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

TL;DR

The paper develops TauSpinner to study NP effects in tau lepton pair production from qqbar annihilation to Z/gamma* with decays, by extending the spin-amplitude formalism to include anomalous dipole form factors and a phase shift between vector and axial-vector couplings, all embedded in an Improved Born Approximation for EW corrections. It introduces a reweighting algorithm that separately handles production and spin weights, enabling NP scenarios to be tested on existing collider samples without regenerating events. Numerical results show that NP can noticeably modify transverse spin correlations and certain decay observables while leaving cross-sections only weakly affected near the Z pole, highlighting the importance of spin information in NP searches. The work delivers a practical, configurable tool for exploring CP-violating and dipole-moment NP in tau production at the LHC and beyond, with options for frame choices and compatibility with EW corrections.

Abstract

The possible anomalous New Physics contributions to dipole and weak dipole moments of the $τ$ lepton bring renewed interest in development and revisiting charge-parity violating signatures in $τ$-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 $\bar q q \to τ^+ τ^-$ production processes, with $τ$ 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 $τ$ 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 $τ$ 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 $τ^\pm \to ρ^\pm ν_τ\to π^\pm π^0 ν_τ$ decays. Information on how to use and configure the TauSpinner program is given in Appendix.

Figures (6)

• Figure 1: Relation between absolute value of phase difference $|\Phi_{v^\prime} - \Phi_{a^\prime}|$ and phase-shift $\Phi$ of transformation (\ref{['eq:Phi_tau_shift']}) for $\tau$ lepton (solid line), and of transformation (\ref{['eq:Phi_q_shift']}) for up quark (dashed line) and down quark (dotted line).
• Figure 2: Distribution of $m_{\tau\tau}$ and $\cos\theta$ of generated events from $q \bar{q} \to \tau\tau$ process in $pp$ collisions at 13 TeV centre-of-mass energy.
• Figure 3: Distribution of $r_{xx}$ (left plot) and $r_{xy}$ (right plot) as a function of invariant mass $m_{\tau\tau}$. Compared are the SM predictions using ${\cal M}^{IBA}$ (black open circles) and ${\cal M}^{BA}$ with effective couplings (blue triangles).
• Figure 5: Distribution of $r_{tz}$ as a function of invariant mass $m_{\tau\tau}$. Compared are the SM predictions using ${\cal M}^{IBA}$ (black open circles) and NP ones (red and blue triangles): $\Phi = \pm 0.1$ (left plot) and $X=0.1$ or $Y=0.1$ (right plot).
• Figure 6: Distribution of spin correlations sensitive kinematical observables. Compared are the SM predictions ${\cal M}^{IBA}$ (black open circles) and NP ones (red and blue triangles) with $\Phi = \pm 0.1$. Both $\tau$ leptons decay via $\tau^\pm \to \rho^{\pm} \nu_\tau \to \pi^\pm \pi^0 \nu_\tau$.