Methods for a measurement of $\tau$ polarization asymmetry in the decay $Z\rightarrow \tau\tau$ at LHC and determination of the effective weak mixing angle

TL;DR

This paper presents a method to measure the tau lepton's polarization asymmetry in Z boson decays at the LHC, enabling precise determination of the effective weak mixing angle with reduced systematic uncertainties.

Contribution

The paper introduces an optimal observable method for tau polarization measurement at the LHC, achieving significantly lower theoretical systematic uncertainties compared to previous experiments.

Findings

Systematic uncertainty on tau polarization is estimated at 1.41e-4.

Method achieves about 50 times smaller uncertainty than LEP results.

Analyzing power is enhanced by considering tau+ and tau- spin correlations.

Abstract

In this paper a general method to measure the longitudinal polarization of $\tau$ lepton in the process $pp \rightarrow Z^{0} \rightarrow \tau\tau$ is described. The method of optimal observable allows to distinguish between the $\tau$ lepton helicity states with maximum possible sensitivity. The optimal observable for the main $\tau$ decay modes ($e/\mu\nu\nu$, $\pi\nu$, $\rho\nu$, $a_{1}\nu$) that can be identified by CMS or ATLAS detectors is described. The analyzing power for $\tau$ polarization can be further gained by taking into account a correlation between longitudinal spin states of $\tau^{+}$ and $\tau^{-}$. The theoretical systematic uncertainty on the $\tau$ polarization measured using the $\tau \rightarrow 3\pi\nu$ decays is estimated to be $(\Delta P_{\tau})_{model} = (1.41 \pm 1.37)\times 10^{-4}$. This value is approximately 50 times smaller than the best uncertainty on $\tau$ polarization measurement given by combination of all LEP results. An approach to propagate the measured $\tau$ polarization averaged over the $Z^{0}$ lineshape and parton density functions to the electroweak parameters is also discussed.