Uncertainties in constraining low-energy constants from

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