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A self-calibrating, double-ratio method to test tau lepton universality in W boson decays at the LHC

Measurements in $W^+W^-$ events at LEP2 and in $B$ hadron semileptonic decays at B factories and LHCb provide intriguing hints of a violation of lepton universality in the charged current coupling of tau leptons relative to those for electrons and muons. We propose a novel, self-calibrating method to test tau lepton universality in $W$ boson decays at the LHC. We compare directly the ratio of the numbers of selected $\ell-τ$ and $e-μ$ final states in di-leptonic $tt$ events with that in $Z/γ^*\rightarrowτ^+τ^-$ events. Here $\ell=e$ or $μ$ and $τ$ is a candidate semi-hadronic tau decay. This "double-ratio" cancels to first order sensitivity to systematic uncertainties on the reconstruction of $e$, $μ$, and $τ$ leptons, thus improving very significantly the precision to which tau lepton universality can be tested in $W$ boson decay branching ratios at the LHC. Using particle-level Monte Carlo events, and a parameterised simulation of detector performance, we demonstrate the effectiveness of the method and estimate the most significant residual sources of uncertainty arising from experimental and phenomenological systematics. Our studies indicate that a single experiment precision on the tau lepton universality test of around 1.4% is achievable with a data set of 140 fb$^{-1}$ at $\sqrt{s}$ = 13 TeV. This would improve significantly upon the precision of 2.5% on the four-experiment combined LEP2 measurements. If the central value of the proposed new measurement were equal to the central value of the LEP2 measurement this would yield an observation of BSM physics at a significance level of around 5 $σ$.