$B$ Spectroscopy from NRQCD with Dynamical Fermions

We present a lattice investigation, partially including the effects of dynamical quarks, of the heavy-light mesons using NRQCD for the heavy quark and the Wilson action for the light quark. We performed an extensive calculation of the spectrum employing a multi-state, multi-exponential fitting analysis which enabled us to extract the $2S-1S$ splitting as well as the ${}^1{P}_1-\bar{S}$ and hyperfine splittings. The Wilson action introduces a large systematic error into the calculation, and within this uncertainty we obtain agreement with experiment. We performed a comprehensive calculation of the heavy-light meson mass, investigating three methods and their range of validity. The agreement found between these methods confirms that Lorentz invariance can be restored at this order in NRQCD by a constant shift to all masses. We calculated spectroscopic quantities over a wide range in heavy quark mass and were able to perform a detailed investigation of heavy quark symmetry around the $b$ quark mass. In particular, we extracted the nonperturbative coefficients of terms in the heavy quark expansion of the meson binding energy. We demonstrate the importance of using tadpole-improved operators in such a calculation.