Charged-Current Elastic Scattering at the Electron-Ion Collider

TL;DR

This work evaluates the feasibility of measuring charged-current elastic scattering $e^-p\rightarrow \nu_e n$ at the Electron-Ion Collider to access the nucleon's axial form factor $F_A(t)$ and the axial radius $r_A$. By leveraging crossing symmetry with neutrino data, high-luminosity polarized beams, and a forward neutron detector, the study estimates a CCE cross section of a few fb and identifies a dominant background from leading-neutron photoproduction that would require a dedicated forward veto, potentially in a second detector. The analysis shows that, even with optimistic background suppression, extracting $F_A(t)$ would be challenging and would benefit from a combined fit to $|t|$-dependent cross sections and target-spin asymmetries, potentially achieving competitive constraints on $M_A$ and thus $r_A$ with sufficient luminosity (order 500~fb$^{-1}$). The paper also discusses related charged-current processes, noting that exclusive CC channels might offer favorable experimental handles, and provides a roadmap for pursuing a challenging but potentially impactful measurement of nucleon axial structure at the EIC.

Abstract

We discuss the measurement of the charged-current elastic scattering process $e^-p\rightarrowν_e n$ at the Electron-Ion Collider (EIC). This process provides sensitivity to the poorly constrained axial form factor of the nucleon, which encodes the spatial distribution of weak charge. Collisions of electrons with polarized protons enable measuring the axial form factor via the $e^{-\!}\,\vec{p} \to ν_e\,n$ target-spin asymmetry for the first time. We conclude that a measurement of charged-current elastic scattering at the EIC will, perhaps unsurprisingly, prove very challenging. However, with dedicated instrumentation at a second EIC detector, the measurement may be possible.

Figures (7)

• Figure 1: Diagram of the CCE process. In the elastic process, unlike charged-current deep inelastic scattering, the $W^-$ does not resolve the partonic structure of the nucleon and the process is sensitive to the axial form factor.
• Figure 2: Compilation of data for the reaction $\nu_{\mu} n\rightarrow \mu^- p$ reproduced from Ref. Formaggio:2012cpf. By crossing symmetry, this cross section should be the same as $e^-p\rightarrow\nu_en$, neglecting subleading effects such as lepton masses and higher-order corrections.
• Figure 3: Plot of neutron momentum vs. lab-frame scattering angle for the CCE reaction. Note the small change in neutron momentum as a function of $|t|$ on the $y$-axis.
• Figure 4: Expected event yield in 100 fb$^{-1}$ of integrated luminosity for the EIC in the 10x275 GeV configuration. The bin width in $|t|$ is 0.4 GeV$^2$.
• Figure 5: Momentum vs. pseudorapidity for the highest-momentum charged particle in an event with an $x_L>0.95$ leading neutron as simulated by Pythia6 Sjostrand:2006za.