The Quark-Mass Dependence of Two-Nucleon Systems

We explore the quark-mass dependence of two-nucleon systems. Allowed regions for the scattering lengths in the 1S0 and 3S1 channels as functions of the light-quark masses are determined from the current uncertainty in strong-interaction parameters that appear at next-to-leading order in the effective field theory. Where experimental constraints are absent, as is the case for the quark-mass dependent four-nucleon operators, we use naive dimensional analysis. We find it likely that there is no bound state in the 1S0 channel in the chiral limit. However, given the present uncertainties in strong-interaction parameters it is unclear whether the deuteron is bound or unbound in the chiral limit.