LEP-era universality discrepancy unravelled

The family of charged leptons is composed of the electron, muon (μ) and tau lepton (τ). According to the Standard Model (SM), these particles only differ in their mass: the muon is heavier than the electron and the tau is heavier than the muon. A remarkable feature of the SM is that each flavour is equally likely to interact with a W boson. This is known as lepton flavour universality.

In a new ATLAS measurement reported this week at the LHCP conference, a novel technique using events with top-quark pairs has been exploited to test the ratio of the probabilities for tau leptons and muons to be produced in W boson decays, R(τ/μ). In the SM, R(τ/μ) is expected to be unity, but a longstanding tension with this prediction has existed since the LEP era in the 1990s, where, from a combination of the four experiments, R(τ/μ) was measured to be 1.070 ± 0.026, deviating from the SM expectation by 2.7σ. This strongly motivated the need for new measurements with higher precision. If the LEP result were confirmed it would correspond to an unambiguous discovery of beyond the SM physics.

Tag and probe

To conclusively prove either that the LEP discrepancy is real or that it was just a statistical fluctuation, a precision of at least 1–2% is required — something previously not thought possible at a hadron collider like the LHC, where inclusive W bosons, albeit produced abundantly, suffer from large backgrounds and kinematic biases due to the online selection in the trigger. The key to achieving this is to obtain a sample of muons and tau leptons from W boson decays that is as insensitive as possible to the details of the trigger and object reconstruction used to select them. ATLAS has achieved this by exploiting both the LHC’s large sample of over 100 million top-quark pairs produced in the latest run, and the fact that top quarks decay almost exclusively to a W boson and a b quark. In a tag-and-probe approach, one W boson is used to select the events and the other is used, independently of the first, to measure the fractions of decays to tau-leptons and muons.

The analysis focuses on tau-lepton decays to a muon, rather than hadronic tau decays which are more complicated to reconstruct, thus reducing the systematic uncertainties associated with the object reconstruction. The lifetime of the tau lepton and its lower momentum decay products are exploited by the precise muon reconstruction available from the ATLAS detector to separate muons from tau-lepton decays and muons produced directly by a W decay (so-called prompt muons). Specifically, the absolute distance of closest approach of muon tracks in the plane perpendicular to the beam line, |d₀^μ| (figure 1), and the transverse momentum, p_T^μ, of the muons, are used to isolate these contributions. These variables, in particular |d₀^μ|, are calibrated using a pure sample of prompt muons from Z→μμ data.

The extraction of R(τ/μ) is performed using a fit to |d₀^μ| and p_T^μ where the cancellation of several systematic uncertainties is observed as they are correlated between the prompt μ and τ→μ contributions. This includes, for example, uncertainties related to jet reconstruction, flavour tagging and trigger efficiencies. As a result, the measurement obtains very high precision, surpassing that of the previous LEP measurement.

The measured value is R(τ/μ) = 0.992 ± 0.013 [ ± 0.007 (stat) ± 0.011 (syst) ], forming the most precise measurement of this ratio, with an uncertainty half the size of that from the combination of LEP results (figure 2). It is in agreement with the Standard Model expectation and suggests that the previous LEP discrepancy may be due to a fluctuation.

Though surviving this latest test, the principle of lepton flavour universality will not quite be out of the woods until the anomalies in B-meson decays recorded by the LHCb experiment (CERN Courier May/June 2020 p10) have also been definitively probed.