Exclusive decays of heavy and light mesons

Abstract

In the exclusive decay of the B meson into a ${\mathit{K}}^{\mathrm{*}}$ and a photon, the large recoil momentum creates a difficulty in making a connection between the quark level calculations and the meson states. In the quark model, depending on how the recoil momentum is handled, this can lead to differences of a factor of about 5 in the branching ratio. In order to explore this problem, we look at some other meson processes where there exist some experimental data. For the \ensuremath{\pi} form factor we show that, by imposing current conservation together with relativistic meson and spinor normalizations within the quark model, it is possible to remove a parameter \ensuremath{\kappa} which had previously been introduced to obtain agreement with the form-factor data. The data on the decay \ensuremath{\omega}\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{0}$${\mathrm{\ensuremath{\mu}}}^{+}$${\mathrm{\ensuremath{\mu}}}^{\mathrm{\ensuremath{-}}}$ and \ensuremath{\omega}\ensuremath{\rightarrow}${\mathrm{\ensuremath{\pi}}}^{0}$\ensuremath{\gamma} also show the importance of retaining relativistic meson and spinor normalizations; however, we do not resolve the recoil problem. For the exclusive decays B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$\ensuremath{\gamma} and B\ensuremath{\rightarrow}${\mathit{K}}^{\mathrm{*}}$${\mathit{e}}^{+}$${\mathit{e}}^{\mathrm{\ensuremath{-}}}$ we show the extent to which the heavy-quark symmetries determine these decays, even in regions of large recoil.