Charm spectroscopy on dynamical 2+1 flavor domain wall fermion lattices with a relativistic heavy quark action

We present a preliminary calculation of the charmonium spectrum using the dynamical 2+1 flavor $24^3\times 64$ domain wall fermion lattice configurations generated by the RBC and UKQCD collaborations. We use the relativistic heavy quark action with 3 parameters non-perturbatively determined by matching to experimental quantities. Chiral extrapolation is done on four light sea quark masses from 0.005 to 0.03, with $m_s=0.04$ and $m_{res}=0.003$. We can either predict meson masses assuming the lattice spacing is known from other methods, or calculate the lattice spacing using those quantities