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 $\Lambda_{\rm QCD}/m_b$ is most directly contained in its Laplace transform $\tilde\phi_+(\eta)$. 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 $\tilde\phi_+(\eta)$ and show that it is explicitly independent of the factorization scale. We propose an unbiased parameterization of $\tilde\phi_+(\eta)$ in terms of a small set of uncorrelated hadronic parameters.
Highlights
Light-cone distribution amplitudes (LCDAs) describe the inner structure of hadrons as probed in hard exclusive QCD processes
The corresponding decay amplitudes can be written as the sum of two terms, one in which the relevant hadronic information is encoded in experimentally accessible form factors FBi →Mðq2Þ, and a “hard-scattering” contribution governed by the B meson LCDA
We show that the information that can be probed in hard exclusive processes is entirely and most directly described by the Laplace transform of the LCDA, defined as φþðη; μÞ
Summary
Light-cone distribution amplitudes (LCDAs) describe the inner structure of hadrons as probed in hard exclusive QCD processes They are nonperturbative quantities of fundamental importance for the theory and phenomenology of the strong interactions [1,2,3,4,5]. Some of them are based on QCD sum-rule estimates [6,17,18], while others are inspired by an ad hoc modeling of the LCDA in momentum space [19] or in the so-called dual space [20,21,22], where its one-loop evolution equation takes on a simpler form Most of these models rest on unjustified assumptions, which imply important biases and lead to uncontrolled systematic uncertainties:. We derive an explicit expression for the factorized decay amplitude in (1), in which the factorization scale μ drops out explicitly and large logarithms are resummed to all orders of perturbation theory
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