Isospin Decomposition of Vector and Axial Two-Body Currents via Polarized Electron--Deuteron and Electron--$^3$He Scattering at the Electron-Ion Collider

Abstract

Two-particle two-hole (2p2h) excitations driven by meson-exchange currents (MEC) are among the leading nuclear uncertainties in long-baseline neutrino oscillation experiments. Three models currently implemented in neutrino event generators disagree by 20--40% on the $\omega$-integrated 2p2h cross section in the dip region on carbon (differential disagreements can reach factors of 2--3), and the axial two-body current has no direct experimental constraint beyond tritium $\beta$-decay at $Q^2 = 0$. We propose a measurement program at the Electron-Ion Collider (EIC) using polarized electron scattering on deuteron and $^3$He. Electromagnetic (EM) scattering ($\gamma^*$ exchange) measures the vector MEC. Charged-current (CC) scattering ($W^-$ exchange) on the same targets measures the vector$+$axial MEC. Subtracting the two provides the first direct sensitivity to the axial two-body current, including the $V$--$A$ interference, as a function of momentum transfer. Using $^3$He (2~$pn$ $+$ 1~$pp$ pair) extends the decomposition to $pp$ pairs. Polarized beams and targets give access to six EM response functions on deuteron, four of which have not been previously measured. The tensor analyzing power provides a sign-flip test for $\Delta$-excitation MEC. We present projected sensitivities at $50 fb^{-1}$ on deuteron ($\sim$5 years at $10^{33}$~cm$^{-2}$s$^{-1}$). The EM program can deliver $\sim\!5\!\times\!10^4$ events per $Q^2$ bin constraining the MEC transverse response to $\sim$2% per bin, the beam--target double-spin asymmetry reaches $6$--$13\sigma$ per bin, and the vector MEC $V_{pn}$ is measured to $\sim$6% per bin. The CC channel is statistics-limited, with $\sim$6--38 events per $Q^2$ bin at $50 fb^{-1}$, requiring a luminosity upgrade beyond the current EIC baseline.