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 Monte Carlo KKMC program 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.

Comments: 16 pages, 2 figures; v2: comment on radiative corrections is added in the end of section 2, a few references are updated, corresponds to the journal version