Observation of the $\gamma\gamma\to\tau\tau$ process in Pb+Pb collisions and constraints on the $\tau$-lepton anomalous magnetic moment with the ATLAS detector

This Letter reports the observation of $\tau$-lepton pair production in ultraperipheral lead-lead collisions, $\text{Pb+Pb} \to \text{Pb}(\gamma\gamma \to \tau\tau)\text{Pb}$, and constraints on the $\tau$-lepton anomalous magnetic moment, $a_\tau$. The dataset corresponds to an integrated luminosity of 1.44 nb$^{-1}$ of LHC Pb+Pb collisions at $\sqrt{s_{_\text{NN}}} = 5.02$ TeV recorded by the ATLAS experiment in 2018. Selected events contain one muon from a $\tau$-lepton decay, an electron or charged-particle track(s) from the other $\tau$-lepton decay, little additional central-detector activity, and no forward neutrons. The $\gamma\gamma \to \tau\tau$ process is observed in Pb+Pb collisions with a significance exceeding 5 standard deviations, and a signal strength of $\mu_{\tau\tau} = 1.03^{+0.06}_{-0.05}$ assuming the Standard Model value for $a_\tau$. To measure $a_\tau$, a template fit to the muon transverse-momentum distribution from $\tau$-lepton candidates is performed, using a dimuon ($\gamma\gamma \to \mu\mu$) control sample to constrain systematic uncertainties. The observed 95% confidence-level interval for $a_\tau$ is $-0.057

This Letter presents the observation of the Pb+Pb → Pb( → )Pb process and measurement of   using 1.44 nb −1 of √  NN = 5.02 TeV Pb+Pb data recorded by ATLAS in 2018.The EM fields accompanying the ions coherently create photons that interact to produce -lepton pairs.The cross-section is enhanced by  4 relative to   collisions, where  is the atomic number ( = 82 for lead).The ions can remain intact, enabling selection of low-multiplicity events with one muon originating from one of the -leptons, while the other -lepton decay is reconstructed as either an electron or one or three charged-particle tracks with low transverse momentum.
The ATLAS experiment [47][48][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 (ZDC) [51] are located at  = ±140 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  T > 4 GeV, and at most 50 GeV (3 GeV) of transverse energy deposited in the whole (forward 3.2 < || < 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  →  signal events were produced at leading order in QED using the Starlight 2.0 [57] Monte Carlo (MC) generator, interfaced with Tauola [58,59] for -lepton decays.Final-state radiation (FSR) from the -leptons and charged decay products of -leptons was simulated using Pythia 8.245 [60] and Photos++ 3.61 [61], respectively.One of the dominant background sources is the  →  process, and its contribution is estimated with the aid of MC samples generated using Starlight; Pythia 8 was used to model EM FSR from the muons.The photon-flux distribution in simulated  →  and  →  events was reweighted to that of Superchic 3.05 [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,  →  q, were generated using Pythia 8. Nondiffractive photonuclear events (A → ) 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 -leptons while reducing backgrounds from  →  and  →  q.Three signal regions (SR) then categorize events by the decay signature of the other -lepton.The -SR category additionally requires one electron, and no additional tracks separated from the muon (electron) by Δ  (),trk > 0.1, which targets fully leptonic decays of both -leptons.The different-flavor () requirement suppresses same-flavor backgrounds dominated by  → /.The 1T-SR (3T-SR) category requires exactly one track (three tracks) separated from the muon by Δ ,trk > 0.1, which targets -lepton decays to one or three charged hadrons.The one-track requirement also captures leptonic -lepton decays that fail electron or muon reconstruction.The electric charges of the muon, electron, and tracks must sum to zero.
For both 1T-SR and 3T-SR, events must contain no additional muons satisfying looser criteria and no electrons to reject  → / backgrounds.The looser requirements on muons comprise matched tracks in the ID and MS satisfying  T > 2 GeV and || < 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 Δ clust,  > 0.3 (Δ clust,trk(s) > 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  ,trk(s)  ≡ 1 − |Δ ,trk(s) |/ < 0.4 (0.2).The signal has a narrower  ,trk(s)  distribution in 3T-SR than 1T-SR, motivating the tighter requirement.
For 1T-SR, the  T of the muon-track pair must satisfy  ,trk T > 1 GeV to reject  T -balanced backgrounds, such as  → .To further reduce the  →  background, the  T of the muon, track, and photon (topocluster) system must fulfill  ,trk, (clust) T > 1 GeV for events containing a photon (topocluster) within Δ  (clust),trk = 1 of the track.If there are multiple nearby photons (topoclusters), the highest- T photon (topocluster) is used.The topoclusters considered here must have  T > 2 GeV and not be track-matched; these criteria avoid track-induced topoclusters from, e.g., charged-pion energy deposits.Topoclusters within Δ clust,trk = 0.1 of a track with  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 Δ clust,trk distribution of topoclusters associated with a track peaks at zero.Tracks with  T < 0.7 GeV are not considered in the track-cluster matching as they typically do not deposit significant energy in the calorimeter.
For 3T-SR, the three-track system mass must fulfill  3trk < 1.7 GeV, assuming each track has the charged-pion mass of 140 MeV.This requirement retains three-prong hadronic -lepton decays and suppresses background from exclusive  0 mesons (A →  0 → ) produced simultaneously with  →  events.In this background process, neither muon is correlated with the  system and     typically exceeds 1.7 GeV for a muon with  T of several GeV.
To constrain the  →  background, a control region (CR) of dimuon events called 2-CR is defined.It requires exactly two muons with invariant mass above 11 GeV to suppress quarkonia (Υ() → ) backgrounds and no additional tracks separated from the muons by Δ ,trk > 0.1.
Events must additionally not have ZDC energies satisfying  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 (00) 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 2-CR are all statistically independent.Since the extra forward neutron emissions are not simulated, the  → ℓℓ MC samples are corrected using data-driven probabilities for the 00 event topology, which are found to be between 0.4 and 0.7.These are extracted from 2-CR without the  ZDC requirement, differentially in dilepton invariant mass and dilepton rapidity.
The dominant sources of background after event selection are radiative dimuon ( → ) and photonuclear events with low central-detector activity.
The  →  background is estimated with the aid of MC samples.This process enters 1T-SR when FSR photons substantially modify the dimuon kinematics so as to mimic the signal kinematics, and enters 3T-SR and -SR primarily when photons convert to  +  − in detector material.To improve the modeling of high- T (  T ≳   T ) photon emissions for -and -channel  →  processes, an additional  →  MC sample generated using MadGraph5_aMC@NLO [76] with the photon flux reweighted to Superchic is used instead of Starlight+Pythia 8 if a leading photon has   T > 2 GeV.Comparing the  → () simulated events with data in 2-CR shows reasonable data-to-MC agreement in differential distributions, and normalization to within 5%.The simulated  → () event yield in 2-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  → () events enter 1T-SR, 3T-SR, and -SR, respectively.
Diffractive photonuclear backgrounds with low particle activity are estimated using fully data-driven methods.Dedicated CRs are introduced, called 2T-CR (4T-CR), which apply the same selection as 1T-SR (3T-SR), but require an additional track satisfying  T < 0.5 GeV.Furthermore, the  ZDC < 1 TeV requirement is removed on either side to enrich the sample with events from photonuclear processes.To suppress the  →  signal contamination in 2T-CR, the two-track system mass must fulfill  2trk > 1 GeV; if  2trk < 1 GeV, the acoplanarity of the muon and highest- 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  unmatch TC = 0 to  unmatch TC ≤ 8, both in CRs and SRs.The 2T-CR (4T-CR) templates for  unmatch TC distributions are normalized to the event yield in 1T-SR (3T-SR) in the region 4 ≤  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 2T-CR and 4T-CR is soft ( T < 0.5 GeV), its possible correlation with topocluster activity is very small.This method estimates that 13 (2.8)photonuclear events enter 1T-SR (3T-SR); photonuclear events are expected to be negligible in -SR.
Other sources of background are predicted to be negligible in the SRs.Nondiffractive photonuclear interactions are estimated using the Starlight+Dpmjet-III sample and are found to be negligible in all three SRs.The Pythia 8 simulation of  →  q estimates dĳet backgrounds contribute less than 0.3 events in both 1T-SR and 3T-SR.Similarly, the contribution from resolved  interactions, as estimated with Pythia 8 [79], is found to be negligible.Exclusive  0 -meson production with simultaneous  →  production in 3T-SR is studied using a data-driven method.Template distributions for this process are built from events with two muons and two additional charged-particle 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  3trk > 1.7 GeV, so this background is expected to be negligible in 3T-SR.
Systematic uncertainties affecting the measurement arise from the reconstruction of leptons, photons, charged-particle 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  T -and -dependent probability corresponding to the material uncertainty.Uncertainties in the topocluster reconstruction efficiency and energy calibration are estimated using  →  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 1T-SR (3T-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  →  background.Uncertainties in modeling -lepton decays are estimated using Pythia 8 [81] as an alternative MC simulation to Tauola.The effect of -lepton spin correlations in Tauola is implemented using helicity amplitudes from the  * →  process.This modeling is therefore cross-checked by comparing signal events simulated using two versions of Pythia 8: v8.245 uses helicity amplitudes from the  * →  process, whereas v8.305 uses the  →  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 ± 19, 9 ± 3, and 2.8 ± 0.7 expected background events in 1T-SR, 3T-SR, and -SR, respectively.The background-only hypothesis is rejected with significance exceeding 5, establishing the observation of the  →  process at ATLAS.The signal significance is highest in 1T-SR, while -SR has the largest signal-to-background ratio.The pre-fit signal-plus-background hypothesis predicts 543 ± 111, 93 ± 20, and 35 ± 8 events in 1T-SR, 3T-SR, and -SR, respectively, which is compatible with the observed data.The signal strength    , defined as the ratio of the observed signal yield to the SM expectation assuming the SM value for   , 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 2-CR, so their impact on the measurement precision is minimized since they are constrained by 2-CR.The dominant pre-fit 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, -lepton decay modeling, and track reconstruction efficiency.
To measure   , an alternative fit is performed where   is the only free parameter using the   T distribution in the three SRs and 2-CR;   T is chosen because of its high sensitivity to   [46].Simulated signal samples with various   values are employed.In the nominal sample,   is set to its SM value.Signal templates for alternative   hypotheses are obtained by reweighting the nominal sample in three dimensions, differentially in  invariant mass,  rapidity, and rapidity difference between the two -leptons, according to calculations from Ref. [46].These calculations parameterize the  coupling by  1 ( 2 )  +  2 ( 2 )  2      , where   is the photon four-momentum,   = i[  ,   ]/2 the spin tensor, and the form factors satisfy  1 ( 2 → 0) = 1 and  2 ( 2 → 0) =   .A similar parameterization 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   values are created to model the dependence of the   T distribution on   in the three SRs.
Figure 1 shows the   T distributions of the four analysis regions for the data and post-fit expectation.The fit describes the data well.
The best-fit value of   is   = −0.041,with the corresponding 68% CL and 95% CL intervals being (−0.050, −0.029) and (−0.057, 0.024), 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   , caused by the interference of the SM and BSM amplitudes [29,30,46].The expected 95% CL interval is −0.039 <   < 0.020.The impact of systematic uncertainties on the final results is small relative to statistical uncertainties.Figure 2 shows the   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. Figure 2: Measurements of   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   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.
In summary, -lepton pair production in ultraperipheral heavy-ion collisions, Pb+Pb → Pb( → )Pb, is observed by ATLAS with a significance exceeding 5 in 1.44 nb −1 of √  NN = 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 -lepton anomalous magnetic moment, corresponding to −0.057 <   < 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 -lepton, and the results are competitive with existing lepton-collider constraints.The crucial computing support from all WLCG partners is acknowledged gratefully, in particular from CERN, the ATLAS Tier-1 facilities at TRIUMF (Canada), NDGF (Denmark, Norway, Sweden), CC-IN2P3 (France), KIT/GridKA (Germany), INFN-CNAF (Italy), NL-T1 (Netherlands), PIC (Spain), ASGC (Taiwan), RAL (UK) and BNL (USA), the Tier-2 facilities worldwide and large non-WLCG resource providers.Major contributors of computing resources are listed in Ref. [86].
[32] ATLAS Collaboration, Measurement of exclusive  → ℓ + ℓ − production in proton-proton collisions at [75] The momentum of the track system is defined as the vectorial sum of the momentum of each track considered:  [78] Rapidity gaps are defined as regions in rapidity with few or no topoclusters or tracks.

Figure 1 :
Figure 1: Muon transverse momentum distributions in the (top-left) 1T-SR, (top-right) 3T-SR, (bottom-left) e-SR, and (bottom-right) 2-CR categories.Black markers denote data and stacked histograms indicate the different components contributing to the regions.Post-fit distributions are shown with the signal contribution corresponding to the best-fit   value (  = −0.041).For comparison, signal contributions with alternative   values are shown as solid red (  = −0.06)or dashed blue (  = 0.04) lines.The bottom panel shows the ratio of the data to post-fit predictions.Vertical bars denote uncertainties from the finite number of data events.Hatched bands represent ±1 systematic uncertainties of the prediction with the constraints from the fit applied.