On the Quark Mass Dependence of Two Nucleon Observables

We study the implications of lattice QCD determinations of the S-wave nucleon-nucleon scattering lengths at unphysical light quark masses. It is found that with the help of nuclear effective field theory (NEFT), not only the quark mass dependence of the effective range parameters, but also the leading quark mass dependence of all the low energy deuteron matrix elements can be obtained. The quark mass dependence of deuteron charge radius, magnetic moment, polarizability and the deuteron photodisintegration cross section are shown based on the NPLQCD lattice calculation of the scattering lengths at 354 MeV pion mass and the NEFT power counting scheme of Beane, Kaplan and Vuorinen. Further improvement can be obtained by performing the lattice calculation at smaller quark masses. Our result can be used to constrain the time variation of isoscalar combination of u and d quark mass m_q, to help the anthropic principle study to find the m_q range which allows the existence of life, and to provide a weak test of the multiverse conjecture.