NLO radiative corrections for Forward-Backward and Left-Right Asymmetries at a B-Factory

TL;DR

This paper calculates electroweak radiative corrections to parity-violating and forward-backward asymmetries in electron-positron collisions at 10.58 GeV, providing essential theoretical input for precision measurements at Belle II.

Contribution

First comprehensive calculation of one-loop electroweak corrections to asymmetries at B-factory energies, including bremsstrahlung effects and validation against Monte Carlo simulations.

Findings

Significant relative corrections to asymmetries were found.

Non-trivial scattering angle dependence of asymmetries.

Validated calculations with independent Monte Carlo results.

Abstract

This paper presents the first calculations of the parity-violating polarization asymmetry and forward-backward asymmetry of the $e^- e^+ \rightarrow \mu^+ \mu^- (\gamma)$ process at a center-of-mass energy of 10.58 GeV with up to one-loop electroweak radiative corrections. The calculations are relevant for future precision electroweak measurements at the Belle~II experiment, which is now collecting data at the SuperKEKB $e^- e^+$ collider with a center-of-mass energy at the mass of the $\Upsilon(4S)$ resonance. In this paper we take under full control the bremsstrahlung process at the conditions of Belle II/SuperKEKB, and the possibilities for a soft photon approach are discussed. The scale of the obtained relative corrections to the parity-violating and forward-backward asymmetries is significant and the scattering angle dependencies of the asymmetries is non-trivial. As an additional validation cross-check using an independent formulation, the calculated asymmetries are compared to results from the KK Monte Carlo generator.