TauSpinner algorithms for including spin and New Physics effects in $\bar q q \rightarrow Z/\gamma^* \to \tau \tau$ process

TL;DR

This paper presents TauSpinner algorithms that incorporate spin effects and New Physics contributions, such as anomalous dipole moments, into tau pair production processes at the LHC, enabling detailed analysis of CP violation signatures.

Contribution

The paper introduces extensions to the TauSpinner program for including anomalous tau dipole moments and New Physics effects in tau pair production, with detailed algorithms and implementation guidance.

Findings

Implementation of spin and New Physics effects in TauSpinner.

Distribution analysis of spin correlations with New Physics contributions.

Numerical impact on tau decay signatures and CP violation observables.

Abstract

The possible anomalous New Physics contributions to dipole and weak dipole moments of the $\tau$ lepton bring renewed interest in development and revisiting charge-parity violating signatures in $\tau$-pair production in $Z$-boson decay at energies of the LHC. In this paper, we discuss effects of anomalous contributions to polarisation and spin correlations in the $\bar q q \to \tau^+ \tau^-$ production processes, with $\tau$ decays included. Because of the complex nature of the resulting distributions, Monte Carlo techniques are useful, in particular of event reweighing with studied New Physics phenomena. Extensions of the Standard Model spin amplitudes, within Improved Born Approximation used for matrix element, are implemented in the TauSpinner program. This is mainly with $\tau$ dipole and weak dipole moments in mind, but is applicable to arbitrary New Physics interactions, provided they can be encapsulated into the Standard Model $2 \to 2$ structure of matrix element extensions. Implementation allows one also to introduce arbitrary phase-shift between vector and axial-vector couplings of $Z$ boson to $\tau$ leptons, which would have impact on observed transverse spin correlations. Basic formulas and algorithm principles are presented, together with distributions for spin correlation matrix. Numerical examples of impact on experimental signatures are shown in case of $\tau^\pm \to \rho^\pm \nu_\tau \to \pi^\pm \pi^0 \nu_\tau$ decays. Information on how to use and configure the TauSpinner program is given in Appendix.