Towards testing $(g-2{)}_{\tau }$ in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$: radiative corrections and projections for Belle II

Abstract

The arguably most promising avenue towards testing physics beyond the Standard Model in the anomalous magnetic moment of the $\tau$ proceeds via suitably constructed asymmetries in $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ in the presence of a polarized electron beam. Such a program, as could be realized at Belle II assuming a polarization upgrade of the SuperKEKB $e^{+}{e}^{-}$ collider, crucially relies on a careful consideration of radiative corrections. In this work, we present the complete one-loop result for the fully polarized $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ process and its implementation in the Monte-Carlo integrator McMule. As an application, we discuss projections relevant for measurements at Belle II, both with and without electron polarization, and outline the necessary steps for a generalization to next-to-next-to-leading order.

Comments: 32 pages, 9 figures, expressions for one-loop diagrams provided as Mathematica notebook; journal version