Measuring the Weak Mixing Angle in the DUNE Near-Detector Complex

The planned DUNE experiment will have excellent sensitivity to the vector and axial couplings of the electron to the $Z$ boson via precision measurements of neutrino-electron scattering. We investigate the sensitivity of DUNE-PRISM, a movable near detector in the direction perpendicular to the beam line, and find that it will qualitatively impact our ability to constrain the weak couplings of the electron. We translate these neutrino-electron scattering measurements into a determination of the weak mixing angle at low scales and estimate that, with seven years of data taking, the DUNE near detector can be used to measure ${\sin }^2{\theta }_W$ with about 2% precision. We also discuss the impact of combining neutrino-electron scattering data with neutrino trident production at DUNE-PRISM.

Figure 1

Ratio of the number of events expected from ${\nu }_e-e+{\overline{\nu }}_e-e$ scattering to that of ${\nu }_{\mu }-e$ scattering, in neutrino-mode running, as a function of the off-axis distance.

Figure 2

Allowed regions in the plane $g_V\times g_A$ from CHARM-II [37] (gray, at 90% C.L.), LSND [38] (dotted light-brown, at $1\sigma$ C.L.), and TEXONO [39] (dot-dashed light-violet, at $1\sigma$ C.L.), and the estimated 90% C.L. sensitivity from on-axis (7 years) DUNE electron scattering (dashed green) and tridents ($♆$) (dashed purple), as well as DUNE-PRISM electron scattering (dark-blue) and tridents (light-blue), assuming the SM value z(red star).

Figure 3

Neutrino-electron event rates as a function of $E_e{\theta }_e^2$ for the first 5 off-axis positions. For each position, the three histograms correspond to three pairs of vector and axial couplings $(g_V,g_A)$: $(-0.02,-0.5)$ (solid); $(-0.48,-0.04)$ (dotted); and (0.47,0.01) (dashed). Error bars illustrating the statistical and systematic errors are included for the SM case (solid histogram).

Figure 4

${\sin }^2{\theta }_W$ in the $\overline{\mathrm{MS}}$ scheme (light blue line) as a function of $Q$, obtained from a fit to existing data (gray data points), together with the DUNE on-axis (dark blue data point) and DUNE-PRISM (green data point) sensitivities to this angle. The horizontal error bars indicate the range of $Q$ values accessible to DUNE neutrino-electron scattering. Note that the Tevatron, LHC, and SLC data points were slightly shifted from $Q=M_Z$ to improve readability.