Electroweak Physics with Polarized Electron Beams in a SuperKEKB Upgrade

Consideration is being given to upgrading the SuperKEKB e$^+$e$^-$ collider with polarized electron beams, which would open a new program of precision electroweak physics at a centre-of-mass energy of 10.58GeV, the mass of the $\Upsilon(4S)$. These measurements include $\sin^2\theta_W$ obtained via left-right asymmetry measurements of e$^+$e$^-$ transitions to pairs of electrons, muons, taus, charm and b-quarks. The precision obtainable at SuperKEKB will match that of the LEP/SLC world average and will thereby probe the neutral current couplings with unprecedented precision at a new energy scale sensitive to the running of the couplings. At SuperKEKB the measurements of the individual neutral current vector coupling constants to b-quarks and c-quarks and muons in particular will be substantially more precise than current world averages and the current 3$\sigma$ discrepancy between the SLC A$_{LR}$ measurements and LEP A$_{FB}^b$ measurements of $\sin^2\theta_W^{eff}$ will be addressed. This paper will include a discussion of the necessary upgrades to SuperKEKB. This program opens an exciting new window in searches for physics beyond the Standard Model.