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

TL;DR

This work assesses precision electroweak measurements via elastic neutrino–electron scattering (EνES) using a companion detector in the plane of a high-energy muon storage ring. By exploiting both $\nu_μ$ and $\nu_e$ fluxes, the study quantifies how well one can extract SM neutral-current couplings ($g_V$, $g_A$) and the weak mixing angle $\sin^2\theta_W$ across a low-$Q$ range, including possible running, with muon-beam energies up to $E_μ = 5$ TeV (corresponding to $\sqrt{s}=10$ TeV). The results indicate that running in $\sin^2\theta_W(Q)$ could be detected and zero neutrino radii excluded at high significance, while flavor-dependent neutrino couplings and neutrino charge radii can be constrained to sub-permil precision in favorable configurations. The analysis highlights the unique sensitivity of a muon-collider neutrino source to the $Q$-dependence of electroweak parameters and outlines future avenues, including QEνES, νDIS, and trident channels, for expanding the physics reach.

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 $ν_μ$ and $ν_e$ scattering on electrons (E$ν$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$ν$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 $\sin^2θ_W$. We estimate that with the neutrinos from a $E_μ= 1.5$~TeV (or higher) muon collider, the hypothesis that $\sin^2θ_W$ does not ``run'' can be safely ruled out.

Figures (10)

• Figure 1: Schematic (not to scale) of the neutrino flux geometry in the plane of a muon storage ring (or collider) of radius $R$ and tangential distance $L$ to a short, hockey-puck-shaped neutrino detector of diameter $w$ located in the plane defined by the storage ring. The decay products from clockwise circulating $\mu^+$ are shown in red, while those from the counter-clockwise circulating $\mu^-$ are shown in blue. The arc length $S_d$ indicates the region where "useful" muon decays contribute the neutrino flux inside the solid angle defined by the fiducial detector area.
• Figure 2: Top: Electron recoil energy spectra, for different stored-muon energies $E_\mu = 0.25$ GeV, 1.5 TeV, and 5 TeV, as a function of the momentum transfer $Q = \sqrt{2 m_e E_r}$, for negatively charged muons. Bottom: $\sin^2\theta_W(Q)$ as a function of the momentum transfer, assuming no new physics beyond the standard model. Some of the existing measurements are also shown PRESCOTT1979524Wood:1997zqDzuba:2012kxSLACE158:2005uayNuTeV:2001whx. The Q$_{\rm weak}$ and E-158 measurements are slightly offset for clarity.
• Figure 3: Sensitivity to $g_V$ and $g_A$ at $2\sigma$ C.L., for the three benchmark muon energies in a single-sign $\mu^+$ storage ring (SR, dotted contours) and $\mu^+ \mu^-$ collider (MC, solid contours) from E$\nu$ES scattering in the nearby neutrino detector. The preferred contours centered around the SM expectation, assuming fixed $\sin^2\theta_W$ as in Table \ref{['tab:rates']}, in the lower quadrant of the $g_V$-$g_A$ plane are shown (degenerate regions lie outside of the shown range), with the inset panel showing a close-up view of just the MC and SR sensitivity. The allowed regions from TEXONO TEXONO_GVGA, LSND LSND_GVGA, and CHARM-II CHARM_GVGA are also shown.
• Figure 4: Left: sensitivity (2$\sigma$ C.L.) to the electroweak neutrino couplings in the $(g^{\nu_e}_{L},g^{\nu_{\mu}}_{L})$ plane for the three benchmark muon energies in a $\mu^+$ storage ring or $\mu^+\mu^-$ collider from E$\nu$ES scattering in a nearby neutrino detector, assuming the SM null hypothesis. Right: Sensitivity to the neutrino charge radii in the $\braket{r_{\nu_e}^2}-\braket{r_{\nu_\mu}^2}$ plane; the $\braket{r_{\nu_\alpha}^2} = 0$ null hypothesis is ruled out for both the electron and muon neutrino charge radii well beyond a few standard deviations for the muon collider.
• Figure 5: Total (top panels) and subtracted (bottom panels) E$\nu$ES spectra for $E_\mu = 5$ TeV stored muons, comparing results with a fixed $\sin^2\theta_W$ assumption at some average $\braket{Q}$ (chosen based on the peak of the recoil-electron energy spectrum) to those with a running $\sin^2\theta_W(Q)$. $\sqrt{N_{\rm Running}}$ statistical errors are shown for each subtracted histogram.