Snowmass 2021 White Paper on Upgrading SuperKEKB with a Polarized Electron Beam: Discovery Potential and Proposed Implementation

74 pages, 56 figures, contribution to Snowmass 2021Upgrading the SuperKEKB electron-positron collider with polarized electron beams opens a new program of precision physics at a center-of-mass energy of 10.58 GeV. This white paper describes the physics potential of this `Chiral Belle' program. It includes projections for precision measurements of $\sin^2\theta_W$ that can be obtained from independent left-right asymmetry measurements of $e^+e^-$ transitions to pairs of electrons, muons, taus, charm and b-quarks. The $\sin^2\theta_W$ precision obtainable at SuperKEKB will match that of the LEP/SLC world average, but at the centre-of-mass energy of 10.58 GeV. Measurements of the couplings for muons, charm, and $b$-quarks will be substantially improved and the existing $3\sigma$ discrepancy between the SLC $A_{LR}$ and LEP $A_{FB}^b$ measurements will be addressed. Precision measurements of neutral current universality will be more than an order of magnitude more precise than currently available. As the energy scale is well away from the $Z^0$-pole, the precision measurements will have sensitivity to the presence of a parity-violating dark sector gauge boson, $Z_{\rm dark}$. The program also enables the measurement of the anomalous magnetic moment $g-2$ form factor of the $\tau$ to be made at an unprecedented level of precision. A precision of $10^{-5}$ level is accessible with 40~ab$^{-1}$ and with more data it would start to approach the $10^{-6}$ level. This technique would provide the most precise information from the third generation about potential new physics explanations of the muon $g-2$ $4\sigma$ anomaly. Additional $\tau$ and QCD physics programs enabled or enhanced with having polarized electron beams are also discussed in this White Paper. This paper includes a summary of the path forward in R&D and next steps required to implement this upgrade and access its exciting discovery potential