The longest-range part of the nuclear force due to the one-pion exchangegoverns the energy dependence of the scattering amplitude in the near-thresholdregion and imposes correlations between the coefficients in the effective rangeexpansion. These correlations may be regarded as low-energy theorems and areknown to hold to a high accuracy in the neutron-proton 3S1 partial wave. Wegeneralize the low-energy theorems to the case of unphysical pion masses andprovide results for the correlations between the coefficients in the effectiverange expansion in this partial wave for pion masses up to Mpi ~ 400 MeV. Wediscuss the implications of our findings for the available and upcominglattice-QCD simulations of two-nucleon observables.
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