Observation of the γγ → ττ process in Pb+Pb collisions and constraints on the τ -lepton anomalous magnetic moment with the ATLAS detector at LHC

. This paper reports the observation of τ -lepton pair production in ul-traperipheral lead-lead collisions, Pb ( γ ) Pb ( γ ) → ττ and constraints on the τ - lepton anomalous magnetic moment, a τ , measured by the ATLAS experiment. The dataset corresponds to an integrated luminosity of 1.44 nb − 1 of LHC Pb + Pb collisions at √ s NN = 5.02 TeV. Selected events contain one muon from a τ -lepton decay, an electron or charged-particle track(s) from the other τ -lepton decay, little additional central-detector activity, and no forward neutrons. The γγ → ττ process is observed in Pb + Pb collisions with a signal strength of µ ττ = 1.03 + 0 . 06 − 0 . 05 . To measure a τ , a template ﬁt to the muon transverse-momentum distribution from τ -lepton candidates is performed, using a dimuon ( γγ → µµ ) control sample to constrain systematic uncertainties. The observed 95% conﬁdence-level interval for a τ is ( − 0 . 057 , 0 . 024).

Photon-induced events arise from interactions between the EM fields surrounding the beam particles at colliders.Observing photon-induced τ-lepton pairs (γγ → ττ) predicted to occur at the Large Hadron Collider (LHC) [19][20][21][22][23][24][25][26] would open the way to hadron-collider probes of a τ .Currently, the most precise single-experiment measurement is a τ ¼ −0.018ð17Þ by the DELPHI Collaboration [27,28] using γγ → ττ events at the Large Electron Positron (LEP) collider.The OPAL [29] and L3 [30] Collaborations also set constraints using radiative τ-lepton decays [31].At the LHC, photon-induced dilepton production has only been measured in the dielectron (ee) and dimuon (μμ) channels, using proton-proton (pp) [32][33][34][35][36][37] and lead-lead (Pb þ Pb) collisions [38][39][40][41][42][43].The ττ channel is challenging due to hadronic backgrounds and neutrinos in τ-lepton decays diluting visible final-state kinematics.This renders triggering and reconstruction more difficult, especially in highluminosity pp collisions.Strategies to overcome these experimental obstacles using heavy-ion collisions were proposed in Refs.[44][45][46].This Letter presents the observation of the Pb þ Pb → Pbðγγ → ττÞPb process and measurement of a τ using 1.44 nb −1 of Pb þ Pb data recorded by ATLAS in 2018 at a nucleon-nucleon (NN) center-of-mass energy of ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV.The EM fields accompanying the ions coherently create photons that interact to produce τ-lepton pairs.The cross section is enhanced by Z 4 relative to pp collisions, where Z is the atomic number (Z ¼ 82 for lead).The ions can remain intact, enabling selection of lowmultiplicity events with one muon originating from one of the τ leptons, while the other τ-lepton decay is reconstructed as either an electron or one or three charged-particle tracks with low transverse momentum.
The ATLAS experiment [47-49] is a multipurpose particle detector with cylindrical geometry [50], comprising an inner-detector (ID) tracker, EM and hadronic calorimeters, and a muon spectrometer (MS).The zero-degree calorimeters (ZDCs) [51] are located at z ¼ AE140 m from the interaction point and detect neutral particles such as neutrons emitted from interacting nuclei.A two-level trigger system [52,53] was used to select events containing one muon with p T > 4 GeV and, at most, 50 GeV (3 GeV) of transverse energy deposited in the whole (forward 3.2 < jηj < 4.9) calorimeter [54].An extensive software suite [55] is used in the reconstruction and analysis of real and simulated data, in detector operations and in the trigger and data acquisition systems.Standard data-quality requirements are imposed [56].The average number of hadronic interactions per bunch crossing was 0.003.
Samples of simulated γγ → ττ signal events were produced at leading order in QED using the STARLIGHT2.0 [57] Monte Carlo (MC) generator, interfaced with TAUOLA [58,59] for τ-lepton decays.Final-state radiation (FSR) from the τ leptons and charged decay products of τ leptons was simulated using PYTHIA8.245[60] and PHOTOS3.61[61], respectively.One of the dominant background sources is the γγ → μμ process, and its contribution is estimated with the aid of MC samples generated using STARLIGHT; PYTHIA8 was used to model EM FSR from the muons.The photon-flux distribution in simulated γγ → ττ and γγ → μμ events was reweighted to that of SUPERCHIC3.05 [62], differentially in dilepton invariant mass and dilepton rapidity.In the STARLIGHT and SUPERCHIC simulations, no restriction on the Coulomb breakup of either nucleus was imposed.Dijet samples from photon-induced diquark production, γγ → q q, were generated using PYTHIA8.Nondiffractive photonuclear events (γA → X) were simulated with STARLIGHT interfaced with DPMJET-III [63].All MC samples were passed through a detailed detector simulation based on GEANT4 [64,65].
Selected events must contain exactly one muon, which targets a muonic decay of one of the τ leptons while reducing backgrounds from γγ → μμ and γγ → q q.Three signal regions (SRs) then categorize events by the decay signature of the other τ lepton.The μe-SR category additionally requires one electron and no additional tracks separated from the muon (electron) by ΔR μðeÞ;trk > 0.1, which targets fully leptonic decays of both τ leptons.The different-flavor (μe) requirement suppresses same-flavor backgrounds dominated by γγ → μμ=ee.The μ1T-SR (μ3T-SR) category requires exactly one track (three tracks) separated from the muon by ΔR μ;trk > 0.1, which targets τ-lepton decays to one or three charged hadrons.The onetrack requirement also captures leptonic τ-lepton decays that fail electron or muon reconstruction.The electric charges of the muon, electron, and tracks must sum to zero.
For both μ1T-SR and μ3T-SR, events must contain no additional muons satisfying looser criteria and no electrons to reject γγ → μμ=ee backgrounds.The looser requirements on muons comprise matched tracks in the ID and MS satisfying p T > 2 GeV and jηj < 2.5.To suppress hadronic backgrounds such as photonuclear processes, there must be no topoclusters separated from the muon (track or three-track system [75]) by ΔR clust;μ > 0.3 (ΔR clust;trkðsÞ > 1.0); this requirement is referred to as the topocluster veto.To further reduce photonuclear backgrounds, the acoplanarity between the muon and the track (three-track system) must satisfy A μ;trkðsÞ ϕ ≡ 1 − jΔϕ μ;trkðsÞ j=π < 0.4ð0.2Þ.The signal has a narrower A μ;trkðsÞ ϕ distribution in μ3T-SR than μ1T-SR, motivating the tighter requirement.
For μ1T-SR, the p T of the muon-track pair must satisfy p μ;trk T > 1 GeV to reject p T -balanced backgrounds, such as γγ → μμ.To further reduce the γγ → μμγ background, the p T of the muon, track, and photon (topocluster) system must fulfill p μ;trk;γðclustÞ T > 1 GeV for events containing a photon (topocluster) within ΔR γðclustÞ;trk ¼ 1 of the track.If there are multiple nearby photons (topoclusters), the highest-p T photon (topocluster) is used.The topoclusters considered here must have p T > 2 GeV and not be track matched; these criteria avoid track-induced topoclusters from, e.g., chargedpion energy deposits.Topoclusters within ΔR clust;trk ¼ 0.1 of a track with p T > 0.7 GeV extrapolated to the calorimeter are considered track matched.Low-multiplicity events in minimum-bias data are used to correct for the bending due to the magnetic field, such that the ΔR clust;trk distribution of topoclusters associated with a track peaks at zero.Tracks with p T < 0.7 GeV are not considered in the track-cluster matching, as they typically do not deposit significant energy in the calorimeter.
For μ3T-SR, the three-track system mass must fulfill m 3trk < 1.7 GeV, assuming each track has the chargedpion mass of 140 MeV.This requirement retains threeprong hadronic τ-lepton decays and suppresses background from exclusive ρ 0 mesons (γA → ρ 0 → ππ) produced simultaneously with γγ → μμ events.In this background process, neither muon is correlated with the ππ system and m ππμ typically exceeds 1.7 GeV for a muon with p T of several GeV.
To constrain the γγ → μμ background, a control region (CR) of dimuon events called 2μ-CR is defined.It requires exactly two muons with invariant mass above 11 GeV to suppress quarkonia [ϒðnSÞ → μμ] backgrounds and no additional tracks separated from the muons by ΔR μ;trk > 0.1.
Events must additionally not have ZDC energies satisfying E ZDC > 1 TeV on each side, mainly to suppress photonuclear backgrounds where ion dissociation typically occurs.This class of events with no forward neutrons detected (0n0n) corresponds to the absence of Coulomb breakup of either nucleus.Such breakup typically proceeds through the giant dipole resonance and induces the emission of one or more neutrons [40].This requirement also fully suppresses lepton-pair production in which the initial photon emission results in the dissociation of one or both nuclei [40].The SRs and 2μ-CR are all statistically independent.Since the extra forward neutron emissions are not simulated, the γγ → ll MC samples are corrected using data-driven probabilities for the 0n0n event topology, which are found to be between 0.4 and 0.7.These are extracted from 2μ-CR without the E ZDC requirement, differentially in dilepton invariant mass and dilepton rapidity.
The dominant sources of background after event selection are radiative dimuon (γγ → μμγ) and photonuclear events with low central-detector activity.
The γγ → μμγ background is estimated with the aid of MC samples.This process enters μ1T-SR when FSR photons substantially modify the dimuon kinematics so as to mimic the signal kinematics and enters μ3T-SR and μe-SR primarily when photons convert to e þ e − in detector material.To improve the modeling of high-p T (p γ T ≳ p μ T ) photon emissions for t-and u-channel γγ → μμ processes, an additional γγ → μμγ MC sample generated using MADGRAPH5_AMC@NLO [76] with the photon flux reweighted to SUPERCHIC is used instead of STARLIGHT þ PYTHIA8 if a leading photon has p γ T > 2 GeV.Comparing the γγ → μμðγÞ simulated events with data in 2μ-CR shows reasonable data-to-MC agreement in differential distributions and normalization to within 5%.The simulated γγ → μμðγÞ event yield in 2μ-CR is 15% lower than data if STARLIGHT photon-flux calculations are used due to known limitations of STARLIGHT [40,77].Before the fit to data, this method estimates 70, 6.5, and 2.8 γγ → μμðγÞ events enter μ1T-SR, μ3T-SR, and μe-SR, respectively.
Diffractive photonuclear backgrounds with low particle activity are estimated using fully data-driven methods.Dedicated CRs are introduced, called μ2T-CR (μ4T-CR), which apply the same selection as μ1T-SR (μ3T-SR), but require an additional track satisfying p T < 0.5 GeV.Furthermore, the E ZDC < 1 TeV requirement is removed on either side to enrich the sample with events from photonuclear processes.To suppress the γγ → ττ signal contamination in μ2T-CR, the two-track system mass must fulfill m 2trk > 1 GeV; if m 2trk < 1 GeV, the acoplanarity of the muon and highest-p T track is required to exceed 0.2.The event yields in CRs are extrapolated to SRs by loosening the veto on topoclusters not matched to the muon or tracks from n unmatch TC ¼ 0 to n unmatch TC ≤ 8, both in CRs and SRs.The μ2T-CR (μ4T-CR) templates for n unmatch TC distributions are normalized to the event yield in μ1T-SR (μ3T-SR) in the region 4 ≤ n unmatch TC ≤ 8.In this region, the signal and dimuon background contributions are found to be negligible, and events exhibit properties that suggest nonexclusive diffractive production, such as a small or no rapidity gap [78].As the additional track in μ2T-CR and μ4T-CR is soft (p T < 0.5 GeV), its possible correlation with topocluster activity is very small.This method estimates that 13 (2.8)photonuclear events enter μ1T-SR (μ3T-SR); photonuclear events are expected to be negligible in μe-SR.
Other sources of background are predicted to be negligible in the SRs.Nondiffractive photonuclear interactions are estimated using the STARLIGHTþDPMJET-III sample and are found to be negligible in all three SRs.The PYTHIA8 simulation of γγ → q q estimates dijet backgrounds contribute less than 0.3 events in both μ1T-SR and μ3T-SR.Similarly, the contribution from resolved γγ interactions, as estimated with PYTHIA8 [79], is found to be negligible.Exclusive ρ 0 -meson production with simultaneous γγ → μμ production in μ3T-SR is studied using a data-driven method.Template distributions for this process are built from events with two muons and two additional chargedparticle tracks.The acoplanarities of both the muon pair and the track pair must be below 0.05.All events in these templates are found to have m 3trk > 1.7 GeV, so this background is expected to be negligible in μ3T-SR.
Systematic uncertainties affecting the measurement arise from the reconstruction of leptons, photons, chargedparticle tracks and topoclusters, the signal and background modeling, and integrated luminosity.
Uncertainties in the muon momentum scale and resolution follow those in Ref. [80].The analysis includes uncertainties in the data-to-MC correction factors applied to simulated samples for the muon trigger and reconstruction efficiencies.Uncertainties in the reconstruction, identification, and energy calibration of electrons and photons are evaluated in accord with Ref. [72].The uncertainty in the inclusive track reconstruction efficiency is dominated by the uncertainty in the amount of ID material [67].This uncertainty is applied in the simulation by randomly removing tracks with a p T -and η-dependent probability corresponding to the material uncertainty.Uncertainties in the topocluster reconstruction efficiency and energy calibration are estimated using γγ → ee events where one of the electrons emits a hard bremsstrahlung photon due to its interaction with detector material [72].
Uncertainties in the photonuclear background evaluation are estimated by repeating the procedure with alternative requirements for CRs.These resemble the μ1T-SR (μ3T-SR) selection except that the track (three-track system) has the same electric charge as the muon candidate.The difference between the photonuclear background contribution evaluated with alternative and nominal CRs defines the uncertainties, affecting both the normalization and differential distributions.Uncertainties in modeling the photon flux are estimated by using the STARLIGHT MC samples without reweighting to SUPERCHIC.This affects the normalization and differential distributions of the signal and γγ → μμ background.Uncertainties in modeling τ-lepton decays are estimated using PYTHIA8 [81] as an alternative MC simulation to TAUOLA.The effect of τ-lepton spin correlations in TAUOLA is implemented using helicity amplitudes from the γ Ã → ττ process.This modeling is therefore cross-checked by comparing signal events simulated using two versions of PYTHIA8: v8.245 uses helicity amplitudes from the γ Ã → ττ process, whereas v8.305 uses the γγ → ττ elementary process.The difference between the two implementations is found to be negligible, and no further systematic uncertainty is assigned.
The uncertainty in the integrated luminosity is 1.9%, obtained with the LUCID-2 detector [82] using methods similar to Ref. [83] for the primary luminosity measurements.
After applying the event selection, a total of 532, 85, and 39 data events are observed, compared with 84 AE 19, 9 AE 3, and 2.8 AE 0.7 expected background events in μ1T-SR, μ3T-SR, and μe-SR, respectively.The background-only hypothesis is rejected with significance exceeding 5σ, establishing the observation of the γγ → ττ process at ATLAS.The signal significance is highest in μ1T-SR, while μe-SR has the largest signal-to-background ratio.The prefit signal-plus-background hypothesis predicts 543 AE 111, 93 AE 20, and 35 AE 8 events in μ1T-SR, μ3T-SR, and μe-SR, respectively, which is compatible with the observed data.The signal strength μ ττ , defined as the ratio of the observed signal yield to the SM expectation assuming the SM value for a τ , is measured using a profile-likelihood fit [84,85]  Approximately 80 nuisance parameters representing the systematic uncertainties are included in the fit.Many systematic uncertainties are correlated between the SRs and 2μ-CR, so their impact on the measurement precision is minimized since they are constrained by 2μ-CR.The dominant prefit contribution is the photon-flux uncertainty, which mainly affects the signal yield (by approximately 20%), with a significantly smaller impact on the signal shape found upon decorrelation from the normalization component.After the fit, the photon-flux uncertainty becomes subdominant and luminosity uncertainty becomes negligible relative to other sources.The leading contributions to the total systematic uncertainty are the estimation of the muon trigger efficiency, τ-lepton decay modeling, and track reconstruction efficiency.
To measure a τ , an alternative fit is performed where a τ is the only free parameter using the p μ T distribution in the three SRs and 2μ-CR; p μ T is chosen because of its high sensitivity to a τ [46].Simulated signal samples with various a τ values are employed.In the nominal sample, a τ is set to its SM value.Signal templates for alternative a τ hypotheses are obtained by reweighting the nominal sample in three dimensions, differentially in ττ invariant mass, ττ rapidity, and rapidity difference between the two τ leptons, according to calculations from Ref. [46].These calculations parametrize the ττγ coupling by where q ν is the photon four-momentum, σ μν ¼ i½γ μ ; γ ν =2 the spin tensor, and the form factors satisfy F 1 ðq 2 → 0Þ ¼ 1 and F 2 ðq 2 → 0Þ ¼ a τ .A similar parametrization was used in previous LEP measurements [27,29,30], which exploits the near-zero virtuality of initial-state photons.A total of 14 templates for different a τ values are created to model the dependence of the p μ T distribution on a τ in the three SRs. Figure 1 shows the p μ T distributions of the four analysis regions for the data and postfit expectation.The fit describes the data well.
The best-fit value of a τ is a τ ¼ −0.041, with the corresponding 68% and 95% confidence level (CL) intervals being ð−0.050; −0.029Þ and ð−0.057; 0.024Þ, respectively.The higher-than-expected observed yields lead to the highly asymmetric 95% CL interval.This arises from the nearly quadratic signal cross section dependence on a τ , caused by the interference of the SM and BSM amplitudes [29,30,46].The expected 95% CL interval is −0.039 < a τ < 0.020.The impact of systematic uncertainties on the final results is small relative to statistical uncertainties.Figure 2 shows the a τ measurement alongside previous results obtained at LEP.The precision of this measurement is similar to the most precise single-experiment measurement by the DELPHI Collaboration.
In summary, τ-lepton-pair production in ultraperipheral heavy-ion collisions, Pb þ Pb → Pbðγγ → ττÞPb, is observed by ATLAS with a significance exceeding 5σ in 1.44 nb −1 of ffiffiffiffiffiffiffi ffi s NN p ¼ 5.02 TeV data at the LHC.The observed event yield is compatible with that expected from the SM prediction within uncertainties.The events are used to set constraints on the τ-lepton anomalous magnetic moment, corresponding to −0.057 < a τ < 0.024 at 95% CL.The measurement precision is limited by statistical uncertainties.This result introduces the use of hadron-collider data to test electromagnetic properties of the τ lepton, and the results are competitive with existing lepton-collider constraints.2. Measurements of a τ from fits to individual signal regions (including the dimuon control region) and from the combined fit.These are compared with existing measurements from the OPAL [29], L3 [30], and DELPHI [27] experiments at LEP.A point denotes the best-fit a τ value for each measurement if available, while thick black (thin magenta) lines show 68% CL (95% CL) intervals.The expected interval from the ATLAS combined fit is also shown.l þ l − production in proton-proton collisions at ffiffi ffi s p ¼ 7 TeV with the ATLAS detector, Phys.Lett. B 749, 242 (2015).
[33] ATLAS Collaboration, Measurement of the exclusive γγ → μ þ μ − process in proton-proton collisions at ffiffi ffi s p ¼ [50] ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the center of the detector and the z axis along the beam pipe.The x axis points from the IP to the center of the LHC ring, and the y axis points upward.Cylindrical coordinates ðr; ϕÞ are used in the transverse plane, ϕ being the azimuthal angle around the z axis.The pseudorapidity is defined in terms of the polar angle θ as η ¼ − ln tanðθ=2Þ.The transverse momentum (energy) is denoted by p T (E T ).Angular distances are measured in units of ΔR ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi  C 72, 1926 (2012).
[75] The momentum of the track system is defined as the vectorial sum of the momentum of each track considered: p syst trk ¼ P i p i trk .
Mattelaer, H.-S. Shao, T. Stelzer, P. Torrielli, and M. Zaro, The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations, J. High Energy Phys. 07 ( 2014

FIG. 1 .
FIG. 1. Muon transverse-momentum distributions in the (top left) μ1T-SR, (top right) μ3T-SR, (bottom left) μe-SR, and (bottom right) 2μ-CR categories.Black markers denote data and stacked histograms indicate the different components contributing to the regions.Postfit distributions are shown with the signal contribution corresponding to the best-fit a τ value (a τ ¼ −0.041).For comparison, signal contributions with alternative a τ values are shown as solid red (a τ ¼ −0.06) or dashed blue (a τ ¼ 0.04) lines.The bottom panel shows the ratio of the data to postfit predictions.Vertical bars denote uncertainties from the finite number of data events.Hatched bands represent AE1σ systematic uncertainties of the prediction with the constraints from the fit applied.
FIG.2.Measurements of a τ from fits to individual signal regions (including the dimuon control region) and from the combined fit.These are compared with existing measurements from the OPAL[29], L3[30], and DELPHI[27] experiments at LEP.A point denotes the best-fit a τ value for each measurement if available, while thick black (thin magenta) lines show 68% CL (95% CL) intervals.The expected interval from the ATLAS combined fit is also shown.