Spin correlations in $\tau$-lepton pair production due to anomalous magnetic and electric dipole moments

Abstract

We present a simple algorithm for the calculation of event weights embedding the effects of anomalous electric and magnetic dipole moments in simulation of $e^-e^+\to \tau^-\tau^+ (n\gamma)$ events, and the subsequent decay of the $\tau$ leptons produced. The impact of these weights on the spin-correlation matrix and the total cross-section is taken into account. The algorithm is prepared to work in-situ the {\tt KKMC} Monte Carlo, without the need for introducing any external change to the generator libraries. As an example, $e^-e^+ \to \tau^-\tau^+ (n\gamma), \; \tau^- \to \rho^- \nu_\tau \to \pi^- \pi^0 \nu_\tau, \ \tau^+ \to \rho^+ \bar{\nu}_\tau \to \pi^+ \pi^0 \bar{\nu}_\tau$ events were simulated at a center-of-mass energy of 10.58 GeV. The distributions of the acoplanarity angle between the planes spanned by the $\pi^- \pi^0$ and the $\pi^+ \pi^0$ momenta of respectively $\rho^-$ and $\rho^+$ decays and in the rest-frame of the entirely visible $\rho^-\rho^+$ system, are presented for different values of the coupling constants incorporating anomalous electric and magnetic dipole moments in the $\tau^- \tau^+ \gamma$ vertex.