  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.
