Nuclear forces in the chiral limit

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We investigate the behaviour of the nuclear forces as a function of the light quark masses (or, equivalently, pion mass) in the framework of chiral effective field theory at next-to-leading order. The nucleon–nucleon force is described in terms of one and two-pion exchange and local short distance operators, which depend explicitly and implicitly on the quark masses. The pion propagator becomes Coulomb-like in the chiral limit and thus one has significant scattering in all partial waves. The pion–nucleon coupling depends implicitly on the quark masses and we find that it becomes stronger in the chiral limit. There is a further quark mass dependence in the S-wave four-nucleon couplings, which can be estimated by means of dimensional analysis. We find that nuclear physics in the chiral limit becomes natural. There are no new bound states, the deuteron binding energy is B D CL=9.6±1.9 +1.8 −1.0 MeV, and the S-wave scattering lengths take values of a few fm, a CL ( 1S 0)=−4.1±1.6 +0.0 −0.4 fm and a CL ( 3S 1)=1.5±0.4 +0.2 −0.3 fm. We also discuss the extrapolation to larger pion masses pertinent for the extraction of these quantities from lattice simulations.