Evolution of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi></mml:math> meson light-cone distribution amplitude in Laplace space
Anne Mareike Galda, Matthias Neubert
Abstract
The $B$ meson light-cone distribution amplitude is a central quantity governing nonperturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{QCD}}/{m}_{b}$ is most directly contained in its Laplace transform ${\stackrel{\texttildelow{}}{\ensuremath{\phi}}}_{+}(\ensuremath{\eta})$. We derive the renormalization-group (RG) equation satisfied by this function and present its exact solution. We express the RG-improved QCD factorization theorem for the decay ${B}^{\ensuremath{-}}\ensuremath{\rightarrow}\ensuremath{\gamma}{\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ in terms of ${\stackrel{\texttildelow{}}{\ensuremath{\phi}}}_{+}(\ensuremath{\eta})$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parametrization of ${\stackrel{\texttildelow{}}{\ensuremath{\phi}}}_{+}(\ensuremath{\eta})$ in terms of a small set of uncorrelated hadronic parameters.