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

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.

arXiv comment9 pages, 11 figures, published version, includes Erratum, which corrects Figs. 2-6 due to the incorrect c_D relation between 3N forces and two-body currents used

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