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

The paper discusses the one-loop (NLO) electroweak radiative corrections to the $e^- e^+ \rightarrow f {\bar f} (\gamma)$ process with longitudinally polarized electrons when for a final state fermions electrons are excluded. The focus of this paper is the investigation of the parity-violating polarization asymmetry and forward-backward asymmetry. The calculations are relevant for precision electroweak measurements of the Belle II experiment, which is being installed on the SuperKEKB $e^- e^+$ collider designed for 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, the possibilities for soft photon approximation are discussed. The scale of the obtained relative corrections to the parity-violating and forward-backward asymmetries is significant and their scattering angle dependencies non-trivial.