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

Abstract

We investigate the sensitivity of a companion neutrino detector situated in the plane of a high-energy, high-intensity muon storage ring to elastic $\hat{I}{½}_{\hat{I}}¼$ and $\hat{I}{½}_e$ scattering on electrons (E$\hat{I}½$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$\hat{I}½$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 ${\sin }^2\hat{I}{¸}_W$. We estimate that with the neutrinos from a $E_{\hat{I}}¼=1.5$~TeV (or higher) muon collider, the hypothesis that ${\sin }^2\hat{I}{¸}_W$ does not ``run'' can be safely ruled out.

Accepted for publication in JHEP. Corrected charge radius sensitivity estimate, revised detector distance benchmark, and included discussions based on calculational comparisons with the NLO electron scattering cross section. 22 pages, 11 figures