Evolution of the $B$-Meson Light-Cone Distribution Amplitude in Laplace Space

Abstract

The $B$-meson light-cone distribution amplitude is a central quantity governing non-perturbative hadronic dynamics in exclusive $B$ decays. We show that the information needed to describe such processes at leading power in ${\Lambda }_{\mathrm{QCD}}/m_b$ is most directly contained in its Laplace transform ${\tilde{\varphi }}_{+}(\eta )$. 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 $B^{-}\to \gamma {\ell }^{-}\bar{\nu }$ in terms of ${\tilde{\varphi }}_{+}(\eta )$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of ${\tilde{\varphi }}_{+}(\eta )$ in terms of a small set of uncorrelated hadronic parameters.

Comments: 7 pages, 2 nice figures; version accepted for publication in Phys. Rev. D (Rapid Communications)