Isolating the axial two-body current via electromagnetic and charged-current lepton scattering on polarized light nuclei

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. The axial two-body current that drives the weak nuclear responses is constrained by integrated weak rates at very low momentum transfer, tritium $\beta$-decay at $Q^2=0$ and muon capture on ${}^3$He at $Q^2\approx 0.01$ GeV${}^2$. We develop a method to isolate that current. Electromagnetic scattering on a nucleus probes only the vector two-body current, while charged-current scattering on the same target probes the vector and axial currents together. Their difference isolates the axial-sensitive combination as a function of momentum transfer. Carried out on a sequence of polarized light nuclei, the method conditionally separates the $pn$ and $pp$ pair contributions to the vector and axial MEC. The spin-dependent response functions accessible with polarized beams decompose the current into its underlying meson-exchange mechanisms. We quantify the experimental requirements and find the program to be demanding: the dominant electromagnetic observables require an energy-transfer resolution of order 60 MeV and control of the impulse-approximation baseline at the few-percent level, while the charged-current measurement is limited by the separation of two forward neutrons and by data-driven control of background. If the axial strength is at least comparable to the vector one, a few hundred inverse femtobarns give a first direct test of the electromagnetic prediction. The experimental requirements are not fully satisfied at present detectors but could lie within reach of a future high-luminosity polarized light-ion collider.