Uncertainties in constraining low-energy constants from $^3$H $\beta$ decay

TL;DR

This paper investigates how cutoff dependence in chiral effective field theory affects the extraction of low-energy constants from tritium beta decay, revealing underestimated uncertainties in current three-nucleon force models.

Contribution

It demonstrates the significant impact of regulator cutoff dependence on the determination of the low-energy constant c_D from tritium beta decay data.

Findings

Cutoff dependence significantly influences Gamow-Teller matrix elements.

Current models underestimate uncertainties in c_D due to cutoff effects.

Range of c_D compatible with experimental half-life is broader than previously thought.

Abstract

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from $^3$H $\beta$ decay. The half-life is very precisely known, so that the Gamow-Teller matrix element has been used to fit the coupling $c_D$ of the axial-vector current to a short-range two-nucleon pair. Because the same coupling also describes the leading one-pion-exchange three-nucleon force, this in principle provides a very constraining fit, uncorrelated with the $^3$H binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such $^3$H half-life fits have only been performed at a fixed cutoff value. We show that the cutoff dependence due to the regulators in the axial-vector two-body current can significantly affect the Gamow-Teller matrix elements and consequently also the extracted values for the $c_D$ coupling constant. The degree of the cutoff dependence is correlated with the softness of the employed NN interaction. As a result, present three-nucleon forces based on a fit to $^3$H $\beta$ decay underestimate the uncertainty in $c_D$. We explore a range of $c_D$ values that is compatible within cutoff variation with the experimental $^3$H half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter.