Neutral Pion Electroproduction off Light Nuclei in Chiral Perturbation Theory

Abstract

Threshold pion electroproduction on tri-nucleon systems is investigated in the framework of baryon Chiral Perturbation Theory (ChPT) at next-to-leading one-loop order O(q⁴) in the chiral expansion. To this order in small momenta, the production operator is a sum of one- and two-nucleon terms. While the one-nucleon terms resemble the impulse approximation, the two-nucleon contributions represent corrections due to the relevant nuclear interactions, e.g. pion-exchange interactions, which prove to be dominant, and due to recoil effects of the participating nucleons, which appear to be negligible. We calculate the expectation value of the production operator using chiral wave functions in a three-dimensional approach without partial wave expansion. The resulting integrals are evaluated using adaptive Monte Carlo integration, the VEGAS algorithm of Lepage. We obtain results for the threshold production multipoles E₀₊ and L₀₊ on ³He and ³H and comment on the sensitivity to the fundamental neutron amplitude E^π⁰n₀₊.<br />³He appears to be a particularly promising target to extract information about the neutron amplitude. This idea is usually invoked for spin-dependent quantities since the ³He wave function is strongly dominated by the principal S-state component which suggests that its spin is largely driven by the one of the neutron.