Tritium $\beta$-decay in chiral effective field theory

TL;DR

This paper calculates tritium beta-decay matrix elements using chiral effective field theory, including loop corrections, and compares results with phenomenological models to improve understanding of weak interactions in nuclei.

Contribution

It incorporates one-loop corrections in the axial current within chiral EFT for tritium beta-decay, providing new insights into the size of loop contributions and low-energy constants.

Findings

Loop corrections can dominate one-pion exchange contributions.

Calculated low-energy constants match experimental data.

Results highlight importance of higher-order corrections in nuclear weak processes.

Abstract

We evaluate the Fermi and Gamow-Teller (GT) matrix elements in tritium $\beta$-decay by including in the charge-changing weak current the corrections up to one loop recently derived in nuclear chiral effective field theory ($\chi$ EFT). The trinucleon wave functions are obtained from hyperspherical-harmonics solutions of the Schrodinger equation with two- and three-nucleon potentials corresponding to either $\chi$ EFT (the N3LO/N2LO combination) or meson-exchange phenomenology (the AV18/UIX combination). We find that contributions due to loop corrections in the axial current are, in relative terms, as large as (and in some cases, dominate) those from one-pion exchange, which nominally occur at lower order in the power counting. We also provide values for the low-energy constants multiplying the contact axial current and three-nucleon potential, required to reproduce the experimental GT matrix element and trinucleon binding energies in the N3LO/N2LO and AV18/UIX calculations.