Local chiral interactions, the tritium Gamow-Teller matrix element, and the three-nucleon contact term

TL;DR

This paper calculates the tritium beta decay Gamow-Teller matrix element using chiral three-nucleon interactions, refines low-energy constants, and discusses implications for nuclear spectra and neutron matter, providing explicit axial current expressions up to N4LO.

Contribution

It introduces new determinations of LECs c_D and c_E from trinucleon data and derives explicit axial current expressions up to N4LO in configuration space.

Findings

Predictions slightly overestimate empirical GT value by 1-4%.

New LECs c_D and c_E fitted to trinucleon data.

Provides explicit N4LO axial current expressions.

Abstract

The Gamow-Teller (GT) matrix element contributing to tritium $\beta$ decay is calculated with trinucleon wave functions obtained from hyperspherical-harmonics solutions of the Schr\"odinger equation with the chiral two- and three-nucleon interactions including $\Delta$ intermediate states that have recently been constructed in configuration space. Predictions up to N3LO in the chiral expansion of the axial current (with $\Delta$'s) overestimate the empirical value by 1--4 \%. By exploiting the relation between the low-energy constant (LEC) in the contact three-nucleon interaction and two-body axial current, we provide new determinations of the LECs $c_D$ and $c_E$ that characterize this interaction by fitting the trinucleon binding energy and tritium GT matrix element. Some of the implications that the resulting models of three-nucleon interactions have on the spectra of light nuclei and the equation of state of neutron matter are briefly discussed. We also provide a partial analysis, which ignores $\Delta$'s, of the contributions due to loop corrections in the axial current at N4LO. Finally, explicit expressions for the axial current up to N4LO have been derived in configuration space, which other researchers in the field may find useful.