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We use Bayesian statistics to infer the breakdown scale of pionless effective field theory in its standard power counting and with renormalization of observables carried out using the power-divergence subtraction scheme and cutoff regularization. We condition our inference on predictions of the total neutron-proton scattering cross section up next-to-next-to leading order. We quantify a median breakdown scale of approximately 1.4 mpi . The 68% degree of belief interval is [0.96, 1.69]mpi . This result confirms the canonical expectation that the pion mass is a relevant scale in low-energy nuclear physics. 

Abstract We calculate the S -factor for proton–proton fusion using chiral effective field theory interactions and currents. By performing order-by-order calculations with a variety of chiral interactions that are regularized and calibrated in different ways, we assess the uncertainty in the S -factor from the truncation of the effective field theory expansion and from the sensitivity of the S -factor to the short-distance axial current determined from three- and four-nucleon observables. We find that S (0) = (4.100 ± 0.024(syst) ± 0.013(stat) ± 0.008( g A )) × 10 −23 MeV fm 2 , where the three uncertainties arise, respectively, from the truncation of the effective field theory expansion, use of the two-nucleon axial current fit to few-nucleon observables and variation of the axial coupling constant within the recommended range. The increased value of S (0) compared to previous calculations is mainly driven by an increase in the recommended value for the axial coupling constant and is in agreement with a recent analysis based on pionless effective field theory.