Measuring tau g-2 using ATLAS Pb+Pb collisions

Relativistic heavy-ion beams at the LHC are accompanied by a large flux of equivalent photons, leading to photon-induced processes. Measurements of photon-induced production of tau lepton pairs can be used to constrain the tau lepton's anomalous magnetic dipole moment (g-2). A recent ATLAS measurement using muonic decays of tau leptons in association with electrons and tracks is presented. This provides one of the most stringent limits on g-2 of the tau lepton to date.


Introduction
Precise measurements of anomalous magnetic moments of leptons  ℓ = 1 2 ( ℓ − 2) (where  ℓ is the -factor) provide a powerful tool to test the validity of the Standard Model (SM) and investigate beyond the SM (BSM) scenarios, such as lepton compositeness [1] or supersymmetry [2].
In the case of electrons and muons, their anomalous magnetic moments are among the most precisely measured observables in nature [3][4][5][6] and are powerful probes for BSM phenomena.The -lepton can be even more sensitive to some BSM processes, however the measurement of -lepton renders experimental challenges, due to its short lifetime.The most stringent limits on   (−0.052 <   < 0.013) were set by the DELPHI experiment [7] at LEP and the central value was reported to be compatible with the prediction, however with an error one order of magnitude larger than the predicted value ( exp  = −0.018(17) compared to  pred ,SM = 0.00117721( 5)) [8].In this study,   is probed using the Pb+Pb→Pb( → )Pb process, illustrated in Figure 1, in which the presence of  vertices gives sensitivity to electromagnetic couplings [9][10][11].This reaction arises in so-called ultra-peripheral heavy-ion collisions (UPC) in the ATLAS detector [12], when the distance between two incoming nuclei is larger than twice the ion radius.The nuclei are surrounded by strong electromagnetic fields which can be viewed as a coherent flux of photons [13,14].Thus, UPC can lead to photon-photon interactions.Utilizing UPC has several advantages compared to photon-photon interactions in proton-proton collisions, such as a substantial crosssection enhancement, which scales as  4 (with  representing the atomic number, which is 82 for Pb).Furthermore, the low level of pile-up provides a clean environment enabling low transverse momentum ( T ) thresholds in the trigger and offline reconstruction [15].
2 (g e 2) is among the most precisely measured observables in nature [1,2].The muon counterpart a µ is measured to 1 part in 10 7 [3] and reports a longstanding 3 4 deviation from the SM prediction, which may be a harbinger of new physics.

Experimental method
The analysis utilizes 1.44 nb −1 of √  NN = 5.02 TeV Pb+Pb data recorded by ATLAS.The signal samples were generated using the Starlight 2.0 Monte Carlo (MC) generator [16].For the decay of -leptons, the simulation was interfaced with Tauola [17], and for modeling of the final-state radiation, Pythia 8.245 and Photos++ 3.61 [18,19] were employed.The photon-flux distribution was re-weighted to Superchic 3.05 [20].
Signal candidates must contain exactly one muon, targeting a muonic decay of one of the −leptons.The decays of the other −lepton categorize events into three distinct signal regions
After applying the event selection criteria, the two primary sources of background are photoninduced di-muon events and photonuclear events.To estimate the former, Starlight 2.0 and Pythia 8.245 MC generators (or MadGraph5_aMC@NLO [21] in the case of radiative di-muon background) are employed, with the photon-flux distribution re-weighted to Superchic 3.05.For the estimation of the latter, a data-driven approach is adopted.This method involves constructing supplementary CRs, which are similar to the SRs but with modifications such as requiring an additional low- T track and the removal of the ZDC requirement.These CRs are used to estimate the contribution of photonuclear events to the background.
The analysis strategy hinges on two key dependencies: the cross-section dependence of  →  and the shape dependence of muon transverse momentum (  T ) on the parameter   .To extract the value of   , a fit is carried out to the   T distribution in both the SRs and 2-CR.

Observation of the 𝜸𝜸 → 𝝉𝝉 in Pb+Pb
The  →  process in Pb+Pb collisions is observed with a significance much exceeding 5 standard deviations.Notably, the highest significance is achieved in the 1T-SR, while the -SR exhibits the highest signal-to-background ratio among the signal regions.
The signal strength (   ) is defined as a ratio of the observed signal yield to the SM prediction, assuming the SM value of   .It is determined with a profile-likelihood fit with    being the only parameter of interest.The measured value is    = 1.03 +0.06 −0.05 (tot) = 1.03 +0.05 −0.05 (stat.)+0.03 −0.03 (syst.), which is consistent with unity.
To measure   , a profile-likelihood fit is conducted in three SRs and 2-CR in which   is the only free parameter.The choice of using the   T distribution is motivated by its high sensitivity to   .The analysis makes use of templates with various   values and in the nominal signal sample,   is set to the SM value.Samples representing different   hypotheses are generated by reweighting the nominal sample in three dimensions:  invariant mass, rapidity, and the difference in pseudorapidity between the two -leptons [10].This parametrization aligns with the one employed in prior LEP measurements [7,22,23].In total, 14 samples encompassing a range of   values are utilized in the analysis.
Pre-fit and post-fit distributions of   T in the 1T-SR are shown in Figure 2. The fit to the data is seen to provide a good description, and it is evident that the uncertainties decrease noticeably in the post-fit distribution.It is worth noting that the difference between the SM and BSM values of   depend on   T .The best-fit   value is determined to be   = −0.041,with corresponding 68% and 95% confidence levels (CL) of (−0.050, −0.029) and (−0.057, 0.024), respectively.The highly asymmetric 95% CL interval is a result of the observed yields being higher than expected, and the almost quadratic dependence of the cross-section on   , which arises due to the interference between SM and BSM amplitudes [9,10].Figure 3 presents a comparison of the   measurements with the previous results obtained by LEP [7,22,23].The expected 95% CL limits from the combined

PoS(EPS-HEP2023)319
Measuring tau g-2 using ATLAS Pb+Pb collisions Weronika Stanek-Maslouska fit are −0.039<   < 0.020.The precision of the measurement is competitive with previous studies at electron colliders, however, the statistical uncertainties are significant in comparison to the systematic uncertainties.and from the combined fit, compared with existing measurements performed at LEP [7,22,23].A point denotes the best-fit   value for each measurement if available, while thick black (thin magenta) lines show 68% (95%) confidence level intervals.Figure from [15].

Conclusions
The process of -lepton production in ultra-peripheral Pb+Pb collisions in the ATLAS detector has been observed with a significance much exceeding 5 standard deviations, using 1.44 nb −1 of data at a center-of-mass energy of √  NN = 5.02 TeV.This result indicates the potential of UPCs as a tool for investigating rare SM processes and exploring BSM phenomena.It also introduces the possibility of conducting studies at hadron colliders to probe the electromagnetic properties of -leptons.The constraints obtained on   are competitive with earlier results from electron colliders.