Heavy-light meson spectrum with and without NRQCD

If the charm quark is sufficiently heavy, then lattice NRQCD is an efficient computational method for obtaining the spectrum of mesons with a single charm quark. Recent studies of the S and P-wave meson spectrum have determined the contributions from first, second and third order in the inverse charm mass expansion.[1,2] Second and third order contributions were found to be statistically insignificant for the P-wave mesons, but the S-wave spin splittings (D∗−D and D∗ s−Ds) acquire substantial corrections at both second and third order. It is difficult to make a firm statement about convergence of the expansion from these findings alone. In the present work, the existing results are compared to a new study, where the NRQCD charm quark is replaced by a relativistic charm quark using a D234 fermion action.[3] The new simulations use the same set of gauge field configurations and the same light antiquark propagators as were used in Ref. [2], so the only differences are the heavy quark action (NRQCD versus D234) and the operators used to create or destroy the various meson states. The S-wave masses have been discussed many times in the literature (see Refs. [1,2,4] and references therein), but the P-waves have only recently been extracted from lattice data: the limit of an infinitely heavy quark was studied by Michael and Peisa[5], a subset of the P-wave charmed masses were found by Boyle using the clover action (he also extrapolated to the bottom region)[6], and two groups have used NRQCD to study the charmed and bottom meson spectra[2,4,7,8].