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

TL;DR

This paper calculates tritium beta decay using pionless effective field theory at next-to-leading order, determining a key low-energy parameter and analyzing uncertainties and cutoff dependence.

Contribution

It provides the first next-to-leading order calculation of tritium beta decay in pionless EFT, linking the low-energy parameter to the solar fusion rate.

Findings

Next-to-leading order corrections are about 4% of the decay strength.

The low-energy parameter $L_{1,A}$ is extracted from the tritium half-life.

Results are insensitive to different effective range expansion schemes.

Abstract

We calculate the $\beta$-decay of tritium at next-to-leading order in pionless effective field theory. At this order, a low-energy parameter $L_{1, A}$ enters the calculation that is also relevant for a high-accuracy prediction of the solar proton-proton fusion rate. We use the tritium half-life to determine this parameter and provide uncertainty estimates. We show proper renormalization of our calculation analyzing the residual cutoff dependence of observables. We find that next-to-leading order corrections contribute about $4\%$ to the triton decay Gamow-Teller strength. We show that these conclusions are insensitive to different arrangements of the effective range expansion.