Constraining Neutrino--Nucleon Form Factors with Charged-Current Scattering at the Electron-Ion Collider

Abstract

Next-generation neutrino oscillation experiments such as DUNE require percent-level knowledge of neutrino--nucleon interaction cross sections. The nucleon axial form factor $F_A(Q^2)$, parameterized by the axial mass $\MA$, is the dominant source of uncertainty in the quasi-elastic channel, and the parity-violating structure function $xF_3$ is poorly constrained on free nucleons. We propose using charged-current (CC) electron--proton scattering at the Electron-Ion Collider (EIC) to address both problems simultaneously. The measurement exploits three key features of the EIC: (1)~helicity-selective electron bunches provide \emph{in situ} electromagnetic background rejection; (2)~a longitudinally polarized proton target enables extraction of $F_A(Q^2)$ through the target-spin asymmetry $A_{UL}$; and (3)~the $y$-distribution leverage in CC deep inelastic scattering separates $F_2$ and $xF_3$ on a \emph{free proton}, without nuclear corrections. Using a Fisher-information analysis at $\sqrt{s} = 141\GeV$ with $500\fb^{-1}$ of integrated luminosity, we project the Cramér--Rao statistical floor of $δ\MA \approx 0.03\GeV$ (3\%). Incorporating first-order realistic detector effects: ZDC acceptance, $Q^2$ smearing (5\%), and background noise from helicity subtraction, the projected sensitivity is severely background-limited due to the small signal-to-background ratio ($S/B \approx 3 \times 10^{-4}$) in the elastic channel. Achieving competitive sensitivity ($δ\MA \approx 0.14\GeV$) would require $\sim\!10^{-7}$ background suppression, three orders of magnitude beyond current projections. The CC DIS $y$-distribution provides sub-percent extraction of $xF_3^{\Wminus}$ over $0.05 < x < 0.5$, representing the most robust electroweak measurement in the near term.

Figures (7)

• Figure 1: Published measurements of the nucleon axial mass $M_A$ (data compiled from Refs. Formaggio2012BernardMA). Blue circles: measurements on deuterium (quasi-free nucleon). Red squares: measurements on nuclear targets. Green star: EIC statistical floor ($\delta M_A = 0.032\,\text{GeV}$; see Table \ref{['tab:fisher_results']}). The light blue band shows the world average $M_A = 1.026 \pm 0.021\,\text{GeV}$BernardMA; the dashed red line marks the MiniBooNE central value MiniBooNE_MA.
• Figure 2: Kinematic coverage of the EIC at $\sqrt{s} = 141\,\text{GeV}$ in the $(x, Q^2)$ plane. Gray shading: accessible phase space for $0.01 < y < 0.95$. Green band: elastic CC region ($x \approx 1$). Blue dashed rectangle: CC DIS region used for $xF_3$ extraction. Orange dot-dashed line: $W^2 = 4\,\text{GeV}^2$ (DIS threshold). Diagonal gray lines: constant $y$.
• Figure 3: Helicity filtering for CC elastic signal extraction ($500\,\text{fb}^{-1}$ total, $250\,\text{fb}^{-1}$ per helicity, $P_e = 0.80$). Left: Raw event counts by electron helicity. With 80% polarization, LH bunches contain 90% LH electrons and RH bunches contain 10% LH electrons, so both produce CC events. Right: Polarization-corrected CC signal $(N_\text{LH} - N_\text{RH})/P_e$ (black points with error bars) compared to the true CC signal (green bars). The error bars include the $1/P_e$ amplification factor per Eq. \ref{['eq:helicity_sub']}. Statistical fluctuations arise from Poisson sampling (Sec. \ref{['sec:bg_model']}). Background: exponential in $Q^2$ with $30{,}000$ fb total cross section after veto cuts ($S/B \approx 3 \times 10^{-4}$).
• Figure 4: (a) Target-spin asymmetry $|A_{UL}|$ vs $Q^2$ for different $M_A$ values. The curves separate in the sensitivity window $0.1 < Q^2 < 1\,\text{GeV}^2$. Black circles: ideal statistical floor. With $10^{-4}$ background suppression, the asymmetry uncertainties are $\delta A_{UL} \sim 1$--$10$ (off scale), providing no constraint. (b) Projected $\delta M_A$ vs background suppression factor over the full range. The measurement is severely background-limited: the current baseline ($10^{-4}$) yields $\delta M_A \approx 4\,\text{GeV}$ (unfeasible). Achieving $\delta M_A \lesssim 0.17\,\text{GeV}$ (MiniBooNE precision) requires $10^{-7}$ suppression. The green and red shaded regions indicate competitive and unfeasible regimes, respectively.
• Figure 5: Projected $1\sigma$ confidence contours in the $(g_A, M_A)$ plane for achievable suppression scenarios. Blue: statistical floor (Cramér--Rao bound, $\delta M_A = 0.032\,\text{GeV}$). Green: efficiency only, no background ($\delta M_A = 0.045\,\text{GeV}$). Purple: aggressive R&D scenario with $10^{-8}$ suppression. Red: minimum viable $10^{-7}$ suppression ($\delta M_A \approx 0.13\,\text{GeV}$). The current baseline ($10^{-4}$) yields $\delta M_A \approx 4\,\text{GeV}$---the ellipse would extend far beyond the plot and is not shown. The purple vertical band shows the external $g_A$ constraint from neutron beta decay. Contours use $\Delta\chi^2 = 2.30$ for two parameters.