many different and complimentary channels, providing a sensitive test of theStandard Model and physics beyond it. β The time-dependent decay asymmetry of the channel B → J/ψK S allows a measurementof the angle β . This is known as the “golden” decay mode because the channel is virtuallyfree of penguin pollution (which enters with the same overall phase), resulting in verysmall theoretical uncertainty, of order 1% [59]. CP violation in this channel occurs in theinterference between mixing and decay, where the mixing process introduces a relative CP -violating weak phase of 2 β . Experimentally the CP asymmetry is measured from theratio of the numbers of B and B mesons, N B → f and N B → f , decaying into final state f : A CP = N B → f − N B → f N B → f + N B → f = sin (∆ m d t ) sin (2 β ) − cos (∆ m d t ) cos (2 β ) . (3.7)24he LHCb measured and fitted asymmetries for the J/ψ (1 S ) and (2 S ) states areshown in Fig. 3.5 for 3 fb − of data at 7 and 8 TeV [60]. These measurements arecos (∆ m d t ) = − . ± .
029 and sin (∆ m d t ) = 0 . ± . CP -violation contribution proportional to cos (∆ m d t ) would be an indicationof new physics [59]. The LHCb measurement is now competitive with BaBar and Bellemeasurements; the current world average of sin 2 β = 0 . ± .
019 [61] is dominatedby LHCb together with the B Factory measurements in the complementary channels B → J/ψK S and B → J/ψK L . The measurement by LHCb of sin 2 β in gluonicpenguins will further contribute to this study. Figure 3.5: The LHCb measured and fitted asymmetry in B → J/ψK S decays for (left) the J/ψ (1 S ) and (right) the ψ (2 S ). α The primary method at LHCb for the measurement of α is through an amplitude analysisvia the B → ρπ decay modes [62], however these channels are difficult at LHCb dueto the need to efficiently reconstruct π s. Penguin pollution is present and must beconstrained, with the additional application of isospin symmetry. The precision on α atLHCb is expected to be dominated by systematic uncertainties, and any measurementis not expected to improve on a combination of the B Factory measurements, α = (cid:0) . +4 . − , (cid:1) ◦ [52]. γ A precise measurement of the angle γ is key to understanding the closure (or otherwise)of the unitarity triangle. Constraints on the unitarity-triangle apex largely come fromloop decay measurements which are very sensitive to the presence of new physics. γ is theonly angle accessible at tree level and hence forms a SM benchmark to which the loopmeasurements can be compared (assuming no significant new physics in tree decays). The γ measurement also relies on theoretical input which is very well understood [63, 64].Determination of γ from a combined fit to all measured parameters of the unitaritytriangle currently gives a value γ = (cid:0) . +1 . − . (cid:1) ◦ [52]. Conversely the measurement of γ alone from a combination of all direct measurements from tree decays gives γ = (cid:0) . +5 . − . (cid:1) ◦ .Hence reaching degree-level precision from direct γ measurements is crucial.25HCb makes measurements of γ by a variety of methods, where complementary isvital. Examples of the most sensitive LHCb measurements are outlined below. • γ in the “time integrated” B ± → D K ± modes The measurement of γ is made in direct CP-violation via B ± → D K ± by threedifferent methods: the GLW method (decay into a CP eigenstate) [65, 66], the ADSmethod (decay into a flavour-specific mode) [67], and the GGSZ method (Dalitzanalysis) [68]. These all access γ through interference between the B ± → D K ± and B ± → D K ± decay paths, where the D and D decay to the same final state. Whenusing these methods, the decay modes are self-tagging. In addition time-dependentanalyses are not necessary. For the ALD and GLW modes, the charge-conjugateevent yields are simply counted to determine the CP asymmetries (i.e. effectively a“counting experiment”).Figure 3.6 shows an example of a CP asymmetry in the B ± → D K ± ADS mode [69].Here the D is produced in a Cabibbo favoured mode ( V cb ) but decays via asuppressed mode ( V cd ) into K + π − . This interferes with the D charge-conjugatestate which is produced in a suppressed mode ( V ub ) but decays to the same finalstate K + π − via a favoured mode ( V cs ). The branching fraction for the favoured B decay is only ∼ − , so these measurements require high statistics. The asymmetryobserved in Fig. 3.6 has a magnitude of around 40% and has a significance of 7 σ . Figure 3.6: Example of a CP asymmetry in the ADS mode B ± → D K ± , where the D and D both decay into K + π − . The event yield is shown as a function of DK mass. A specific example of an LHCb analysis using the GGSZ Dalitz method is in thedecay B ± → D K ± where D → K S π + π − or D → K S K + K − [70]. There is a richDalitz plot structure with the presence of large interference effects. The Dalitz spaceis divided up into symmetric bins, chosen to optimise sensitivity. An amplitudeanalysis can then be used to extract γ .In all B ± → D K ± modes and decays listed above, γ can also be extracted from thecorresponding B ± → D K (cid:63) ± modes, albeit with reduced γ sensitivity. In addition B → D ( ∗ ) K ( ∗ ) GGSZ modes are also included in the global fit to extract the γ average value. • γ from the “time-dependent” B s → D − s K + mode The channel B s → D − s K + , and its charge conjugate states, provide a theoreticallyclean measurement of the angle ( γ + φ s ) where φ s is the (small valued) B s mixing26hase, with no significant penguin contribution expected [71]. Here both B s , andvia the mixing diagram B s , can decay to the same final state D − s K + , resultingin interference which is sensitive to γ . The same is true for decay into the chargeconjugate state D + s K − . Hence four time-dependent decay rates are measured: B s → D − s K + , B s → D + s K − , B s → D − s K + and B s → D + s K − . The method isthen to fit two asymmetries of the form A CP = N B → f − N B → f N B → f + N B → f . (3.8)These measurements yield values for the strong phase difference δ QCD between theamplitudes B → f and B → f , the amplitude ratio, and ( γ + φ s ).The current measurement by LHCb in 1 fb − of data yields a value γ = (cid:0) +28 − (cid:1) ◦ [72].This complements the measurements in B ± → D K ± , although with less statisticalprecision. • The γ combination The LHCb measurement of γ averaged over all the above methods, which includesall B , B ± and B s modes, is γ = (cid:0) . +5 . − . (cid:1) ◦ [73]. This measurement dominates thecurrent world average. The confidence limits as a function of γ for the combinationis shown in Fig. 3.7 for the various measurement channels. The agreement between B s and B ± initial states is currently at the 2 σ level. Figure 3.7: Confidence limits as a function of γ in the LHCb combination for the variousmeasurement channels. • The side opposite to β Currently the closure test of the unitarity triangle is limited mainly by the sideopposite to β which has a length proportional to | V ub | / | V cb | in the Standard Model.27his limitation is a consequence of tension between B Factory inclusive and exclusive | V ub | measurements which differ by ∼ . σ [61]. | V ub | is directly proportional to thedecay rate B → X u µ − ν µ , where X u is a meson containing a u quark. Theoreticalinput from Heavy Quark Effective Theory and lattice calculations are also necessaryto calculate | V ub | , although several of the theoretical uncertainties cancel in the ratioto calculate the side. | V ub | / | V cb | is a very difficult measurement at LHCb due to presence of a neutrino,the identification of which was never in LHCb’s original plans. Although the B Factory favoured channel B → π + µ − ν µ cannot currently be identified at LHCb,the equivalent baryonic channel Λ b → pµ − ν µ has been measured. The signal isseparated from the lower-mass backgrounds, shown in Fig. 3.8. Using form factorsfrom lattice calculations, LHCb measures [74] | V ub | = (3 . ± .
15 (exp) ± .
17 (theory) ± .
06 ( | V cb | )) × − This is to be compared to the world average of | V ub | = (3 . ± . × − [61]. ] c mass [MeV/ - m p Corrected ) c C a nd i d a t e s / ( M e V / CombinatorialMis-identified n - m p D n - m c + L n - m c+ L n - m N n - m p LHCb ** Figure 3.8: The ( pµ − ) mass distribution in the measurement of | V ub | , showing the contributionfrom Λ b → pµ − ν µ decays and the various backgrounds. • The side opposite to α The mass difference ∆ m s measured in B s mixing (Fig. 3.3), which is dominatedby the top-quark loop, provides a measurement of the third side of the triangle, V td λV ts . This is proportional to the ratio of mixing frequencies (cid:113) ∆ m d ∆ m s . Correctionsare calculated from the lattice with a theoretical error of ∼ | V td /V ts | is 0 . ± . ± .
008 [49]. Systematic errors can be reduced inthe future by improved lattice QCD calculations.28 .4 Other CP violation measurements B s weak mixing phase φ s in B s → J/ψφ
It can be seen in Fig. 3.3 that V ts appears twice in the B s − B s mixing process, introducinga relative “weak mixing phase”, of φ s to fourth order in λ . The B s mixing phase can bemeasured in the channel B s → J/ψφ , which is governed by a single tree-level diagramwith a negligible penguin contribution. Hence this mode is the strange-quark analogue ofthe golden mode B → J/ψK S in the B system. In the B s system CP asymmetry arisesfrom the interference of the B s → J/ψφ with the mixed process B s → B s → J/ψφ . Inthe Standard Model, φ s is expected to be very small, ∼ . ± .
002 rad [52], hence thischannel is a very sensitive probe for new physics.LHCb reconstructs B s → J/ψφ events in the decay modes
J/ψ → µ + µ − , and φ → K + K − [75]. This B s final state is an admixture of CP -even and odd contributions,therefore an angular analysis of decay products is required. Good tagging performance of B s and B s is important, with a total tagging power in this analysis of 4 . ± . φ s is correlated with ∆Γ s , the width difference of the B s masseigenstates. The decay B s → J/ψπ + π − is also added to improve the sensitivity [76].Contours in the ( φ s , ∆Γ s ) plane are plotted in Fig. 3.9. The LHCb measurements are∆Γ s = 0 . ± . − with the CP -violating phase φ s = − . ± .
025 rad.Figure 3.9 also shows the world-averaged measurement of φ s versus ∆Γ s showing theLHCb result in combination with those from other experiments and the Standard Modelexpectation [61]. Figure 3.9: The measurement of the B s weak mixing phase in the ( φ s , ∆Γ s ) plane, showing theLHCb result in combination with those from other experiments, the Standard Model expectation,and the 1 σ contour of the combination [61]. .4.2 CP violation in charm The Standard Model prediction of CP violation in the charm system is expected to bevery small O (10 − ) → O (10 − ), where CP violation can arise in Cabibbo-suppressed(CS) decays in the interference between tree and penguin amplitudes. In particular LHCbhas measured asymmetries in the direct CP -violating channels D ( D ) → π + π − and D ( D ) → K + K − [77].In the LHCb analysis, D and D decays are identified via two self-tagging decaypaths. “Prompt” decays ( D decays originating from the primary vertex) are characterisedby the presence of a “soft” low-momentum pion from a D ∗ i.e. D ∗ + → D π +soft and thecharge-conjugate mode. “Semileptonic” decays are secondary D ’s which originate fromprompt B decays, i.e. B + → D µ + X and its charge-conjugate state.The raw asymmetry ( A ) for D → h + h − decays ( h = K or π ) is defined as A ( D → f ) = N ( D → f ) − N ( D → f ) N ( D → f ) + N ( D → f ) (3.9)which includes both physics and detector terms: A = A CP + A D + A P . Detectionasymmetry arises from small charge differences associated with the π ± soft or µ ± . Productionasymmetry arises from different production rates of D ∗ and B in pp collisions. Toeliminate these two contributions and cancel associated systematics, the ∆ A CP parameteris measured in LHCb:∆ A CP = A (cid:0) K + K − (cid:1) − A (cid:0) π + π − (cid:1) = A CP (cid:0) K + K − (cid:1) − A CP (cid:0) π + π − (cid:1) . (3.10)The raw symmetries are obtained from mass fits, and then by simply counting the numbersof D ’s decaying to π + π − and K + K − , respectively.A measurement performed with Run 1 and Run 2 LHCb data combined gives∆ A CP = ( − . ± . × − . This is a 5.3 σ measurement of CP violation in the charmsystem and opens a new window for the study of CP violation in the future. CP violation in beauty baryons CP violation has been observed in B , K , and D decays, but not yet in baryon decays. Asearch for CP violation in the multi-body mode Λ b → p + π − π + π − decays was performedon LHCb Run 1 data [78]. This decay proceeds via tree and loop diagrams with similarcontributions and through numerous intermediate resonances, enhancing the possibilityfor CP violation, although in areas where re-scattering effects can play a role. A 3.3 σ deviation from CP symmetry was observed, however introducing 6.6 fb − of Run 2 datahas not confirmed this result [79]. Hence this measurement awaits further statistics, andwill be improved when cleaner 2-body B -baryon decays can be added to the study. CP violation in charmless 3-body B ± decays Yields of B + → π + K + K − and B − → π − K − K + decays show striking asymmetries in theregion of phase space dominated by re-scattering effects [80]. Similarly huge CP -violatingeffects between B + → π + π + π − and B − → π − π − π + decays are observed in a region ofphase space including the ρ (770) and f (1270) resonances [81, 82]. Figure 3.10 shows anexample of the spectacular asymmetries observed in B → πKK decays, which exceed50% at low values of K + K − mass. 30 c / [GeV + K - K m ) c / E n t r i e s / ( . G e V Data + B Model + B LHCb ] c / [GeV - K + K m ) c / E n t r i e s / ( . G e V LHCb
Data - B Model - B Figure 3.10: Yields of (top) B + → π + K + K − and (bottom) B − → π − K − K + decays as afunction of K + K − mass squared. Rare decays
Within the SM the interplay of weak and Higgs interactions implies that Flavour ChangingNeutral Currents (FCNCs) can occur only at higher orders in the electroweak interactionsand are strongly suppressed by the GIM mechanism. This strong suppression makesFCNC processes natural candidates to search for physics beyond the SM. If the newdegrees of freedom do not have the same flavour structure of the quarks/leptons-Higgsinteractions present in the SM, then they could contribute to FCNCs at a comparable (oreven larger) level to the SM amplitudes.In B -meson decays, experimenters have measured b → s and b → d quark transitions,while c → u and s → d transitions have been measured in D -meson and K -meson decays,respectively. At first order, these transitions can occur through two kinds of Feynmandiagram shown in Fig. 4.1. The first corresponds to the so-called “box” diagram anddescribes the mixing between neutral mesons, discussed in Section 3, the example ofFig. 4.1 shows B s mixing. The second kind of diagram, the so-called ”penguin” diagram,is responsible for a large variety of FCNC rare decays. The example shown in Fig. 4.1 isthat of a b → s(cid:96) + (cid:96) − transition. In particular, if the radiated bosons are of electroweaktype ( Z , W or γ -like), the uncertainties in the calculation of the SM predictions due tonon-perturbative QCD effects are drastically reduced as compared with the case where agluon is radiated. These ”electroweak penguins” are the subject of the discussions in thissection. Figure 4.1: Examples of loop processes within the SM that allow FCNC b → s quark transition.On the left is an example of a box diagram and on the right an example of a penguin diagram. Before the first physics run of the LHC accelerator in 2010, the main contributors to thestudy of rare B and D -meson decays were the B Factory experiments (BaBar and Belle)and the Tevatron experiments (CDF and D0). However the production rate of bb pairs inthe e + e − B Factories was typically five orders of magnitude smaller than at the LHC. Inaddition, the lower pp collision energy of the Tevatron (with a correspondingly reduced bb cross section which is proportional to the collision energy), and the detector’s reducedtrigger acceptance for rare B and D -meson decays, implied that LHCb would already bethe most sensitive experiment even after 1 fb − accumulated in 2011. For example, priorto the LHC, the rarest B -meson decay ever measured was B ( B + → K + µ + µ − ) ∼ × − with a 20% precision; Belle and BaBar had analyzed O (200) B → K ∗ (cid:96) + (cid:96) − events andCDF had reached a sensitivity of B ( B s → µ + µ − ) < × − at the 95% C.L. As will beclear from the next sections, LHCb has already reached after Run 1 of the LHC an order32f magnitude larger statistical power. B → µ + µ − The pure leptonic decays of K , D and B mesons are a particular interesting case ofelectroweak penguins, where the final quark leg in Fig. 4.1 (right) needs to be swapped tothe initial state. The helicity configuration of the purely leptonic final state suppressesthe vector and axial-vector contributions by a factor in terms of masses proportionalto (cid:104) m µ m K,D,B (cid:105) . Therefore, these decays are particularly sensitive to new (pseudo-) scalarinteractions. In the case of B and B s -meson decays, the contribution of the absorptivepart can be safely neglected. As a consequence, the rate is well predicted theoretically [83]: B ( B s → µ + µ − ) = (3 . ± . × − and B ( B → µ + µ − ) = (1 . ± . × − . Inthe B s case, this prediction corresponds to a flavour-averaged time-integrated measurement,taking into account the correction due to the non-negligible width difference.The experimental signature is sufficiently clean to reach an expected signal overbackground ratio S/B ∼ B s decay, assuming the SM branching fraction. Themain background in the region around the B s invariant mass is due to combinations ofuncorrelated muons and can be estimated from the mass sidebands. The most importanthandle to reduce this combinatorial background is the invariant mass resolution of theexperiment, σ ∼
23 MeV, which is also crucial to differentiate between B and B s decays(∆ m ∼
87 MeV). Moreover, the large fraction of B → h + h (cid:48)− decays is an important sourceof background due to hadrons being misidentified as muons in the region around the B mass (this background is very small in the B s mass region).Given their experimental detector resolution and trigger acceptance during Run 1and Run 2, the CMS experiment with 61 fb − of data has similar sensitivity to theLHCb experiment with 4 . − of data collected in the same period. Both experimentshave provided a clear observation of the decay B s → µ + µ − (CMS and LHCb observeabout 90 and 30 B s signal candidates with a background of about 40 and 10 eventsrespectively within the invariant mass interval expected to contain 95% of the signal).Neither experiment has yet reached the sensitivity to observe the decay B → µ + µ − .The invariant mass distribution obtained by the LHCb experiment is shown in Fig. 4.2and the LHCb [84] and CMS [85] results are B ( B s → µ + µ − ) = (3 . ± . +0 . − . ) × − and B ( B s → µ + µ − ) = (2 . +0 . − . ± . × − respectively, while for the B decay only limitscan be quoted. The ATLAS collaboration has also published after a measurement [86]using 51 fb − of data, B ( B s → µ + µ − ) = (2 . +0 . − . ) × − in agreement with the previousresults.The B s → µ + µ − very rare decay has been searched for ever since the discovery of B mesons, around 40 years ago. Thanks to the ingenuity and persistence of the experimenters,it has been eventually measured at the LHC and found to be in agreement with theSM within current uncertainties, as shown in Fig. 4.3. Over the next decade it will beextremely interesting to see how the measurement of B ( B → µ + µ − ) evolves, for whichonly upper limits are currently available. 33 igure 4.2: Invariant mass distribution of dimuons selected from Ref. [84]. Superimposed on thedata points in blue (solid line) is the combined fit, and its components as quoted in the insert. B → K ∗ µ + µ − The language of effective field theory is used to parameterise NP contributions in terms ofa sum of local four-fermion operators ( Q i ) which depend only on SM fermions modulatedby Wilson coefficients ( C i ) which in turn depend on the heavy degrees of freedom i.e. NPparticles. The decay B → K ∗ µ + µ − is the so-called “golden mode” to test new vector(axial-vector) couplings, i.e. the C and C Wilson coefficients contributing to the b → s transition. The B → K ∗ µ + µ − channel also complements the b → sγ decay which ismostly sensitive to NP dipole operators (i.e. C ). and also the B s → µ + µ − decay which ismostly sensitive to NP (pseudo-) scalar operators (i.e. C S and C P ). The charge of thepion in the decay K ∗ → Kπ defines the flavour of the B meson and an angular analysiscan be performed unambiguously to test the helicity structure of the electroweak penguin.The above system is completely defined by four variables: q , the square of the invariantmass of the dimuon system, θ l , the angle between the positive lepton and the directionopposite to the B -meson in the dimuon rest frame, θ K , the equivalent angle of the K + in the K ∗ rest frame and φ the angle between the two planes defined by ( K, π ) and( µ + , µ − ) in the B -meson rest frame. The four-fold differential distribution contains atotal of eleven angular terms that can be written in terms of seven q -dependent complexdecay amplitudes. These amplitudes can be expressed in terms of five complex Wilsoncoefficients ( C S , C P , C , C and C ), their five helicity counterparts and six form-factors,which play a role of nuisance parameters in the fit.The LHCb experiment, with 3 fb − of data collected in Run 1, has triggered andselected about 2400 B → K ∗ µ + µ − candidates in the range 0 . < q <
19 GeV withsignal over background ( S/B ) >
5. This is about one order of magnitude larger thanthe samples available at previous experiments (BaBar, Belle and CDF) and similar to34 igure 4.3: Upper limits ( B → µ + µ − ) and eventual measurements of the B s → µ + µ − branchingratio by several experiments over the last 40 years. the samples collected by ATLAS and CMS with ten times the luminosity, however withsignificantly worse S/B .The statistics and the quality of the data accumulated by the LHCb experiment allowsfor a full angular analysis of B → K ∗ µ + µ − decays to be performed for the first time.The results [87] of this “tour de force” analysis mostly agree with SM predictions, howeverwith some hints of disagreement for some specific distributions. In Fig.4.4, two examples ofthe CP -averaged angular coefficients (i.e. the average of the coefficients measured with B and B decays) are shown as a function of q . For these two examples, A FB (modulatingthe sin θ K × cos θ l angular term) and S (modulating the sin(2 θ K ) × sin θ l × cos φ angularterm) seem to agree less well with SM predictions. However these are early days, andmore data will be required (the Run 2 data analysis will be released soon). Also a carefulreassessment of the SM uncertainties are needed before drawing definitive conclusions.Several authors have already attempted to see if the overall pattern of the angularmeasurements is consistent with a given value of the relevant Wilson coefficients. Aspreviously discussed, the inclusive b → sγ measurements strongly constrain non-SM valuesfor C . The scalar C S and pseudo-scalar C P coefficients are constrained, for example, bythe measurement of the branching fraction of the very rare decay B s → µ + µ − . Therefore,the small disagreements observed in the angular analysis of the decay B → K ∗ µ + µ − and other decays, seem to be consistent with a non-SM value of the C Wilson coefficient,as can be seen in Fig. 4.5 taken from Ref. [88].35 igure 4.4: Two examples of the CP -averaged coefficients in the B → K ∗ µ + µ − angular termsas a function of q . The shaded boxes show the SM predictions taken from Ref. [89].Figure 4.5: Constrains on the contribution of NP to the real parts of C and C at the 1 σ and2 σ level taken from Ref. [88], corresponding to different measurements as indicated in the insert.The dotted lines correspond to the status before the latest updates for the 2019 physics winterconferences. In the SM, the electroweak couplings of leptons are flavour independent, or lepton“universal”. However, this may not necessarily be the case for new particles beyond theSM. In particular, if the hints described in the previous section are an indication of newparticles modifying the penguin diagram in Fig. 4.1, it is interesting to measure the ratios36f branching fractions in decays of different lepton families. For example, the ratios R X = (cid:90) d Γ( B → Xµµ ) dq dq (cid:44) (cid:90) d Γ( B → Xee ) dq dq (4.1)between B decays to final states with muons and electrons, where X is a hadron containingan s -quark or d -quark, are predicted to be very close to unity in the SM [90–92]. Theuncertainties from QED corrections are found to be at the percent level [93].LHCb has measured the above ratio in several channels. Using Run 1 and part ofRun 2 data (4 . − ), LHCb measures [94] R K = 0 . +0 . − . (stat) +0 . − . (syst) in the range1 . < q < , about 2 . σ below the SM prediction, and using only Run 1 data(3 fb − ) LHCb measures [95] R K ∗ = 0 . +0 . − . (stat) ± . q range,with a similar level of disagreement with the SM prediction. The latest R K results fromLHCb in bins of q can be seen in Fig. 4.6, compared with previous results from theBaBar and Belle collaborations. The consistency between different experiments, anddifferent channels, although with very different precision, has motivated many theoreticalstudies that relate these hints of lepton non-universality with the discrepancies describedin the previous section. Figure 4.5 shows the status of the compatibility of both sets ofmeasurements when assuming that only the bsµµ Wilson coefficients are modified (and bsee coefficients are as predicted by the SM). Whilst the initial results showed remarkableconsistency between different sets of measurements as shown by the dotted lines in Fig. 4.5,the 2019 latest updates show a less clear picture. As of today, it is difficult to draw reliableconclusions, and more data is eagerly awaited.
Figure 4.6: Measurement of R K as a function of the q bins by different experiments. Spectroscopy
A deep understanding of quantum chromodynamics, the theory of strong interactions, isvital for precision tests of the Standard Model and in searches for new physics beyond.QCD is intensively tested in deep-inelastic-scattering processes and heavy vector bosonproduction, however in the low-energy regime, there is a lack of precise QCD predictions.QCD, being a non-pertubative theory, does not calculate hadron properties, namely massesand decay widths from first principles. Alternative theoretical approaches are developed,such as heavy quark effective theory, heavy quark expansion or lattice calculations.These approaches require verification with experiment in various regimes, e.g. testingthe agreement with data for hadrons with different quark content and quantum numbers.Spectroscopic measurements of hadron masses and widths or lifetimes provide a widevariety of tests for QCD models.Huge production cross sections of charm and beauty in high-energy pp collisions inthe forward region at LHCb [96–112], together with a good reconstruction efficiency,versatile trigger scheme and an excellent momentum and mass resolution, opens upexciting opportunities for spectroscopy measurements. The employment of LHCb’s pow-erful hadron identification system [34, 36, 113] enables a substantial reduction in thecombinatorial background specific to high-energy hadron-hadron collisions. The uniquehadron identification is also especially important for spectroscopy measurements involvingcharged kaons and/or protons in the final state. The excellent momentum and vertexresolutions provided by the LHCb tracking system allows unprecedented precision onmass and width measurements: indeed the most precise measurements of mass for allopen beauty particles and lifetimes of all open heavy flavour particles, currently resultfrom the LHCb experiment [114]. Additional good control over the momentum scale andthe detector alignment [115, 116] also allows the natural widths of hadronic resonances tobe probed with world-leading sub-MeV precision [117–123].Almost 30 new hadrons have been discovered [124] using the Run 1&2 data-set, amongthem several open charm mesons and baryons, double-charm baryon, a charmonium state,several beauty mesons, fifteen beauty baryons, and pentaquark-like P c (4312) + , P c (4400) + and P c (4457) + states. The quantum numbers of many hadrons, especially for charm mesonsand charmonia-like exotic candidates, have been determined using amplitude-analysistechniques. In the case of exotic particles such as pentaquark and tetraquark candidates,the determination of quantum numbers is vital for the understanding of their nature.Large statistics and low levels of background in decays of beauty hadrons with J/ψ → µ + µ − or ψ (2 S ) → µ + µ − final states allow the study of the spectroscopy of light unflavoured orstrange hadrons [125–144]. Selected spectroscopy highlights are discussed in this chapter. Two complementary methods for the study of spectroscopy of charm hadrons have beenexploited in LHCb: • the study of promptly produced charm hadrons, • the study of charm particles produced in weak decays of beauty hadrons, e.g. fromexclusive B → D ( ∗ ) ππ decays. 38he first technique allows the most efficient exploitation of the huge prompt cc productioncross section in high energy hadron collisions, but this is usually affected by a largebackground from light hadrons produced at the pp collision vertex. The second techniqueexploits a full amplitude analysis of the exclusive decays of beauty hadrons and thereforeinvolves much lower statistics, however the method often allows the determination ofquantum numbers of the charm hadrons. The study of Dπ final states enables a searchfor natural spin-parity resonances, ( P = ( − J , labelled as D ∗ ) whilst the study of D ∗ π final states provides the possibility of studying both natural and unnatural spin-paritystates, except for the J P = 0 + case, which is forbidden because of angular momentumand parity conservation. In inclusive D ( ∗ ) π production, the production of any J P stateis permitted. An amplitude analysis of B decays allows a full spin-parity analysis ofthe charmed mesons present in the decay.Both the above approaches are complementary, and have resulted in discoveries ofseveral new charm hadrons, amongst them the excited charm mesons. Many previousmeson and baryon states, discovered earlier by other experiments, have been confirmedwith high statistical significance, and their masses and widths have been measured withhigh precision. For many, the quantum numbers were either measured or constrained. Excited charm mesons in the D ∗ + π − , D + π − and D π + spectra have beenstudied in LHCb using a 1 fb − data-set collected at √ s = 7 TeV [145]. Four resonanceslabelled D (2550), D ∗ J (2600), D (2740) and D ∗ (2750) have been observed. The D (2550),and D (2740) decay angular distributions are consistent with an unnatural spin-parity,whilst the D ∗ J (2600), and D ∗ (2750) states are assigned natural parities. For the D (2550),meson, angular distributions are consistent with a J P = 0 − assignment, however for theother states, no definite assignment exists.The excited charm mesons were also studied in B -decay amplitude analyses of B → D π + π − and B − → D + π − π + decays using the Run 1 data-set [146, 147] and B − → D ∗ + π − π + [148] using a data-set corresponding to 4.7 fb − , collected at √ s = 7,8 and 13 TeV. The D ∗ (2760) and D ∗ (3000) states were observed for the first time [147],and the most precise determination of masses, widths and quantum numbers has been per-formed for the D ∗ (2400) − , D ∗ (2660) − , D ∗ (2760) − [146], D ∗ (2660) , D ∗ (2680) , D ∗ (2760) , D ∗ (3000) [147] and for the D (2420) , D (2430) , D (2550) , D ∗ (2600) , D (2740) , D ∗ (2750) [148] states. Excited D + s mesons were studied both in inclusive production in the D + K and D K + spectra using a data-set of 1 fb − collected at √ s = 7 TeV [149], and throughthe amplitude analysis of B s → D K − π + decays using Run 1 data [150]. It has beenshown that the previously reported D ∗ sJ (2860) + state [149, 151, 152] is an admixture ofspin-1 and spin-3 resonances. The masses and width of new states, dubbed D ∗ s (2860) + and D ∗ s (2860) + , are precisely measured, as well as the masses and widths of the D ∗ s (2573) + and D ∗ s (2700) + [149, 150]. Excited Λ + c baryons were studied in their decays to the D p final state via the am-plitude analysis of Λ b baryon decays using an integrated luminosity sample of 3 fb − collected at √ s = 7 and 8 TeV [153]. The analysis uses a sample of 11 212 ±
126 sig-nal Λ b → D pπ − decays, where the D mesons are reconstructed in the K − π + final state.39he amplitude fit is performed in the four-phase space regions in the Dalitz plot. For thenear-threshold m D p region, an enhancement in the D p amplitude is studied. The en-hancement is consistent with being a resonant state, dubbed the Λ c (2860) + , with quantumnumbers J P =
32 + , and with the parity measured relative to that of the Λ c (2880) + state.The other quantum numbers are excluded with a significance greater than 6 standarddeviations. The phase motion of the
32 + component with respect to the non-resonantamplitudes is obtained in a model-independent way and is consistent with resonant be-havior. The mass of the Λ c (2860) + state is consistent with predictions for an orbitalD-wave Λ + c -excitation with quantum numbers
32 + , based on the nonrelativistic heavyquark-light diquark model and from QCD sum rules in the HQET framework. Also the fitallowed the most precise determination of the masses and widths of the known resonances Λ c (2880) + and Λ c (2940) + , as well as constraining their quantum numbers. Three excited Ξ ∗ c baryons have been observed in the Λ + c K − mass spectrum usingthe Run 2 data-set [154]. The mass difference δm ≡ m ( Λ + c K − ) − m ( Λ + c ) − m ( K − ) spec-trum for selected Λ + c K − combinations is shown in Fig. 5.1. Three narrow structures,denoted Ξ c (2923) , Ξ c (2939) and Ξ c (2965) are clearly visible with a significance ex-ceeding 20 σ for each signal. The data and fit show the least compatibility in the region δm ≈
110 MeV, that could be evidence for a fourth Ξ ∗ c state. Figure 5.1(right) showsthe δm distribution for the signal samples, where a structure in this region is added intothe fit. A large improvement in the fit quality is achieved. ) [MeV] - K ( m ) - +c L ( m ) - - K +c L ( m C a nd i d a t e s / ( M e V ) LHCb(a) 0 100 200 300 ) [MeV] - K ( m ) - +c L ( m ) - - K +c L ( m C a nd i d a t e s / ( M e V ) LHCb(b) - K +c Lfi (2923) c X - K +c Lfi (2939) c X - K +c Lfi (2965) c X + p - K +c Lfi + (2923) c X - K ) + p +c Lfi ( ++c Sfi + (3055) c X - K ) p +c Lfi ( +c Sfi (3055) c X - K ) + p +c Lfi ( ++c Sfi + (3080) c X - K ) p +c Lfi ( +c Sfi (3080) c X BackgroundAdditional component
LHCbRun 2 LHCbRun 2Figure 5.1: Mass difference ∆ m = m Λ + c K − − m Λ + c − m K − distributions [154]. Fits accountingfor (left) three and (right) four excited Ξ ∗ c states are superimposed. Five narrow excited Ω ∗ c baryons have been observed in the Ξ + c K − mass spectrumusing the Run 1 data-set [155]. A large sample of Ξ + c candidates were reconstructed intheir Cabibbo-suppressed mode Ξ + c → pK − π + . In total around 1 . × Ξ + c → pK − π + candidates with with a purity of 83% were selected, shown in Fig. 5.2(left). The massdistribution for Ξ + c K − combinations is shown in Fig. 5.2(right), and five narrow peaks areclearly visible. The natural widths of the peaks are found to be between 0.8 and 8 . Ω c (3050) and Ω c (3119) , are found to be extremely narrow, with95%CL limits of 1.2 and 2.8 MeV, respectively. It is found that the fit improves if an addi-tional broad Breit − Wigner function is included in the 3188 MeV mass region. This broadstructure may represent a single resonance, be the superposition of several resonances, bea feed-down from higher states, or some combination of the above. The interpretation ofthe narrow states is still an open question. The naive quark model expects five states in40he region, but some have to be relatively broad. The molecular model predicts two stateswith J P =
12 + and two with J P =
12 + , and three of the observed states are in remarkableagreement, both in mass and width, with this hypothesis [156]. ) [MeV] + p - pK ( m C a nd i d a t e s / ( M e V ) - K +c X ( m C a nd i d a t e s / ( M e V ) Ξ + c → pK − π + LHCbRun 1 LHCbRun 1
Figure 5.2: (left) Distribution of the reconstructed invariant mass m pK − π + for all Ξ + c candidates.The solid (red) curve shows the result of the fit, and the dashed (blue) line indicates the fittedbackground. (right) Distribution of the reconstructed invariant mass of Ξ + c K − combinations;the solid (red) curve shows the result of the fit, and the dashed (blue) line indicates the fittedbackground [155]. The shaded (red) histogram shows the corresponding mass spectrum fromthe Ξ + c side-bands and the shaded (light grey) distributions indicate the feed-down from partiallyreconstructed Ω c ( X ) resonances. Three weakly decaying states with charm number C = 2 are expected in the quark model:one isospin doublet Ξ cc and one isospin singlet Ω ccs , each with spin-parity J P =
12 + .The properties of these baryons have been calculated with a variety of theoretical models.In most cases, the masses of the Ξ cc states are predicted to lie in the range 3500 to3700 MeV/ c [157]. The masses of the Ξ ++ cc and Ξ + cc states are expected to differ by onlya few MeV/ c due to approximate isospin symmetry. Most predictions for the lifetimeof the Ξ + cc baryon are in the range 50 to 250 fs, and the lifetime of the Ξ ++ cc baryon isexpected to be three to four times longer at 200 to 700 fs, While both are expected tobe produced at hadron colliders the longer lifetime of the Ξ ++ cc baryon should make itsignificantly easier to experimentally observe than the Ξ + cc baryon.Experimentally, there is a longstanding puzzle in the Ξ cc system. Observations ofthe Ξ + cc baryon in the Λ + c K − π + final state at a mass of 3519 ± c with signalyields of 15.9 events over 6 . ± . . σ significance), and 5.62 eventsover 1 . ± .
13 events background in the final state pD + K − (4 . σ significance), werereported by the SELEX collaboration [158, 159]. The SELEX results included a numberof unexpected features, notably a short lifetime and a large production rate relative tothat of the singly charmed Λ + c baryon. The lifetime was reported to be shorter than33 fs at the 90% confidence level, and SELEX concluded that 20% of all Λ + c baryonsobserved by the experiment originated from Ξ + cc decays, implying a relative Ξ cc productionrate several orders of magnitude larger than theoretical expectations. Searches from41he FOCUS [160], BaBar [161], and Belle [162] experiments did not find evidence fora state with the properties reported by the SELEX collaboration, and neither did a searchat LHCb with data corresponding to an integrated luminosity of 0 .
65 fb − [163]. However,because the production environments at all the above experiments differ from that ofSELEX, which studied collisions of a hyperon beam on fixed nuclear targets, these nullresults do not exclude the original observations.LHCb has searched for the Ξ ++ cc decaying into Λ + c K − π + π + using a sample of pp col-lision data at 13 TeV, corresponding to an integrated luminosity of 1.7 fb − . A highlysignificant structure is observed in the mass spectrum, where the Λ + c baryon is recon-structed into pK − π + , shown in Fig. 5.3(left). The structure is consistent with originatingfrom a weakly decaying particle, identified as the doubly charmed baryon Ξ ++ cc . Theobservation of the state is confirmed using an additional sample of data collected at 8 TeV.Soon after, the observation was further confirmed by observing the same state in the decay Ξ ++ cc → Ξ + c π + , shown in Fig. 5.3(right). The mass of the Ξ ++ cc state was measured tobe in very good agreement with the value measured in the Ξ ++ cc → Λ + c K − π + π + decaychannel [164]. The lifetime and mass of the Ξ ++ cc baryon were also precisely mea-sured [165, 166], where the lifetime favours smaller values in the range of the theoreticalpredictions. ] c ) [MeV/ ++cc X ( cand m c C a nd i d a t e s p e r M e V / LHCb 13 TeV C a nd i d a t e s / ( M e V / c ) m ( Ξ + c π + ) (cid:2) MeV / c (cid:3) LHCb
DataTotalSignalBackground
LHCb 1 . − √ s = 13 TeV LHCb 1 . − √ s = 13 TeV Figure 5.3: (Left) Mass distribution of Λ + c K − π + π + candidates with fit projections overlaid [167].(Right) Mass distribution of Ξ + c π + candidates [164]. Excited B + and B mesons have been investigated in the mass distributions of B + π − and B π + combinations using a 3 fb − data sample at 7 and 8 TeV. The B + and B can-didates were reconstructed through the B + → D π + , B + → D π + π + π − , B + → J/ψK + , B → D − π + , B → D − π + π + π − and B → J/ψK ∗ decay chains. Samples of about1.2 million B and 2.5 million B + candidates have been obtained with purity dependingon decay mode, but always better than 80%. The B + π − and B π + mass spectra withrequirements that p T > c are shown in Fig. 5.4, where ten peaking structures arereconstructed. Out of these, six narrow low-mass structures correspond to the decaysof the four B (5721) , + and B ∗ (5747) , + states observed by the CDF and D0 collabora-tions [168–170]: B (5721) → B ∗ π and B (5747) → B ( ∗ ) π . The high statistics of LHCb42as allowed the most precise measurements of the masses and widths of the B (5721) , + and B ∗ (5747) , + states to be made.In addition to the six low-mass structures, four wider high-mass structures are observed,particularly prominent at high pion transverse momentum. These structures are consistentwith the presence of four new excited B mesons, labeled B J (5840) , + and B J (5960) , + ,whose masses and widths are obtained under different hypotheses of their quantumnumbers [171]. (MeV) p B Q
150 200 250 300 350 400 450 500 550 600 650 700 750 800 C a nd i d a t es / ( M e V ) - p ) g + (B +* B fi (5721) B - p ) g + (B +* B fi (5747) * B - p + B fi (5747) * B - p + B fi (5960) J B - p + B fi (5840) J BAssociated ProductionCombinatorial
LHCb ) [MeV] - p )-m( + )-m(B - p + m(B
150 200 250 300 350 400 450 500 550 600 650 700 750 800 P u ll -4-2024 (MeV) p B Q
150 200 250 300 350 400 450 500 550 600 650 700 750 800 C a nd i d a t es / ( M e V ) + p ) g (B B fi + (5721) B + p ) g (B B fi + (5747) * B + p B fi + (5747) * B + p B fi + (5960) J B + p B fi + (5840) J BAssociated ProductionCombinatorial
LHCb ) [MeV] + p )-m( )-m(B + p m(B
150 200 250 300 350 400 450 500 550 600 650 700 750 800 P u ll -4-2024 LHCb Run 1 LHCb Run 1
Figure 5.4: Spectra of ∆ m ≡ m Bπ − m B − m π for (left) B + π − and (right) B π + candidateswith p T ( π ) > c [171]. Orbitally excited B s mesons have been studied using only 1 fb − of data, collectedat √ s = 7 TeV. The B + K − mass spectra were investigated with the B + mesons beingreconstructed in four decay modes. Previously, two narrow peaks had been observed inthe B + K − mass distribution by the CDF and D0 collaborations [172, 173], named the B ∗ s (5830) and B ∗ s (5840) . They are putatively identified as members of j q = HQET dou-blet [174]. The two states are also visible in LHCb data, here as three narrow peaks shownin Fig. 5.5(left), corresponding to the decays B s (5830) → B ∗ + K − , B ∗ s (5840) → B ∗ + K − ,and B ∗ s (5840) → B + K − , where a soft photon from B ∗ + → B + γ is undetected. This isthe first observation of the B ∗ s (5840) → B ∗ + K − decay mode and a J P = 2 + assignmentis favoured for this state. Large statistics, low background and LHCb’s excellent massresolution has allowed the first determination of the B ∗ s (5840) width as well as the mostprecise mass measurements of both states. Due to the small energy release, the positionand the shape of the peaks depends on the mass of the B ∗ + states, allowing the mostprecise determination of the m B ∗ + mass, as well as the mass difference m B ∗ + − m B + . Excited B + c mesons have been searched for via their decays into the B + c π + π − finalstate. A wide peak, interpreted as the B c (2 S ) + , was observed by the ATLAS collaborationusing a sample of about 300 reconstructed B + c → J/ψπ + candidates [175], with a largerelative production rate with respect to the base B + c state. LHCb has searched for thisstate using 2 fb − of data collected at √ s = 8 TeV, observing a sample of 3325 ± B + c → J/ψπ + decays. No signal is observed and an upper limit on the43 ) c C a nd i d a t e s / ( M e V / LHCb - K *+ B fi *s2 B - K *+ B fi s1 B - K + B fi *s2 B c ) [MeV/ - ) - m(K + - m(B) - K + m(B P u ll ] c [MeV/ M D
500 550 600 650 700 ) c C a nd i d a t e s / ( M e V / DataTotal fit + ) S (2 * c B + ) S (2 c B CombinatorialSame-sign
LHCb Run 1+Run 2
LHCb 1 fb − √ s = 7 TeV LHCb Run 1&2 B c (2 S ) ( ∗ )+ → B ( ∗ )+ c π + π − Figure 5.5: (left) The mass difference distribution m B + K − − m B + − m K − in the B + K − mass spectra. The three peaks are identified as (left-to-right) B s (5830) → B ∗ + K − , B ∗ s (5840) → B ∗ + K − , and B ∗ s (5840) → B + K − . The total fit function is shown as a solid blueline, while the shaded red region is the spectrum of like-charge B + K + combinations. The insetshows an expanded view of the B s (5830) /B ∗ s (5840) → B ∗ + K − region. (right) Distribution of∆ M ≡ m B + c π + π − − m B + c in the B + c π + π − mass spectra with fit results overlaid. The same-signdistribution has been normalised to the data in the B c (2 S ) side band region. relative production rate has been obtained [176]. This upper limit is smaller than therelative production rate reported by ATLAS.In 2018, the CMS collaboration, using a huge data set corresponding to 143 fb − collected at √ s = 13 TeV and containing of 7629 ±
225 signal B + c → J/ψπ + decays, reportedobservation of a doublet of two narrow states, interpreted as spin-triplet B c (2 S ) ∗ + and spin-singlet B c (2 S ) + states [177]. These observations were confirmed by LHCb using a 8 . − data-set collected at √ s = 7 , ±
73 signal B + c → J/ψπ + decays.Two narrow peaks with a width compatible with the detector resolution are seen inthe mass-difference m B + c π + π − − m B + c spectrum, shown in Fig. 5.5(right). The local (global)significances of the two peaks are estimated to be 6 . σ (6 . σ ) and 3 . σ (2 . σ ) for thelow-mass and high-mass states, respectively. The low-mass signal is interpreted as thespin-triplet state B c (2 S ) ∗ + , decaying into B ∗ + c π + π − with the subsequent decay of the B ∗ + c into B + c γ . The high-mass peak is attributed to the decay of the spin-singlet B c (2 S ) + stateinto the B + c π + π − final state. Excited Λ b baryons were discovered in the Λ b π + π − mass spectrum using only 1 fb − ofLHCb data, accumulated at √ s = 7 TeV in 2011 [117]. The Λ b candidates were recon-structed via Λ b → Λ + c π − followed by Λ + c → pK − π + . In total (70 . ± . × signal Λ b decays were selected and then combined with π + π − pairs. The Λ b π + π − spectrum inthe region 5 . ≤ m Λ b π + π + ≤ .
95 GeV/ c is shown in Fig. 5.6(left), where two narrowpeaks, consistent with detector resolution, are visible. The significances of the observationsare 5.2 and 10.2 standard deviations for the low-mass and high-mass peaks, respectively.The observed states are interpreted as the doublet of orbitally-excited Λ b (1 P ) stateswith quantum numbers J P =
12 + and
32 + . In 2020 the analysis was updated using the fullRun 1 and 2 data-sets, shown in Fig. 5.6(right). The masses of these states are measuredwith unprecedented precision [121]. 44 c ) (MeV/ − π + π Λ ( M ) c C a nd i d a t e s / ( . M e V / LHCb Λ b (5912) Λ b (5920) backgroundtotal C a nd i d a t e s / ( . M e V ) m Λ ππ [GeV]Λ → Λ +c π − Λ π + π − Λ π + π + Λ π − π − LHCb
LHCb 1 fb − √ s = 7 TeV LHCb Run 1&2 m ( Λ b ππ ) (cid:2) GeV/ c (cid:3) Figure 5.6: (Left) Mass spectrum of Λ b π + π − combinations [117]. The points with error bars arethe data, the solid line is the result of a fit, and the dashed line is the background contribution.(Right) Mass spectrum of (top) Λ b π + π − , (middle) Λ b π + π + and (bottom) Λ b π − π − combinationsin the full Run 1 and 2 data-sets [121]. Using the full Run 1 and 2 data-sets, the mass spectrum of Λ b π + π + combinations, where Λ b → Λ + c π − and Λ b → J/ψpK − , was explored for higher masses of Λ b π + π − combinations.A significant broad structure is found at m ≈ .
150 GeV/ c with a width around 10 MeV,shown in Fig. 5.7(left) [179]. The mass and width agree well when measured in thetwo decay modes Λ b → Λ + c π − and Λ b → J/ψpK − , where the significance exceeds 26 and9 standards deviations, respectively. Since the mass of the new structure is abovethe Σ ( ∗ ) ± b π ∓ kinematic thresholds, the Λ b π + π − mass spectrum is investigated in the Λ b π ± mass regions populated by the Σ ( ∗ ) ± b resonances.The data are split into three non overlapping regions: candidates with a Λ b π ± masswithin the natural width of the known Σ ± b mass, candidates with a Λ b π ± mass withinthe natural width of the known Σ ∗± b mass, and the remaining nonresonant (NR) region.The Λ b π + π − mass spectra in these three regions are shown in Fig. 5.7(right). The spectrain the Σ b and Σ ∗ b regions look different and suggest the presence of two narrow peaks withvery similar widths. The two-signal hypothesis is favoured over the single-signal hypothesiswith a statistical significance exceeding seven standard deviations. The masses of the twostates measured are consistent with predictions for the doublet of Λ b (1 D ) states withquantum numbers J P =
32 + and
52 + .In 2020, the fifth excited Λ b state was observed in the Λ b π + π − mass spectra, usingthe full LHCb Run 1 and 2 data-sets. Two decay modes of the Λ b baryon were used, Λ b → Λ + c π − and Λ b → J/ψpK − , and the significance of the new state, denoted Λ ∗∗ b , isin excess of 14 and 7 standard deviations in the two decay modes, respectively. Thisis shown in Fig. 5.8. Unlike the previously observed four narrow Λ b states, Λ b (5912) , Λ b (5920) , Λ b (6146) and Λ b (6152) , the new state is rather broad, Γ = 72 ± ± Λ b (2 S ) resonance [180]. This resonance is also consistent witha broad excess of events in the Λ b π + π − mass spectrum, previously reported by the CMScollaboration [181]. 45 signalbackgroundtotal LHCb C a nd i d a t e s / ( M e V ) Λ → Λ +c π − Λ → J / ψ pK − m Λ π + π − [GeV] Λ b (6152) Λ b (6146) backgroundtotal LHCbΣ b regionΣ ∗ b regionNR region C a nd i d a t e s / ( M e V ) m Λ π + π − [GeV] LHCb Run 1&2 LHCb Run 1&2 m ( Λ b π + π − ) (cid:2) GeV/ c (cid:3) m ( Λ b π + π − ) (cid:2) GeV/ c (cid:3) Figure 5.7: (left) The mass distribution of selected Λ b π + π − candidates for (top) the Λ b → Λ + c π − and (bottom) the Λ b → J/ψpK − decay modes. (right) Mass distributions of selected Λ b π + π − can-didates for the three regions in Λ b π ± mass: (top) Σ b , (middle) Σ ∗ b and (bottom) the nonreso-nant (NR) region [179]. Λ ∗∗ Λ b (6146) Λ b (6152) Σ b π Σ ∗ b π comb. backgroundtotal backgroundtotal C a nd i d a t e s / ( M e V ) m Λ ππ [GeV]Λ → Λ +c π − Λ π + π − Λ π + π + Λ π − π − LHCb Λ ∗∗ Λ b (6146) Λ b (6152) Σ b π Σ ∗ b π comb. backgroundtotal backgroundtotal C a nd i d a t e s / ( M e V ) m Λ ππ [GeV]Λ → J / ψ pK − Λ π + π − Λ π + π + Λ π − π − LHCb
LHCb Run 1&2 LHCb Run 1&2 m ( Λ b ππ ) (cid:2) GeV/ c (cid:3) m ( Λ b ππ ) (cid:2) GeV/ c (cid:3) Figure 5.8: Mass distribution of selected (top) Λ b π + π − , (middle) Λ b π + π + and (bottom) Λ b π − π − candidates for the (left) Λ b → Λ + c π − and (right) Λ b → J/ψpK − decay modes [121]. Excited Σ ± b baryons have been studied in the Λ b π ± mass spectra using the Run 1LHCb data-set [182]. In total (234 . ± . × signal Λ b baryons were reconstructed inthe decay mode Λ b → Λ + c π − . Distributions of the energy release in the decay, Q ≡ m Λ b π ± − m Λ b − m π , are shown in Fig. 5.9. At low values of Q , there are previously-known signalsfrom Σ ( ∗ ) ± b states, observed and characterised by the CDF collaboration [183, 184]. Newpeaks in the Λ b π − ( Λ b π + ) spectra are visible at Q = 338 . ± . . ± . . σ (12 . σ ), based on the differences in log-likelihoods between46he fits with zero signal and the nominal fit. In the heavy-quark limit, five Σ b (1 P ) statesare expected, and several predictions of their masses have been made. Since the expecteddensity of baryon states is high, it cannot be excluded that the new observed structuresare the superposition of more than one (near-)degenerate state. Taking into account thatthe predicted mass and width depend on the as-yet-unknown spin and parity, the newlyobserved structures are compatible with being Σ b (1 P ) ± excitations. Other interpretations,such as molecular states, may also be possible. [MeV] Q C a nd i d a t e s / ( M e V ) LHCb - p b L (c) - p b L fi - b S - p b L fi - * b S - p b L fi - (6097) b S Background [MeV] Q C a nd i d a t e s / ( M e V ) LHCb + p b L (d) + p b L fi + b S + p b L fi *+ b S + p b L fi + (6097) b S Background (cid:126) (cid:126)
LHCb Run 1 LHCb Run 1
Figure 5.9: The distributions of energy release Q ≡ m Λ b π ± − m Λ b − m π for selected Λ b π ± candi-dates [182]. The points show experimental data. The left (right) plot shows Λ b π + ( Λ b π − ) combi-nations. Ξ (cid:48)− b and Ξ ∗− b baryons have been observed in the Ξ b π − mass spectrum using theLHCb Run 1 data-set [118]. Signal Ξ b candidates were reconstructed in the final state Ξ + c π − with Ξ c → pK − π + . Two peaks are clearly visible in the δm ≡ m Ξ b π − − m Ξ b − m π − spectrum, shown in Fig. 5.10(left), a narrow state at δm ≈ . c and a broader stateat δm ≈
24 MeV/ c . No structure is observed in the wrong-sign sample, nor in the Ξ b massside bands. The fitted natural width of the lower-mass state is found to be consistent withzero. The fitted yields of the lower and higher-mass peaks are 121 ±
12 and 237 ±
24 events,respectively, with statistical significance in excess of 10 standard deviations. The non-zero value of the natural width of the higher-mass state, Γ = 1 . ± . ± .
10 MeV issignificantly different from zero. The signals are interpreted as Ξ (cid:48)− b and Ξ ∗− b baryons. The Ξ ∗ b baryon was first observed at CMS [185], and later studied in detail bythe LHCb collaboration using the Run 1 data-set [119]. The Ξ ∗ b candidates havebeen reconstructed in the decay Ξ ∗ b → Ξ − b π + , with Ξ − b → Ξ c π + and Ξ c → pK − K − π + .The δm distribution, defined as m Ξ − b π + − m Ξ − b − m π + , is shown in Fig. 5.10(right). A nar-row peak is clearly visible with a fitted signal yield of 232 ±
19 events. The non-zerovalue of the natural width of the peak, Γ = 0 . ± .
16 MeV, is also highly significant;the change in log-likelihood when the width is fixed to zero exceeds 30 units. No otherstatistically-significant structures are seen. The peak position and the width are consistentwith, and about a factor of ten more precise than, the CMS measurements [185]. The mea-sured width of the state is in line with theory expectations; a calculation based on lattice47 c m [MeV/ d c E n t r i e s p e r . M e V / - p X + p X ] c m [MeV/ d c E n t r i e s p e r . M e V / LHCb ] c m [MeV/ d c E n t r i e s p e r . M e V / LHCb
LHCbRun 1 LHCbRun 1 Ξ ∗− b → Ξ b π − Ξ (cid:48)− b → Ξ b π − Ξ ∗ b → Ξ − b π + Figure 5.10: (left) The distribution of the mass difference, δm ≡ m Ξ b π − − m Ξ b − m π − ,for Ξ b π − candidates [118]. The points with error bars show right-sign candidates in the Ξ b mass signal region, and the hatched histogram shows wrong-sign candidates with the sameselection. The curve shows the nominal fit to the right-sign candidates. Inset: detail of the region2 . . c . (right) Distribution of δm and the fit for Ξ − b π + candidates [119]. QCD predicts a width of 0 . ± .
16 MeV [186], and another using the P model obtainsa value of 0.85 MeV [187]. The measured production ratio with respect to the Ξ − b state ismeasured to be (28 ± ± pp collisions at 7 and 8 TeV,a large fraction of Ξ − b baryons are produced through feed-down from higher-mass states. A high-mass excited Ξ − b baryon has been observed in the Λ b K − and Ξ b π − massspectra, using a 3.5 fb − LHCb data-set at √ s = 7, 8 and 13 TeV [188]. The Λ b baryons werereconstructed via Λ b → Λ + c π − and Λ b → Λ + c µ − X , with the Ξ b decaying to Ξ b → Ξ + c µ − X ,with Λ + c , Ξ c → pK − π + . Full reconstruction of the Λ b baryon allows the excellent resolutionof the Λ b K − mass spectra to be reached. In addition, partial reconstruction of Λ b and Ξ b baryons in their semileptonic modes allows a significant increase in the sample of Λ b and Ξ b baryons, where the missing neutrinos do not prevent a peaking structure in thespectra of mass differences ( m ” Λ b ” K − m ” Λ b ” ) and ( m ” Ξ b ” π − − m ” Ξ b ). The resolution isimproved by applying the 4-vector constraint ( p H + c + p µ − + p miss ) = m H b , where H + c stands for Λ + c and Ξ + c and H b stands for Λ b and Ξ b .The mass-difference spectra are shown in Fig. 5.11, where the peak locations forall three modes are seen to agree well. The statistical significances of the new excitedbaryon, dubbed the Ξ b (6227) − , are found to be 7 . σ for the Ξ b (6227) − → Λ b K − followedby Λ b → Λ + c π − , 25 σ for the Ξ b (6227) − → Λ b K − followed by Λ b → Λ + c µ − X and 7 . σ forthe Ξ b (6227) − → Ξ b π − followed by Ξ b → Ξ + c µ − X . Four narrow excited Ω b states have been observed in the Ξ b K − mass spectrumusing the full Run 1 and 2 LHCb data-sets [189]. The Ξ b candidates were reconstructedin Ξ + c π − final states with Ξ c → pK − π + . After multivariate selection, a low-backgroundsample of (19 . ± . × Ξ b → Ξ + c π − decays has been obtained. The mass-differencespectrum m ( Ξ b K − ) − m ( Ξ b ) for Ξ b K − combinations exhibits four narrow peaks, shownin Fig. 5.12. The natural widths of the three lower mass states are consistent with zero,48 c ) [MeV/ L ( M - ) - K L ( M
500 600 700 800 900 ) c C and i da t e s / ( M e V / Full fit - K ) - p +c Lfi ( L fi - (6227) b X Combinatorial
LHCb=7,8 TeVs ] c ) [MeV/ L *( M - ) - K L *( M
500 600 700 800 900 ) c C and i da t e s / ( M e V / - K ) X - m +c Lfi ( L fi - (6227) b X Combinatorial
LHCb=7,8 TeVs ] c ) [MeV/ X *( M - ) - p X *( M
400 600 800 ) c C and i da t e s / ( M e V / - p ) X - m +c Xfi ( X fi - (6227) b X Combinatorial
LHCb=7,8 TeVs ] c ) [MeV/ L ( M - ) - K L ( M
500 600 700 800 900 ) c C and i da t e s / ( M e V / Full fit - K ) - p +c Lfi ( L fi - (6227) b X Combinatorial
LHCb=13 TeVs ] c ) [MeV/ L *( M - ) - K L *( M
500 600 700 800 900 ) c C and i da t e s / ( M e V / - K ) X - m +c Lfi ( L fi - (6227) b X Combinatorial
LHCb=13 TeVs ] c ) [MeV/ X *( M - ) - p X *( M
400 600 800 ) c C and i da t e s / ( M e V / - p ) X - m +c Xfi ( X fi - (6227) b X Combinatorial
LHCb=13 TeVs
Figure 5.11: Spectra of mass differences for Ξ ∗ b candidates, reconstructed in the final states(left) Λ b K − , with Λ b → Λ + c π − , (middle) Λ b K − , with Λ b → Λ + c µ − X , and (right) Ξ b π − , with Ξ b → Ξ + c µ − X , along with fits to the data [188]. The top row is for 7 and 8 TeV dataand the bottom is for 13 TeV. The symbol M ∗ represents the mass after the 4-vector con-straint ( p H + c + p µ − + p miss ) = m H b is applied. while the width of the high-mass state is found to be 1 . +1 . − . ± . σ and 2.6 σ , respectively, whilst the two higher-mass peaks exceed 5 σ . The observed Ξ b K − peaks seen here are similar to those observed in the Ξ + c K − invariant mass spectrum [155].Arguably, the simplest interpretation is that the peaks correspond to excited Ω − b states,in particular the L = 1 angular momentum excitation of the ground state, or possibly an n = 2 radial excitation.Many of the quark-model calculations predict L = 1 states in this mass region, and atleast some of the states should be narrow. In particular, using the P model, five statesin this mass region are predicted, with approximately 8 MeV mass splittings; the fourlightest have partial widths, Γ( Ξ b K − ), below 1 MeV, whilst the one with the largestmass has Γ( Ξ b K − ) = 1 .
49 MeV. Conversely, predictions using the chiral quark modelindicate that the J P = (3 / − and (5 / − states are narrow, but the (1 / − statesare wide [190]. Quark-diquark models have also predicted several excited Ω − b states inthe region around 6.3 GeV, with mass splittings similar to that observed here, however,there are no predictions for the decay widths. Molecular models have also been employed,where two narrow J P = (1 / − states are predicted at 6405 MeV and 6465 MeV [156],however do not match well with the LHCb measurements.An alternate interpretation for one or more of the observed peaks is that theyarise from the decay of a higher-mass excited Ω ∗∗− b state to Ξ (cid:48) b ( → Ξ b π ) K − , wherethe π meson is undetected. If the mass of a not-yet-observed Ξ (cid:48) b state is in the region m Ξ b + m π < m Ξ (cid:48) b < m Ξ (cid:48)− b , each of the observed narrow peaks can be interpreted as having49ome from the above decay, provided that the corresponding excited Ω ∗∗− b state is narrow,Γ Ω ∗∗− b ≤ m Ω ∗∗− b = m Ξ (cid:48) b + δm peak ,where δm peak is a measured position of the peak in the m ( Ξ b K − ) − m ( Ξ b ) spectrum. ) [MeV] X ( M ) - - K X ( M
500 550 600 650 700 N u m be r o f c and i da t e s / M e V LHCb
DataFull fitSignalsBackground
LHCb Run 1&2
Figure 5.12: The mass difference δm ≡ m ( Ξ b K − ) − m ( Ξ b ) for selected Ξ b K − candidates [189]. Charmonium states in D ¯ D mass spectra near threshold have been studied usingthe full LHCb statistical sample collected in Runs 1 and 2 [191]. D and D + candidateswere reconstructed in the D → K − π + and D + → K − π + π + decay modes. In total, 3 . × D D and 2 . × D + D − pairs have been selected. The mass spectra for D D and D + D − combinations are shown in Fig. 5.13(left), with the zoomed-in region between3 . ≤ m DD ≤ .
88 GeV/ c presented in Fig. 5.13(right).Four peaking structures are observed in the spectra. Two of the peaks correspond to theknown ψ (3770) and χ c (3930) charmonium states. A narrow peak close to threshold rep-resents partially reconstructed χ c (3872) → D ∗ D decays, subsequently with D ∗ → D γ or D ∗ → D π with the γ or π meson missing. The narrow peak with mass around3840 MeV/ c is identified as a new charmonium state. Its mass value and small naturalwidth suggest an interpretation as the ψ (1 D ) charmonium state with quantum numbers J P C = 3 −− [192]. In addition, prompt hadroproduction of the χ c (3930) and ψ (3770) char-monium states have been observed for the first time, and precise measurements of theirresonance parameters have been performed. Observation of the decays χ c → J/ψµ + µ − using a 4.9 fb − data-set collected at √ s = 7, 8 and 13 TeV enabled the most precise direct determination of the masses ofthe χ c and χ c states and the width of the χ c to be performed with unprecedentedprecision [120]. The observation of these decay modes provides opportunity for the precisemeasurements of the χ c ,c production and polarization, that in turn is vital for tests ofQCD models of charmonia production. 50 .7 3.8 3.9 4 4.1 4.205001000150020002500300035004000 C a nd i d a t e s / ( M e V / c ) m DD (cid:2) GeV/ c (cid:3) D D D + D − LHCb
Figure 2: The mass spectra for selected DD combinations. The open red histogram correspondsto D D pairs, while the hatched blue histogram corresponds to D + D − pairs. Vertical blackdashed lines help to identify the peaks from(left to right) χ c1 (3872) → D ∗ D , ψ (3770) → DD,X(3842) → DD and χ c2 (3930) → DD decays.
The relativistic Breit–Wigner function is convolved with the detector resolution, describedby a sum of two Gaussian functions with common mean and parameters fixed fromsimulation. The effective resolution depends on m D + D − and increases from 0 . c for ψ (3770) → D + D − to 1 . c for χ c2 (3930) → D + D − signals and is approximately10% larger for the D D final state. The background in this region is found to be welldescribed by a second-order polynomial function.An extended unbinned maximum-likelihood fit is performed simultaneously to the D D and D + D − mass spectra. The mass and the natural width of the X(3842) signals inthe D D and D + D − final state are considered as common parameters in this fit whilst allother parameters are allowed to vary independently. All parameters related to the detectorresolution are fixed to values found using simulation. The result of the fit to the datais shown in Fig. 3 and the resulting parameters of interest are summarised in Table 1.The statistical significance of the X(3842) signal is evaluated using Wilks’ theorem [41] tobe above 7 σ for the D D decay mode and above 21 σ for the D + D − decay mode.4 X(3842) bkgtotal D D D + D − LHCb C a nd i d a t e s / ( . M e V / c ) C a nd i d a t e s / ( . M e V / c ) m DD (cid:2) GeV/ c (cid:3) Figure 3: Mass spectra of (top) D D and (bottom) D + D − candidates in the narrow3 . < m DD < . c region. The result of the simultaneous fit described in the textis superimposed.Table 1: Yields, mass and width of the X(3842) state from the fit to DD mass spectra inthe narrow 3 . < m DD < . c region. Uncertainties are statistical only. N X(3842) m X(3842) [MeV/ c ] Γ X(3842) [MeV]D D ±
170 3842 . ± .
16 2 . ± . + D − ± . < m DD < .
20 GeV/ c Two signal components are used to describe the 3 . < m DD < . c region:the X(3842) component, described earlier, and a component for the χ c2 (3930) decay,modelled by the convolution of a relativistic D-wave Breit–Wigner function with the res-olution model described above. The background in this mass region is modelled byan exponential function multiplied by a second-order polynomial function. The total fitconsists of the sum of the background and the X(3842) and χ c2 (3930) signals. A simul-taneous extended binned maximum-likelihood fit to the D D and D + D − mass spectrais performed with the mass and natural width of the X(3842) state fixed to the results5 LHCbRun 1&2 LHCbRun 1&2 m ( DD ) (cid:2) GeV/ c (cid:3) m ( DD ) (cid:2) GeV/ c (cid:3) Figure 5.13: (left) The DD mass spectra. The open (red) histogram shows D D combinationswhilst the dashed (blue) histogram shows D + D − . (right) The mass spectra of (top) D D and(bottom) D + D − combinations in the narrow mass region 3 . ≤ m DD ≤ .
88 GeV/ c , with fitssuperimposed. Different components employed in the fit are indicated in the legend. Observation of ψ (3823) → J/ψπ + π − in B + → ( ψ (3823) → J/ψπ + π − ) K + decaysusing the full LHCb Run 1 and 2 data-sets, has allowed the most precise determinationof the mass of the tensor ψ (3823) state and the best constrained upper limit of itswidth [123]. The observed mass distribution is shown in Fig. 5.14. Within the factor-ization approach, the branching fraction for the decay B + → ψ (3823) K + vanishes, anda non-zero value for this branching fraction allows an evaluation of the contribution ofthe D ( ∗ )+ s ¯ D ( ∗ )0 rescattering amplitudes in the B + → ccK + decays. C a nd i d a t e s / ( M e V / c ) C a nd i d a t e s / ( . M e V / c ) m J/ψπ + π − K + m J/ψπ + π − [GeV/ c ] [GeV/ c ] . < m J/ψπ + π − < .
83 GeV/ c . < m J/ψπ + π − K + < .
30 GeV/ c B + → ψ (3823) K + B + → (cid:0) J/ψπ + π − (cid:1) NR K + comb. ψ (3823) K + comb. bkg.total Figure 5.14: Distributions of the (left)
J/ψπ + π − K + and (right) J/ψπ + π − mass for selected B + → ( ψ (3823) → J/ψπ + π − ) K + candidates [123]. The LHCb collaboration studied Λ b → J/ψpK − decays using the Run 1 data-set [193].In total (26 . ± . × signal Λ b candidates were selected, and an anomalous peak in the51 /ψp mass spectrum is observed, shown in Fig. 5.15(left). If the peak structure representsa resonance which strongly decays into J/ψp , the minimal valence quarks would be ccuub ,a charmonium pentaquark state. A full six-dimensional amplitude fit with resonanceinvariant masses, three helicity angles and two differences between decay planes has beenapplied to describe the data. The amplitude model in the fit contains 14 well-defined Λ ∗ states and two pentaquark states, labelled as P c (4380) + and P c (4450) + . The projectionsof the fit are shown in Fig. 5.15. The masses and widths of the wide P c (4380) + andnarrow P c (4450) + states have been measured. The preferred spin-parity assignments are (cid:16) − ,
52 + (cid:17) , (cid:16)
32 + , − (cid:17) and (cid:16)
52 + , − (cid:17) , where the first value is the J P assignment given bythe best fit. [GeV] p y / J m E v en t s / ( M e V ) LHCb (b) [GeV] pK m E v en t s / ( M e V ) LHCb (a) datatotal fitbackground(4450) c P (4380) c P(1405) L (1520) L (1600) L (1670) L (1690) L (1800) L (1810) L (1820) L (1830) L (1890) L (2100) L (2110) L LHCbRun 1 LHCbRun 1Figure 5.15: The (left) m J/ψp and (right) m Kp mass distributions, showing superimposed fitprojections as solid (red) points. The solid (red) histogram shows the background distribution,the blue shaded histogram represents the P c (4450) + state, and the shaded purple histogramrepresents the P c (4380) + . Each Λ ∗ component is also shown. Following the first observation, the exotic hadronic character of the
J/ψp structurearound 4450 MeV/ c was confirmed in a model-independent way [141]. This analysis gavesimilar results and excluded that the data could be described by the pK − constributionsalone. Further confirmation comes from the amplitude analysis of the Cabibbo-suppresseddecay Λ b → J/ψpπ − [194], where 1885 ±
50 signal candidates were investigated. There aredifferent theoretical interpretations suggested, including a tightly bound duucc statea loosely bound molecular baryon-meson state or a triangle-diagram processes.A partial update of the above analysis was made using the full Run 1&2 data sam-ple [195]. A nine-fold increase of statistics is achieved due to the larger data sample,an improved selection criteria, and increased pp → bb cross-section at √ s = 13 TeV inRun 2. For candidates with a mass consistent with the nominal Λ b baryon mass, the J/ψp and pK − mass spectra were investigated. In the distribution of J/ψp mass, the previouslyreported peaking structure around 4450 MeV/ c was confirmed, and a new narrow peakwith mass around 4312 MeV/ c was found. The Λ ∗ → pK − contributions are clearly seenin the Dalitz plot, shown in Fig. 5.16 (left).Since the newly observed peaks are narrow, the full amplitude analysis faces computa-tional challenges. This is because resolution effects should be included in the formalismwhich complicates the fitting procedure. Conversely, narrow peaks can not be due to52 ) . G e V · C and i da t e s / ( . [GeV m ] [ G e V y J / m LHCb p y / J m W e i gh t ed c and i da t e s / ( M e V ) datatotal fitbackground LHCb + (4312) c P + (4440) c P + (4457) c P *D +c S D +c S LHCbRun 1&2 LHCbRun 1&2 m ( J/ψp ) (cid:2) MeV/ c (cid:3) Figure 5.16: (left) Dalitz plot of Λ b → J/ψpK − candidates. The vertical bands correspond to Λ ∗ resonances. The horizontal bands correspond to the P c (4312) + , P c (4440) + , and P c (4457) + struc-tures at m J/ψp = 18 .
6, 19 .
7, and 19 . , respectively. (right) Projection of the Λ ∗ -suppressed m J/ψp distribution showing a fit with three Breit − Wigner amplitudes and a sixth-order polyno-mial background. The mass thresholds for the Σ c D and Σ c D ∗ final states are superimposed. reflections from Λ ∗ states, motivating the validity of the one-dimensional fit approach tostudy the J/ψp invariant mass. The
J/ψp mass in the narrow-resonance region togetherwith the result of the fit is shown in Fig. 5.16 (right). The previously reported peakaround the 4450 MeV/ c mass is now resolved into a two-peak structure of P c (4440) + and P c (4457) + states. In total, three narrow pentaquark states are observed. The statisticalsignificance of the two-peak interpretation of the previously-reported single P c (4450) + structure is 5 . σ . The statistical significance of a new P c (4312) + state is 7 . σ . The massesand widths of the pentaquark candidates are measured. Taking into account systematicuncertainties, the widths are consistent with the mass resolution. Hence, upper limits onthe natural widths at the 95 % confidence level (CL) are obtained.In summary, whilst the existence of pentaquark-like resonances is certainly beyonddoubt, their exact nature is still unclear. They can be genuine five-quark bound states, or e.g. near-threshold meson-baryon molecules. More studies are required to clarify this. The enigmatic X (3872) particle was discovered in B + decays by the Belle bollab-oration [196]. Subsequently, its existence has been confirmed by several other experi-ments [197–199]. The nature of this state is rather unclear. Among the open possibilitiesare conventional charmonium and exotic states such as D ∗ ¯ D molecules [200], tetra-quarks [201], or their mixtures [202]. Determination of the J P C quantum numbers isimportant to shed light on this ambiguity. The C -parity of the state is positive sincethe X (3872) → J/ψγ decay has been observed [203, 204]. The CDF experiment anal-ysed three-dimensional angular correlations in a relatively high-background sample of2292 ±
113 inclusively-reconstructed X (3872) → J/ψπ + π − , J/ψ → µ + µ − decays, domi-nated by prompt production in p ¯ p collisions. The unknown polarisation of the X (3872)limits the sensitivity of the measurement of J P C [205]. A χ fit of J P C hypotheses to the53inned three-dimensional distribution of the
J/ψ and π + π − helicity angles and the anglebetween their decay planes [206–208], excluded all spin-parity assignments except for 1 ++ and 2 − + .Using √ s = 7 TeV pp collision data corresponding to 1 fb − collected in 2011, the LHCbcollaboration performed the first analysis of the complete five-dimensional angular corre-lations of the B + → X (3872) K + , X (3872) → J/ψπ + π − , J/ψ → µ + µ − decay chain [209].About 38 000 candidates passed the multivariate selection in a ± σ range around the B + m J/ψπ + π − K − mass distribution, with a signal purity of 89%. The ∆ m ≡ m J/ψπ + π − − m J/ψ distribution is shown in Fig. 5.17(left). The fit yields 5642 ±
76 and 313 ±
26 candidatesfor ψ (2 S ) → J/ψπ + π − and X (3872) → J/ψπ + π − signals, respectively.The angular correlations in the B + decay carry information about the X (3872) quantumnumbers. To discriminate between the 1 ++ and 2 − + assignments, a likelihood-ratio testis used. A test statistic t is defined as − L (2 − + ) / L (1 ++ )]. Positive (negative) valuesof the test statistic for the data, t data , favour the 1 ++ (2 − + ) hypothesis. The value ofthe test statistic observed in the data is t data = +99, thus favouring the 1 ++ hypothesis.A rejection of the 2 − + hypothesis with greater than 5 σ significance is demonstrated usinga large sample of pseudo-experiments. As shown in Fig. 5.17(right) the distributionof t is reasonably well approximated by a Gaussian function. Based on the mean andr.m.s. spread of the t distribution for the 2 − + experiments, this hypothesis is rejectedwith a significance of 8 . σ . Hence the obtained results correspond to an unambiguousassignment of the X (3872) state to be 1 ++ .The above result rules out the explanation of the X (3872) as a conventional η c (1 D ) state. Among the remaining possibilities are the χ c (2 P ) charmonium state,and unconventional explanations such as a D ∗ ¯ D molecule tetraquark state charmoni-um-molecule mixture. ) [MeV] y ) - M(J/ y J/ - p + p M(600 800 1000 1200 1400 N u m be r o f c and i da t e s / ( . M e V ) LHCb
550 600020040060080010001200 (2S) y
750 800010203040506070
X(3872) ) ] ++ (1 L )/ -+ (2 L = -2 ln[ t -200 -100 0 100 200 N u m be r o f e x pe r i m en t s / b i n data t -+ =2 PC Simulated J ++ =1 PC Simulated J
LHCb
LHCb 1 fb − √ s = 7 TeV LHCb 1 fb − √ s = 7 TeV m ( J/ψπ + π − ) − m ( J/ψ ) (cid:2) MeV/ c (cid:3) − L (2 − + ) L (1 ++ ) Figure 5.17: (left) Distribution of ∆ m ≡ m ( J/ψπ + π − ) − m ( J/ψ ) for B + → J/ψπ + π − K − candi-dates. The fits of the ψ (2 S ) and X (3872) signals are displayed. The solid blue, dashed red, anddotted green lines represent the total fit, signal component, and background component, respec-tively. (right) Distribution of the test statistic t ≡ − L (2 − + ) L (1 ++ ) for the simulated experimentswith J P C = 2 − + (black circles on the left) and with J P C = 1 ++ (red triangles on the right).The value of the test statistic for the data, t data , is shown by the solid vertical line. With a larger 3 fb − data-set at √ s = 7 and 8 TeV, the analysis has been repeated inthe decay X (3872) → J/ψρ without an assumption on the orbital angular momentum54210]. The analysis confirmed the J P C = 1 ++ assignment for the X (3872) state and alsoset an upper limit of 4% at 90% C.L. on the D-wave contribution.A precise determination of the mass and width of the X (3872) state was performedusing two minimally overlapping data-sets. The first was the 3 fb − Run 1 data-setin which the X (3872) particles were now selected from decays of hadrons containing b quarks [122]. The second was the full Run 1 and 2 data-sets using a sample of(547 . ± . × B + → J/ψπ + π − K + decays [123]. In both cases the X (3872) wasreconstructed in the X (3872) → J/ψπ + π − final state. The mass and width were determinedfrom a fit to the J/ψπ + π − mass distribution assuming a Breit–Wigner line shape forthe X (3872) state, measured as follows:m X (3872) = 3871 . ± . ± .
07 MeV/ c , Γ BW = 1 . ± . ± .
10 MeV , m X (3872) = 3871 . ± . ± .
03 MeV/ c , Γ BW = 0 . +0 . − . ± .
21 MeV , where the first and the second lines correspond to Refs. [122] and [123], respectively.The above measurements represent the most precise determination of the mass ofthe X (3872) state and the first measurements of its width. The measured mass correspondsto the binding energy δE , defined as m D c + m D ∗ c − m X (3872) c , which is 70 ±
120 keV.Whilst the proximity of the measured mass of the X (3872) to the D D ∗ thresh-old [211–215] favours the interpretation of this state as a D D ∗ molecule, the large produc-tion cross-section of the X (3872) [197, 198, 213, 216, 217] disfavours this. The pure molecu-lar interpretation is further disfavoured by the observation of the decay X (3872) → ψ (2 S ) γ .The ratio of the decay rates to ψ (2 S ) γ and J/ψγ final states is very sensitive to the natureof the X (3872) state. This is predicted to be in the range (3 − × − for a DD ∗ molecule1 . −
15 for a pure charmonium state and 0 . − X (3872) → ψ (2 S ) γ decays using the decay chain B + → X (3872) K + , X (3872) → ψ (2 S ) γ . The analysis was based on a 1 fb − data sampleat 7 TeV and 2 fb − at 8 TeV. The significance of the B + → ( X (3872) → ψ (2 S ) γ ) K + signal is 4.4 standard deviations. The branching fraction, normalised to that of the X (3842) → J/ψγ decay mode, is measured to be B ( X (3842) → ψ (2 S ) γ ) B ( X (3842) → J/ψγ ) = 2 . ± . ± . . This result is compatible with, but more precise than, previous measurements [204, 218],and strongly disfavours a pure molecular interpretation of the X (3872) state. Structures in the
J/ψφ system have acquired great experimental and theoreticalinterest since the CDF collaboration reported 3 . σ evidence (14 ± . +8 . − . ± . X (4140) mass peak in a sample of 75 ±
11 re-constructed B + → J/ψφK + decays [219]. Much larger widths are expected for charmoniastates at this mass, therefore its possible interpretations as a molecular state, a tetraquarkstate, a hybrid state or a rescattering effect have been discussed. The X (4140) structurewas confirmed by CMS [220] and D0 [221, 222], however searches in B + → J/ψφK + decayswere negative in the Belle [223, 224] and BaBar [225] experiments.Using a 0.37 fb − data-set at √ s = 7 TeV (346 ±
20 signal B + → J/ψφK + decays) LHCbinitially found no evidence for the narrow X (4140) structure [226], in 2 . σ disagreementwith the measurement by CDF, seen in Fig 5.18(left). However, using a significantly55arger sample of 4286 ± B + → J/ψφK + decays (the Run 1 data-set), with roughlyuniform efficiency across the entire J/ψφ mass region, LHCb performed a full amplitudeanalysis, including resonant contributions from K ∗ resonances decaying into φK + andpossible resonances in the J/ψφ system [142, 143]. Four resonance contributions labeledas X (4140), X (4274), X (4500) and X (4700) with quantum numbers 1 ++ , 1 ++ , 0 ++ and0 ++ , respectively, are observed, shown in Fig. 5.18(right). The statistical significancevaries from 5 . . σ . The widths of the states are found to be between 56 and 120 MeV,significantly exceeding the narrow-width of the X (4140) reported by CDF. C and i da t e s / M e V (a) + K fy J/ fi + BLHCb ) [MeV] y )-M(J/ fy M(J/ C and i da t e s / M e V (b) [MeV] fy J/ m C a nd i d a t e s / ( M e V ) LHCb
LHCb 0 .
37 fb − √ s = 7 TeV LHCbRun 1 m ( J/ψφ ) − m ( J/ψ ) (cid:2) MeV/ c (cid:3) m ( J/ψφ ) (cid:2) MeV/ c (cid:3) Figure 5.18: (left) The distribution of mass difference m ( J/ψφ ) − m ( J/ψ ) in a 0.37 fb − data-setfor selected B + → J/ψφK + candidates [226]. A fit of the X (4140) signal on top of a smoothbackground is superimposed (solid red line). The dashed blue (dotted blue) lines illustratesthe expected X (4140) ( X (4274)) signal yield from the CDF measurement [219]. The top andbottom plots differ by the background function used in the fit: (top) an efficiency-correctedthree-body phase-space; (bottom) a quadratic function multiplied by the efficiency-correctedthree-body phase-space factor. (right) The distribution of J/ψφ mass in the full Run 1 data-setfor B + → J/ψφK + candidates (black data points) compared with the results of the amplitudefit containing eight K ∗ + → φK + contributions (shown with open symbols) and five X → J/ψφ resonance contributions (shown as hatched histograms) [142, 143]. The total fit is given bythe red histogram.
The charged charmonium-like state Z c (4430) − was first observed by the Belle col-laboration in the ψ (2 S ) π − mass spectrum of B → ψ (2 S ) K − π − decays [227]. The state ap-peared as as a narrow (Γ = 44 +17+30 − − MeV) structure with a significance of 6 . σ . Later, thecollaboration performed a full amplitude analysis of 2010 ± ± B → ψ (2 S ) K − π − sig-nal decays, determining the quantum numbers as J P = 1 + , and finding a much broaderwidth of Γ = 200 +41+26 − − MeV [228].The LHCb experiment has collected about 25 ,
000 signal B decays (the Run 1 data set)and observed the Z c (4430) − with a significance exceeding 13 . σ [137]. Model-independentas well as full amplitude analyses were performed. The spin-parity is confirmed as 1 + ,other hypotheses are excluded by at least 9 . σ .Exotic particles with quantum numbers which can decay into η c π − are predicted inseveral models [229]. Using a 4 . − data sample at 7, 8 and 13 TeV, the LHCb collabo-ration has performed a Dalitz-plot analysis of B → η c K + π − decays, where the η c meson56s reconstructed in the η c → pp final state [230]. Evidence was found for a new exoticresonance in the η c π − system, later dubbed the X (4100) − by the PDG. The significanceof this new resonance exceeds three standard deviations. J/ψJ/ψ mass spectrum
The production of
J/ψJ/ψ pairs in high-energy pp collisions was observed for the first timeby the LHCb experiment using a 37.5 pb − data sample collected in 2010 at √ s = 7 TeV[231]. The J/ψJ/ψ mass spectrum was studied in a sample of 116 ±
16 signal pairs, andno structures was found. The subsequent analysis of 279 pb − of data collected in 2015at √ s = 13 TeV [232] showed the dominant role of the double-parton scattering (DPS)mechanism for J/ψJ/ψ production over the single-parton scattering mechanism (SPS). Thisin turn includes both a non-resonant SPS contribution and cccc tetraquark production.Using the full Run 1 and 2 data-set, the
J/ψJ/ψ mass spectrum was studied in moredetail [233]. The data, shown in Fig. 5.19, were found to be inconsistent with the hy-pothesis of non-resonant SPS plus DPS in the 6 . < m J/ψJ/ψ < . c range, where cccc tetraquarks decaying into J/ψJ/ψ pairs are expected. A narrow peaking structure at m J/ψJ/ψ ≈ . c matching the lineshape of a resonance, and a broader structure nearto threshold, were found. DataTotal fitResonanceInterferenceInterference BWDPSNRSPS
LHCb Run 1 + Run 2 C a nd i d a t e s / ( M e V / c ) m J/ψJ/ψ (cid:2)
MeV/ c (cid:3) LHCbRun 1&2
Figure 5.19: The
J/ψ -pair mass spectrum with the fit result superimposed. The fit accounts forthe interference between a resonance and non-resonant SPS contribution [233].
The global significances of the broader structure close to threshold or the narrow peakaround 6 . c (provided that the other structure exists), are determined to be largerthan 5 standard deviations. The structures are consistent with hadron states made up offour charm quarks, alternatively they may also result from near-threshold rescatteringeffects, as the χ c χ c and χ c χ c thresholds sit at 6829 . c and 6925 . c ,respectively. 57 .8 Light hadron spectroscopy η − η (cid:48) mixing has been studied by LHCb in B s ) → J/ψη ( (cid:48) ) decays, resulting in fourobserved decays modes, using the Run 1 data-set [234]. The η and η (cid:48) were identified in thedecay modes η (cid:48) → ηπ + π − , η → π + π − π and η (cid:48) → ρ γ . For decays of B s ( B ) mesons, the η ( (cid:48) ) mesons are formed from initial ss ( dd ) quark pairs, hence the measurement of the ratiosof branching fractions of these decays allows a precise measurement of the η − η (cid:48) mixingangle. It also probes the gluonium component in the η (cid:48) meson. Excited strange mesons have been studied in the φK + system from a full amplitudefit of B + → J/ψφK + decays using the LHCb Run 1 data-set [142, 143]. Even though nopeaking structures are observed in the φK + mass distributions. correlations in the decayangles reveal a rich spectrum of K ∗ + resonances. In addition to the angular informationcontained in the K ∗ + and φ decays, the J/ψ decay also helps to probe these resonances,as the helicity states of the K ∗ + and J/ψ mesons originating from the B + decay must beequal. Unlike the earlier scattering experiments investigating K ∗ → φK decays, a goodsensitivity to states with both natural and unnatural spin-parity combinations is achieved.The dominant 1 + partial wave has a substantial non-resonant component, and atleast one resonance that has a significance of 7 . σ . There is also 2 σ evidence that thisstructure can be better described with two resonances matching expectations for two2 P excitations of the kaon. Also prominent is the 2 − partial wave which contains atleast one resonance at 5 . σ significance. This structure is also better described withtwo resonances at 3 . σ significance. Their masses and widths are in good agreementwith the well-established K (1770) and K (1820) states, matching the predictions forthe two 1 D kaon excitations. The 1 − partial wave exhibits 8 . σ evidence for a resonancewhich matches the K ∗ (1680) state, which was well established in other decay modes, andmatches expectations for the 1 D kaon excitation. This is the first observation of itsdecay to the φK final state. The 2 + partial wave has a smaller intensity but provides5 . σ evidence for a broad structure that is consistent with the K ∗ (1980) state, previouslyobserved in other decay modes, and matches expectations for the 2 P state. The K (1830)state (3 S candidate), earlier observed in the φK decay mode in K − p scattering, isalso confirmed at 3 . σ significance. Its mass and width is now properly evaluated withuncertainties for the first time. 58 Measurements not originally planned in LHCb
While originally designed to study the production and decay of b and c hadrons, LHCbhas extended its physics programme to also include other areas, such as physics with jets,the production of W and Z bosons, searches for new particles in open mode, and nuclearcollisions. Selected highlights are summarised below. W and Z LHCb has measured the production of Z and W bosons inclusively [235] and in associationwith jets, reconstructed in mainly muonic final states, using the data collected at √ s =8 TeV [236]. Also decays to e + e − [237], τ + τ − [238] and eν [239], have been measured,however the muon channel is the most efficient due to the excellent performance of themuon system (see Sect. 2.6). The Z → µ + µ − decay shows a spectacularly clean signal, asshown in Fig. 6.1(a) [240]. The W → µν channel also manifests in a clear signal, shownin Fig. 6.1(b) [235]. The absolute and differential cross sections, their ratios, and chargeasymmetries have been measured and compared to theoretical predictions. Figure 6.2(Left) shows the comparison of W and Z cross section measurements to SM predictions,showing good agreement. Figure 6.1: (a) Invariant mass distribution of dimuon pairs in the Z -candidate sample. (b)LHCb data compared to QCD, electroweak and heavy flavour background, for positive (left)and negative (right) muon p T spectra of W candidates [235]. Measurements of jets at LHCb address several interesting areas of study: • Jet properties and heavy-quark jet tagging; • The constraining of proton parton density functions (PDFs) and to probe hardQCD in a unique kinematic range. Figure 6.3 shows the domain in the (x,Q ) planecovered by the LHCb detector, complementing the kinematic ranges of ATLAS andCMS; 59 -jet m T p / m T p E v e n t s / ( . ) =8 TeVsData, j + W ElectroweakQCD
LHCb
Figure 6.2: (Left) The W versus Z measured production cross sections, showing comparisonwith theoretical predictions. (Right) Contributions to the selected W plus jet sample in thediscriminating variable p µT /p µ − jetT (described in the text). • Direct searches for the Higgs boson decaying to b ¯ b and c ¯ c final states; • Direct searches for long-lived beyond-the-SM particles decaying into jets.Jets are reconstructed in LHCb using a particle flow algorithm [241] clustered using theanti- kT algorithm with R = 0.5 [242]. The calibration of jet reconstruction is performedin data using Z → µ + µ − decays which also contain a jet, where the jet is reconstructedback-to-back with respect to the Z . The efficiency for reconstructing and identifying jetsis around 90% for jets with transverse momentum p T >
20 GeV/ c . Furthermore, LHCbhas developed a method to tag jets [241] and to determine whether they correspond toa b or c quark or to a lighter quark. Jets are tagged whenever a secondary vertex (SV)is reconstructed close enough to the jet in terms of R = (cid:112) (∆ φ + ∆ η ). This provides alight-jet mistag rate below 1%, with an efficiency for b ( c ) jets of ∼
65% ( ∼ b from c jets. Asummary of the obtained performance is shown in Fig. 6.4, where the efficiency of flavouridentification is plotted as a function of the misidentification of light jets. Production of W and Z with jets. W and Z production have also been studied inassociation with jets [236], in W + j , Z + j , W + b ¯ b and W + c ¯ c . Jets are reconstructedas described above, whilst Z and W bosons are reconstructed mainly in muonic finalstates. The production of W boson plus jets is discriminated from misidentified QCDbackground processes using a muon isolation variable, which is built as the ratio betweenthe p T of the jet containing the muon and the p T of the muon alone. Figure 6.2(b) showsthe distribution of this variable, with genuine muons from the W boson peaking at 1.Figure 6.5 shows the comparison of the measured cross-sections in LHCb with theoreticalexpectations, showing very good agreement.LHCb has measured the W ± + b ¯ b , W ± + c ¯ c , production cross sections using a sampleof pp collisions taken at √ s = 8 TeV with a high- p T isolated lepton from the W decay60 -6 -5 -4 -3 -2 -1 x -2 -1 Q y =0 y =0 y =2 y =2 y =4 y =4 y =6 y =6 LHC 8 TeV Kinematics
ATLAS/CMSLHCbCDF/D0HERAFixed Target
Figure 6.3: The region in the x − Q plane probed by LHCb, compared to ATLAS, CMS andprevious experiments. (electron or muon) and two heavy flavour ( b or c ) tagged jets in the final state. Theheavy-quark tagging uses the method described above. In this analysis, the W + c ¯ c channelis studied for the first time.In order to extract the different signal components, a simultaneous four-dimensionalfit is performed on the µ + , µ − , e + and e − samples. Here the electron channels are used toincrease statistics. The four variables used in the fit are the dijet mass, a multivariatediscriminator to separate t ¯ t from W + b ¯ b and W + c ¯ c events and a multivariate discriminatorto separate b - and c -jets, used for both accompanying jets [243]. In this fit, the backgroundfrom QCD multi-jets is extrapolated from a control sample in data, while other backgroundcontributions are fixed to SM theoretical expectations. Only the signal components arethen unconstrained. The projections of the resulting fit on four input variables for the µ + sample are illustrated in Fig. 6.6. The statistical significance of the measured W + + b ¯ b , W + + c ¯ c , W − + b ¯ b , W − + c ¯ c and t ¯ t production cross sections are 7.1 σ , 4.7 σ , 5.6 σ , 2.5 σ and 4.9 σ , respectively. The cross sections measured in the LHCb fiducial acceptance agreewell with the Next-to-Leading-Order (NLO) theory predictions.61 igure 6.4: Simulated efficiencies for SV-tagging a b, c -jet as a function of mistag probability fora light-quark jet. Search for long-lived new particles.
The LHCb detector has been designed tomeasure very rare decays of b quarks, with the aim of detecting the presence of newbeyond-the-SM particles through their couplings in loops, which could change the expectedSM branching ratios. This implies reaching mass scales higher than those explored in open new particle searches, where the particle is produced directly in pp collisions. Thetraditional way to search for new particles is, as for ATLAS and CMS, reconstructingtheir decays through exclusive final states in their invariant masses, or with missingenergy techniques. Here hermiticity is a mandatory feature of the detector. In all cases,assumptions on their coupling, their production mechanism, and on their decay modesmust be made, and the search is therefore guided by theoretical models.For LHCb, the most promising final states are those decays which form a secondaryvertex, for which the LHCb VELO (see Sect. 2.2) is extremely efficient, i.e. the newparticles are long lived. Several negative results have been published which are oftenless sensitive than the General-Purpose Detector (GPD) results. However in some cases,LHCb can extend the exclusion region. An example is given in Fig. 6.7 for a Higgs-likeparticle H decaying into jets forming a separate secondary vertex. The LHCb exclusionregion is compared with that of ATLAS and CMS, which demonstrates the complementaryof the LHC experiments. The limits are, in this specific case, competitive, despite a factor10 less luminosity. Production of t ¯ t pairs. Top quark production is an excellent example where theforward acceptance of the LHCb detector has several advantages with respect to thecentral region instrumented by ATLAS and CMS. The t quark cross-section can provideimportant constraints on the large- x gluon PDF, where the forward kinematic regionis particularly sensitive. In addition the forward region provides a greater fraction ofevents with quark-initiated production than in the central region, and enhances the sizeof t ¯ t asymmetries visible at LHCb. The challenge for LHCb to measure t ¯ t productionis the small acceptance and the impossibility of a missing energy measurement. Also62 heory/Data0.8 1 1.2 j) + W ( s ) j - W ( s ) Zj ( s WZ R Z + W R Z - W R – W R LHCb = 8 TeVs
DataPOWHEGaMC@NLO ) Wj ( A Wj ( A Figure 6.5: Comparison with theoretical calculations of measured cross sections for W and Z production accompanied by jets. The orange bands represent the statistical uncertainty only,the yellow bands are the quadratic sum of statistical and systematic uncertainties. the fact that the luminosity is limited by the need to reduce multiple interactions formeasurements in the b sector, disfavours t ¯ t statistics.Top-quark production is presented here at √ s =13 TeV, which gives an increase in theproduction rate of an order of magnitude with respect to 8 TeV, and which brings thesenew channels into statistical reach. The t ¯ t analysis is based on an integrated luminosity of2 fb − , and with eµb measured in the final state. Hence the final state is the decay chain t ¯ t → bW + bW − → e + µ − bb , where at least one b -jet is reconstructed. This is a very purefinal state, as the second lepton suppresses W + b ¯ b production and the different flavouredleptons suppress Z + b ¯ b . The signal purity is illustrated in Fig. 6.8(a), and the observablecross section is measured to be σ t ¯ t = 126 ±
19( (stat)) ±
16( (syst)) ± Z → b ¯ b decay. This measurement is an important validation of the LHCb jet re-construction and b -tagging performance. Two b -tagged jets are reconstructed, with athird balancing jet also reconstructed to help control the QCD background and definesignal and control regions using a multivariate technique. The background-subtractedsignal distribution is shown in Fig. 6.8(b) [244]. The signal is observed with a statisticalsignificance of 6 σ and the measured cross section is found to be compatible with SMpredictions at next-to-leading order. 63 [GeV] jj m E v e n t s / ( G e V ) LHCb = 8 TeVsa) uGB E v e n t s / ( . ) LHCb = 8 TeVsb)
BDT(b|c) j - - E v e n t s / ( . ) LHCb = 8 TeVsc)
BDT(b|c) j - - E v e n t s / ( . ) LHCb = 8 TeVsd)
Figure 6.6: Projections of the simultaneous four-dimensional fit for the µ + sample [243] to:(a) the dijet mass, (b) the discriminator to separate t ¯ t from W + b ¯ b and W + c ¯ c , and (c) thediscriminator to separate b and c leading jets (d) sub-leading jets. In light blue is W + b ¯ b , ingreen t ¯ t , in red W + c ¯ c and in black the background. The possibility that dark matter particles may interact via unknown forces, almost not feltby SM particles, has motivated substantial effort to search for dark-sector forces (see [245]for a review). A dark-force scenario involves a massive dark photon, A (cid:48) . In the minimalmodel, the dark photon does not couple directly to charged SM particles, but it can gain aweak coupling to the SM electromagnetic current via kinetic mixing. The strength of thiscoupling is suppressed by a factor (cid:15) with respect to the SM photon. If the kinetic mixingarises from processes whose amplitudes involve one or two loops containing high-massparticles, perhaps even at the Planck scale, then 10 − ≤ (cid:15) ≤ − is expected [245].Constraints have been placed on visible A (cid:48) decays by previous beam-dump, fixed-target, collider and rare meson decay experiments; the few-loop region is ruled out for darkphoton masses m ( A (cid:48) ) ∼
10 MeV/ c . Additionally, the region (cid:15) < × − is excludedfor m ( A (cid:48) ) < . c , along with about half of the remaining few-loop region belowthe dimuon threshold. Many ideas have been proposed to further explore the [ m ( A (cid:48) ) , (cid:15) ]parameter space, including an inclusive search for A (cid:48) → µ − µ + decays with the LHCbexperiment. A dark photon produced in proton-proton collisions via γ ∗ – A (cid:48) mixing inheritsthe production mechanisms of an off-shell photon with m ( γ ∗ ) = m ( A (cid:48) ), therefore boththe production and decay kinematics of the A (cid:48) → µ + µ − and γ ∗ → µ + µ − processes are64 igure 6.7: Comparison of the LHCb exclusion region for the Branching Ratio of H H → π V π V ,where π V is a long-lived particle decaying to jets. Exclusion regions for ATLAS and CMS arealso shown. identical.LHCb has performed searches for both prompt-like and long-lived dark photons [246]produced in pp collisions at a centre-of-mass energy of 13 TeV, using A (cid:48) → µ + µ − decays anda data sample corresponding to an integrated luminosity of 1.6 fb − collected during 2016.The prompt-like A (cid:48) search is performed from near the dimuon threshold up to 70 GeV,above which the m ( µ + µ − ) spectrum is dominated by the Z boson. The prompt-likedimuon spectrum is shown in Fig. 6.9.Three main types of background contribute to the prompt-like A (cid:48) search: prompt off-shell γ ∗ → µ + µ − , which is irreducible; resonant decays to µ + µ − , whose mass peak regionsare excluded in the search (see Fig. 6.9), and various types of misidentification, whichare highly suppressed by the stringent muon-identification and prompt-like requirementsapplied in the trigger.For the long-lived dark photon search, i.e. with displaced dimuon vertices, the stringentcriteria applied in the trigger make contamination from prompt muon candidates negligible.The long-lived A (cid:48) search is restricted to the mass range 214 ≤ m ( A (cid:48) ) ≤
350 MeV/ c , wherethe data sample potentially provides sensitivity. In this case the background compositionis dominated by photon conversions to µ + µ − in the VELO, b -hadron decays where twomuons are produced in the decay chain, and the low-mass tail from K → π + π − decays65 igure 6.8: (Left) The eµb invariant mass for all 44 selected t ¯ t candidates, illustrates theexcellent signal purity. (Right) The background-subtracted dijet mass spectrum showing theZ → b ¯ b signal [244]. m ( µ + µ − ) [ MeV ] C a nd i d a t e s / σ [ m ( µ + µ − ) ] /2 LHCb √ s = 13 TeV prompt µ + µ − µ Q µ Q hh + hµ Q ⇒ isolationapplied prompt-like sample p T ( µ ) > p ( µ ) >
20 GeV
Figure 6.9: The prompt-like µ + µ − mass spectrum. where both pions are misidentified as muons.In the dark-photon searches, no evidence for a signal is found, and 90% CL exclusionregions are set on the γ − A (cid:48) kinetic-mixing strength, shown in Fig. 6.10. The constraintsplaced on prompt-like dark photons are the most stringent to date for the mass range10 . ≤ m ( A (cid:48) ) ≤
70 GeV/ c , and are comparable to the best existing limits for m ( A (cid:48) ) ≤ . c . The search for long-lived dark photons is the first to achieve sensitivity using adisplaced-vertex signature. These results demonstrate the unique sensitivity of the LHCbexperiment to dark photons, even using a data sample collected with a trigger that isinefficient for low-mass A (cid:48) → µ + µ − decays. Using knowledge gained from this analysis,the software-trigger efficiency for low-mass dark photons has been significantly improvedfor 2017 data taking.In Run 3 to come, the planned increase in luminosity and removal of the hardware-trigger stage should increase the number of expected A (cid:48) → µ + µ − decays in the low-massregion by O (100– − igure 6.10: Results of the dark photon search. Both prompt-like (top) and displaced (centre)exclusions are shown. Ultra-relativistic heavy-ion collisions allow the study of the so-called Quark-Gluon Plasma(QGP) state of matter, a hot and dense medium of deconfined quarks and gluons whereheavy quarks are crucial probes. Produced via hard interactions at the early stage of thenucleus-nucleus collision, before the QGP formation, heavy quarks experience the entireevolution of the QGP. A correct interpretation of these probes requires a full understandingof Cold Nuclear Matter (CNM) effects, which are present regardless of the formation ofthe deconfined medium. To disentangle the CNM from genuine QGP effects, heavy-flavourproduction in proton-nucleus collisions is studied.The LHCb experiment has collected data of proton-lead ( p Pb) and lead-lead (PbPb)collisions. Since the LHCb detector covers only one direction of the full acceptance, thereare two distinctive beam configurations for the pPb collisions. In the forward (backward)configuration, the proton (lead) beam enters the LHCb detector from the interactionpoint. The proton beam and the lead beam have different energies per nucleon in thelaboratory frame, hence the nucleon-nucleon centre-of-mass frame is boosted in the protondirection with a rapidity, y , shift. This results in the LHCb acceptance for the forwardconfiguration as 1 . < y <
4, and for the backward configuration − < y < − . O (10 − ) mbar, allowing measurements of p -gas and ion-gascollisions, and operating LHCb as a fixed target experiment. Since 2015, LHCb hasexploited SMOG in physics runs using special fills not devoted to pp physics, with avariety of beam ( p or Pb) and target configurations. This allows unique production studieswhich are relevant to cosmic ray and heavy-ion physics.67he heavy-ion results on heavy-flavour production in p Pb, PbPb and fixed-targetcollisions collected by LHCb bring yet more diversity and complementarity into thefield. Also in this context, the excellent momentum resolution and particle identificationprovided by LHCb are especially suited for measuring heavy quark production. The LHCbcollaboration joined the other participants into the LHC heavy-ion collider programmewith a p Pb run at 5 TeV in 2013 and with a PbPb run in 2015. Following these pioneeringdata runs, significantly larger data-sets have been successfully recorded.
Fixed target collisions.
LHCb has reported first measurements of heavy-flavour pro-duction with the fixed-target mode [248].
J/ψ production cross-sections and D yields havebeen measured in p He collisions at √ s NN = 86 . p Ar collisions at √ s NN = 110 . < y < .
6. The cross-section measurements are madefor p He data only, since the luminosity determination is only available for this sample.After correction for acceptances, efficiencies and branching fractions, the cross-sectionsare extrapolated to the full phase space. The D measurement is used to extract the c ¯ c cross-section. The J/ψ and cc measurements are compared in Fig. 6.11 with otherexperiments at different centre-of-mass energies and with theoretical predictions.With p He data, LHCb also measured the antiproton production cross section [249],a very interesting direct determination, helping the interpretation of the antiprotoncosmic-ray flux detected by space experiments [250].
Figure 6.11:
J/ψ (left) and c ¯ c (right) cross-section measurements as a function of the centre-of-mass energy, compared with other experimental data (black points). The bands correspond tofits based on NLO NRQCD calculations for J/ψ and NLO pQCD calculations for c ¯ c , respectively.More details are given in [248]. Collider mode.
In collider mode, the LHCb experiment has collected proton-leadcollision data at √ s NN = 5 TeV in 2013 and at 8.16 TeV in 2016. The 2013 datasample corresponds to an integrated luminosity of 1 . ± .
02 nb − for the forwardand 0 . ± .
01 nb − for the backward regions, whilst the 2016 data corresponds to13.6 ± − for the forward and 20.8 ± − for the backward. These data samplesare used to measure quarkonium and open charm or beauty production.Υ(nS)-meson production is studied in the decay to two opposite-sign muons [251]. Themeasurements include the differential production cross-sections of Υ(1S), Υ(2S) states and68uclear modification factors, performed as a function of transverse momentum and rapidityin the nucleon-nucleon centre-of-mass frame of the Υ(nS) state. Also the productioncross-sections for the Υ(3S) is measured, integrated over phase space, and the productionratios between all three Υ(nS) states are determined.The three states are well identified in both p Pb and Pb p configurations as shown inFig. 6.12. The nuclear modification factors are compared with theoretical predictions,and suppressions for bottomium in p Pb collisions are observed. The LHCb measurementsimprove the understanding of cold nuclear matter effects down to low p T . Figure 6.12: Invariant-mass distribution of µ + µ − pairs from the (left) p Pb and (right) Pb p samples after trigger and offline selections. Over the years 2011 - 2018, both the LHC machine and the LHCb detector performedextremely well, providing great improvements with respect to the B Factory measurements,in particular the pioneering CP violation measurements (Sect. 3), the observation of therarest beauty meson decays (Sect.4) and the discovery of pentaquarks (Sect. 5). LHCbalso observed and reported a number of interesting hints of anomalies related to theflavour sector, which has generated much theoretical attention, especially relating to raredecays and lepton flavour universality. The precision achieved by the experiment is in linewith prior expectations, as documented in [252], and which demonstrates the remarkableunderstanding of all aspects of the detector.To further pursue these exciting results and fully exploit the flavour physics potentialof the LHC, the LHCb detector required an upgrade, to increase the rate and efficiencyof data taking beyond the Long Shutdown 2 (LS2). Consequently the LHCb detector isnow undergoing a major upgrade that is well underway, and will allow the experiment topursue its superb performance into the future.At present, the hardware-based trigger limits the amount of data taken each year to amaximum of about 2 fb − . In addition, most of the detector sub-systems would not copewith higher luminosity due to either their outdated readout electronics or radiation-induced69amage sustained during Run 1 and Run 2 data taking. The initial ideas regarding theupgrade were formulated in 2011 [253], and further solidified in 2012 when the TechnicalDesign Report was released [254]. Many of the subdetector components are largelyunchanged in the upgrade, with the exception of a new pixel vertex detector replacingthe current VELO, the TT stations being replaced by a new silicon micro-strip upstreamtracker (UT), and the straw outer chambers replaced by a scintillating fibre detector.Details of each subdetector upgrade can be found in refs. [254–258].The crucial point of the upgrade project is to build a reliable and robust detectorcapable of operating at higher luminosity without compromising the excellent physicsperformance of the current detector. This, in turn, cannot be achieved by redesigningthe hardware components alone, but has to be augmented by a new innovative andflexible trigger system. A critical part of the upgrade strategy is the design of a so-called“trigger-less” front-end electronics system capable of reading out the full detector at 40MHz, i.e. at the LHC clock frequency. Completely new and novel chips have been designedand tested for the pixel sensors [255] the UT [256] and RICH detectors [257].The upgraded detector will operate at an instantaneous luminosity of 2 · cm s − which allows collection of around 10 fb − of data per year as a target, also keeping pacewith Belle II [259], the other major flavour-physics experiment. Figure 7.1 shows thecorresponding time-line for LHCb operations over the next decade. Figure 7.1: A time-line showing the operations of the LHC and the HL-LHC over the nextdecade, including long shutdown (LS) periods, as can be estimated today. The operationalperiods of LHCb and Belle II are shown [259].
To efficiently run at increased luminosity, the present hardware-based trigger will bereplaced, and events will be selected by the software-based HLT alone. To cope with themuch higher event rate (typically five proton-proton interactions per beam crossing), aflexible software trigger will be employed and coupled with a re-optimized network capableof handling a multi-terabyte data stream. The upgraded trigger will process every event(the visible rate at LHCb is estimated to reach 30 MHz) using information from everysub-detector to enhance its decision and maximize signal efficiencies, especially for thehadronic channels. The precision of particle identification and track-quality informationwill be identical than ”offline” and able to reduce the rate down to 20-100 kHz. The newtrigger strategy will increase the triggering efficiency for the hadronic channels by a factor2 to 4 with respect to Run 1 [260], corresponding to an increase of a factor 10 to 20 forthe hadronic yields.Finally, plans for a further future upgrade (called Upgrade II) to use the full potentialof flavour physics during the HL-LHC operation have now started [261, 262]. This upgradewould require a complete redesign of the detector able to take data at instantaneous70uminosities of 2 · cm s − , and collect ∼
50 fb − of data per year, guaranteeing LHCboperation beyond 2030.The LHCb Upgrades I and II will significantly improve the reach of key physicsmeasurements. By way of example, the precision quoted in Section 3.3.3 on today’smeasurement of the CKM angle γ, O (5 ◦ ), will be improved to 1 ◦ with the new Upgrade Ihadronic trigger and luminosity increase. This further improves to 0 . ◦ with the largestatistics accumulated with LHCb Upgrade II. As discussed in Section 4.1, currently thereis not enough sensitivity to measure the rare decay B ( B → µ + µ − ). With LHCb UpgradeI, a first observation should be possible, but it will require Upgrade II to reach a ∼ B and B s into the µ + µ − final state, and will constitute a clean andpowerful test of extensions beyond the SM. In ten years of operation at the LHC, the LHCb experiment has delivered a remarkablyrich programme of physics measurements. In this paper the 25-year evolution of theexperiment since its inception has been described, and its successes and achievementshave been summarised. The diversity of the physics output has truly shown LHCb to bea “general-purpose detector in the forward region”.Over the last ten years, LHCb has measured the CKM quark mixing matrix elementsand CP violation parameters to world-leading precision in the b - and c -quark systems.The experiment has measured very rare decays of b and c mesons and baryons, some withbranching ratios down to order 10 − , testing Standard Model predictions to unprecedentedlevels. Hints of new physics in rare-decay angular distributions and through tests oflepton universality in electron-muon decay modes have generated considerable theoreticalinterest. The global knowledge of b and c quark states has improved significantly, throughdiscoveries of many new resonances already anticipated in the quark model, and also by theobservation of new exotic tetraquark and pentaquark states. In addition, many interestingmeasurements have been made that were not anticipated in the original LHCb proposal,such as electroweak physics, jet measurements, new long-lived particle searches and heavy-ion physics. An incredibly rich harvest of fundamental results has been produced, manyof these will remain in textbooks for years to come.LHCb has recently been upgraded and will start data-taking early in 2022 at a factor 5higher luminosity, incorporating new subdetectors and a software-based trigger. Statisticsin hadronic modes will be improved by at a factor 10–20, allowing much more precisemeasurements, especially of very rare b - and c -hadron decays. In addition, the futureplanned Upgrade II at the (HL)-LHC early in 2030 will ensure that LHCb maintains itslead in flavour physics for at least the next two decades. LHCb is at present a collaboration of about 1000 authors. The rich variety of outstandingresults has been made possible by the dedicated work of many colleagues: detector buildersand operators, data verifiers and analysts. 71e would like to acknowledge the important roles played by T. Nakada as firstspokesman and by the late H.J.Hilke as Technical Coordinator, who successfully managedthe realisation of this very complex detector.Finally, we would also like to thank our colleagues P. Koppenburg and G. Passalevawho made helpful and insightful comments to this paper.72 eferences [1] S. L. Glashow, J. Iliopoulos, and L. Maiani,
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