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.

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

References in corpus (37)

• QCD Factorization for $B\to \pi \pi$ Decays: Strong Phases and CP Violation in the Heavy Quark Limit
• QCD factorization for exclusive, non-leptonic B meson decays: General arguments and the case of heavy-light final states
• QCD factorization for B->PP and B->PV decays
• Symmetry-breaking corrections to heavy-to-light B meson form factors at large recoil
• Systematic approach to exclusive B ->V l^+l^-, V gamma decays
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Asymptotics of Heavy-Meson Form Factors
• The B-Meson Distribution Amplitude in QCD
• Matching QCD and HQET heavy--light currents at two loops and beyond
• Renormalization-Group Evolution of the B-Meson Light-Cone Distribution Amplitude
• Radiative leptonic decays of B mesons in QCD
• Light-Cone Distribution Amplitudes for Heavy-Quark Hadrons
• B meson distribution amplitude from B --> γl ν
• Model-Independent Properties of the B-Meson Distribution Amplitude
• Factorization in leptonic radiative B -> gamma eνdecays
• Factorization and Sudakov Resummation in Leptonic Radiative B Decay
• Factorization, the light-cone distribution amplitude of the B-meson and the radiative decay B -> gamma l nu_l
• Three-loop anomalous dimension of the heavy-light quark current in HQET
• Two-Loop QCD Corrections to the Heavy-to-Light Quark Decay
• Fermionic Corrections to the Heavy-Quark Pair Production in the Quark-Antiquark Channel
• Two-loop QCD correction to differential semi-leptonic b --> u decays in the shape-function region
• Radiative leptonic decay $B\to \gamma \ell {\nu }_{\ell }$ with subleading power corrections
• Soft contribution to $B\to \gamma \ell {\nu }_{\ell }$ and the $B$-meson distribution amplitude
• B->gamma e nu Transitions from QCD Sum Rules
• NNLO corrections to inclusive semileptonic B decays in the shape-function region
• Factorization and dispersion relations for radiative leptonic $B$ decay
• B-Meson Light-Cone Distribution Amplitude: Perturbative Constraints and Asymptotic Behaviour in Dual Space
• NNLO corrections to B --> X_u l nu in the shape-function region
• Two-loop evolution equation for the B-meson distribution amplitude
• Conformal symmetry of the Lange-Neubert evolution equation
• Two-loop conformal generators for leading-twist operators in QCD
• Two-Loop Radiative Jet Function for Exclusive $B$-Meson and Higgs Decays
• Renormalization and Scale Evolution of the Soft-Quark Soft Function
• Decoupling of heavy-quark loops in light-light and heavy-light quark currents
• Operator product expansion for B-meson distribution amplitude and dimension-5 HQET operators
• Three-loop soft function for heavy-to-light quark decays
• Integrability in heavy quark effective theory

Cited by in corpus (15)

• $B\to D\ell {\nu }_{\ell }$ form factors beyond leading power and extraction of $|V_{cb}|$ and $R(D)$
• Precision calculations of the double radiative bottom-meson decays in soft-collinear effective theory
• QCD sum rules for parameters of the $B$-meson distribution amplitudes
• Radiative Quark Jet Function with an External Gluon
• Systematic Parametrization of the Leading $B$-meson Light-Cone Distribution Amplitude
• Power corrections to quasi-distribution amplitudes of a heavy meson
• Semileptonic $B_s\to K_0^{\ast }(1430)$ transitions with the light-cone sum rules
• Study on pure annihilation type B to V gamma decays
• Perturbative QCD analysis of neutral $B$-meson decays into $\sigma \sigma ,\sigma f_0$ and $f_0{f}_0$
• Pure annihilation decays of $B_s^0\to a_0^{+}{a}_0^{-}$ and $B_d^0\to K_0^{\ast +}{K}_0^{\ast -}$ in the PQCD approach
• Phenomenological studies on neutral $B$-meson decays into $J/\psi f_1$ and ${\eta }_c{f}_1$
• Form factors of $B_{(s)}$ to light scalar mesons with the $B$-meson LCSR
• Charged and Neutral ${\bar{B}}_{u,d,s}\to \gamma$ Form Factors from Light Cone Sum Rules at NLO
• Determination of $B$-meson distribution amplitudes from $B\to \pi ,K,D$ transition form factors
• QCD factorization for the $B\to \gamma \ell {\nu }_{\ell }$ decay beyond leading power