TauSpinner algorithms for including spin and New Physics effects in $γγ\rightarrow ττ$ process

TL;DR

This work tackles constraining tau dipole moments and CP-violating signatures in $\gamma\gamma \rightarrow \tau^-\tau^+$ production by deriving a dipole-form-factor extension of the amplitude and embedding it in TauSpinner. It provides the spin-density matrix $R_{ij}$ expanded to fourth order in $A(0)$ and $B(0)$, along with a cross-section formula and frame conventions necessary for reweighting. Numerical studies show that while the total cross-section shifts modestly under plausible NP, spin-correlation observables offer enhanced sensitivity, especially in certain $m_{\tau\tau}$ and angular regions and across multiple tau decay channels. The approach enables flexible MC reweighting for $pp$ and PbPb collisions and can be extended to other NP scenarios that can be expressed through similar form-factors, facilitating experimental constraints on tau dipole moments.

Abstract

The possible anomalous New Physics contributions to electric and magnetic dipole moments of the $τ$ lepton has brought renewed interest in development of new charge-parity violating signatures in the $τ$-pair production at Belle II energies, and also at higher energies of the LHC and the FCC. In this paper, we discuss effects of anomalous contributions to cross-section and spin correlations in the $γγ\to τ^-τ^+$ production processes, with $τ$ decays included. Such processes have been observed in the $pp$ and PbPb collisions at CERN LHC experiments. Because of complex nature of the resulting distributions, Monte Carlo techniques are useful, in particular of event reweighting with studied New Physics phenomena. For the $γγ$ processes, extensions of the Standard Model amplitudes are implemented in the TauSpinner program. This is mainly with electric and magnetic dipole moments in mind, but algorithm can be easily extended to other New Physics interactions, provided they can be encapsulated into similar form-factors in the Standard Model structure of matrix elements. Basic formulas and algorithm principles are presented, numerical examples are provided as illustration. Information on how to use the program is given in Appendix of the paper.

Figures (12)

• Figure 1: Distribution of invariant mass of the $\tau\tau$ system and $\cos\theta$ of the scattering angle for the analyzed sample of $\gamma \gamma \to \tau \tau$ events.
• Figure 2: Spin averaged element $R_{tt}$ as a function of $m_{\tau \tau}$: integrated over the full phase space (top plots), restricted to $\theta = \pi/3 \times [0.8-1.2]$ (middle plots) and restricted to $\theta = 2\pi/3 \times [0.8-1.2]$ (bottom plots). Compared SM and SM+NP with six models: $A=0.002$, $0.005$, $0.02$ and $B=0$ (left column) and $A=0.0$, $B=0.002$, $0.005$, $0.02$ (right column). Curves marked with $\star$ (shown in green) always denote the largest anomalous moment: $A=0.02$ (left column), or $B=0.02$ (right column).
• Figure 3: Spin-correlation matrix elements $r_{xx}$, $r_{yy}$, $r_{zz}$ and $r_{xy}$ as functions of $m_{\tau \tau}$. Notation is the same as in Fig. \ref{['Fig:Rtt']}. Except $r_{xy}$, these are elements with sizable SM contributions.
• Figure 4: Spin-correlation matrix elements $r_{xx}$, $r_{yy}$ and $r_{zz}$ as functions of $\cos\theta$. Notation is the same as in Fig. \ref{['Fig:Rtt']}. These elements have sizable contributions from the SM.
• Figure 5: Spin-correlation matrix elements $r_{xy}$, $r_{zx}$ and $r_{zy}$ as functions of $\cos\theta$. Notation is the same as in Fig. \ref{['Fig:Rtt']}. Elements $r_{xy}$, $r_{zx}$ have negligible SM contributions, but non-negligible NP ones, while $r_{zy}$ is sizable already in the SM and attain additional contribution from NP.