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Measurements in $W^+W^-$ events at LEP2 and in $B$ hadron semileptonic decaysat B factories and LHCb provide intriguing hints of a violation of leptonuniversality in the charged current coupling of tau leptons relative to thosefor electrons and muons. We propose a novel, self-calibrating method to testtau lepton universality in $W$ boson decays at the LHC. We compare directly theratio of the numbers of selected $\ell-\tau$ and $e-\mu$ final states indi-leptonic $tt$ events with that in $Z/\gamma^*\rightarrow\tau^+\tau^-$events. Here $\ell=e$ or $\mu$ and $\tau$ is a candidate semi-hadronic taudecay. This "double-ratio" cancels to first order sensitivity to systematicuncertainties on the reconstruction of $e$, $\mu$, and $\tau$ leptons, thusimproving very significantly the precision to which tau lepton universality canbe tested in $W$ boson decay branching ratios at the LHC. Using particle-levelMonte Carlo events, and a parameterised simulation of detector performance, wedemonstrate the effectiveness of the method and estimate the most significantresidual sources of uncertainty arising from experimental and phenomenologicalsystematics. Our studies indicate that a single experiment precision on the taulepton universality test of around 1.4% is achievable with a data set of 140fb$^{-1}$ at $\sqrt{s}$ = 13 TeV. This would improve significantly upon theprecision of 2.5% on the four-experiment combined LEP2 measurements. If thecentral value of the proposed new measurement were equal to the central valueof the LEP2 measurement this would yield an observation of BSM physics at asignificance level of around 5 $\sigma$.

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