  The longest-range part of the nuclear force due to the one-pion exchange
governs the energy dependence of the scattering amplitude in the near-threshold
region and imposes correlations between the coefficients in the effective range
expansion. These correlations may be regarded as low-energy theorems and are
known to hold to a high accuracy in the neutron-proton 3S1 partial wave. We
generalize the low-energy theorems to the case of unphysical pion masses and
provide results for the correlations between the coefficients in the effective
range expansion in this partial wave for pion masses up to Mpi ~ 400 MeV. We
discuss the implications of our findings for the available and upcoming
lattice-QCD simulations of two-nucleon observables.
