Radiative and pionic decays of heavy-light mesons using HISQ quarks

In this thesis we use the highly improved staggered quark (HISQ) formalism to study the radiative and pionic transitions of charmed mesons within the framework of lattice QCD. The HISQ action is one of the most accurate formulations of charm quarks and is a result of a perturbative Symanzik improvement program to reduce lattice discretization errors. Decay widths are calculated in numerical simulations on an ensemble of gauge field configurations with $N_f=2+1$ asqtad sea quarks generated by the MILC collaboration. In addition we study $H_s^\ast$ and charmonium radiative decays as well as meson electric form factors. Experimental measurements of the decay ratios of vector charmed $D^{\ast\pm0}$ and charmed strange $D_s^{\ast\pm}$ mesons, show a few curious features that are of great phenomenological interest in the study of low energy hadronic physics. Unlike most mesons, the strong hadronic decay modes of $D^{\ast0}$ and $D_s^{\ast\pm}$, are not dominant. However, while the neutral $D$ has a radiative mode that is competitive with its pionic mode, the charged $D$ meson's radiative decay is highly suppressed relative to that of the neutral. This suppression provides a detailed probe of strong interactions and is apparently due to an interesting near cancellation that takes place between the photon's coupling to the charm quark and to the down antiquark. The results are in agreement with all of the available experimental data, and in particular, we show that the HISQ action successfully accounts for the near cancellation of the charmed $D^{\ast\pm}$ radiative decay. The relative suppression is demonstrated in our result for the ratio of the radiative form factors of $D$ mesons $V^\pm(0)/V^0(0)=0.126(36)$ computed at heavier than physical $u/d$ quark masses. The quoted errors are purely statistical. Evidence from other lattice studies indicate small systematic errors in continuum and sea quark chiral extrapolations. Valence quark chiral extrapolation increases our errors by about 50\%. A rough extrapolation suggests an agreement with the measured radiative width within $2\sigma$.