Uncertainties in constraining low-energy constants from 3H β decay

We discuss the uncertainties in constraining low-energy constants of chiral effective field theory from H-3 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 H-3 binding energy fit used to constrain another low-energy coupling in three-nucleon forces. However, so far such H-3 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 H-3 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 H-3 half-life and estimate the resulting uncertainties for many-body systems by performing calculations of symmetric nuclear matter.