Electroweak Observables in Neutrino-Electron Scattering from a Muon Storage Ring

We investigate the sensitivity of a companion neutrino detector situated in the plane of a high-energy, high-intensity muon storage ring to elastic $\nu_{\mu}$ and $\nu_e$ scattering on electrons (E$\nu$ES). Assuming a muon collider with center-of-mass energies of up to 10~TeV, we report sensitivity to the weak couplings $g_V$ and $g_A$ up to around 0.05% relative error, and sensitivity to the weak mixing angle in the momentum transfer $Q \in [10^{-2}, 2]$~GeV range up to around 0.03% relative error. E$\nu$ES measurements with high-energy muon storage rings allow one to directly interrogate the momentum-transfer regime associated with the NuTeV anomaly. This level of precision allows unique sensitivity to the momentum-dependence of $\sin^2\theta_W$. We estimate that with the neutrinos from a $E_\mu = 1.5$~TeV (or higher) muon collider, the hypothesis that $\sin^2\theta_W$ does not ``run'' can be safely ruled out.