Left-right asymmetry calculation comparisons and projected sensitivity to the weak mixing angle in polarized Bhabha scattering at 10.58 GeV

Consideration is being given to upgrading the SuperKEKB electron-positron collider with the introduction of electron-beam polarization. This would enable a unique precision electroweak physics program that opens new ways to search for physics beyond the Standard Model. The upgrade would enable Belle II to make a number of high precision measurements, one of which is the left-right cross-section asymmetry in the $e^+e^-\rightarrow e^+e^-$ Bhabha scattering process. The expected level of precision in such a measurement will require the theoretical values of the asymmetry to be calculated at least to the next-to-leading order (NLO) level, and the implementation of simulation event generators with a similar level of precision. In this study, we compare the calculations of the ReneSANCe Monte Carlo generator with those of an independent NLO calculation to determine the level of agreement in this process. A 2.3% difference between the calculations is found and attributed to some higher-order effects being accounted for in the ReneSANCe generator. Using the published Belle II efficiency for selecting Bhabha events and assuming a 40 ab$^{-1}$ dataset having 70% polarization, the projected uncertainty on the weak mixing angle, sin$^2\theta_W$ , is calculated using ReneSANCe to be $\pm$0.00032 or better. Combining this with left-right asymmetry measurements from muons and taus under the assumption of lepton universality yields a projected overall uncertainty of $\pm$0.00019 on sin$^2\theta_W$ with SuperKEKB upgraded to have polarized electron beams.