Radiative leptonic decays of B mesons in QCD

TL;DR

The paper analyzes radiative leptonic B decays in the high-photon-energy region using QCD factorization and HQET, expressing the leading-twist form factors as convolutions of a universal B-meson light-cone wave function with a calculable hard kernel, and showing $f_V(E_\gamma)=f_A(E_\gamma)$ at leading order. It includes one-loop corrections and all-orders Sudakov resummation, which suppresses the spectrum at large $E_\gamma$. A practical framework is developed to extract the CKM element $|V_{ub}|$ by comparing B- and D-based radiative decays, with a model-independent bound on the hadronic input via positivity of the B-meson wave function. The work connects a clean QCD-based description of the nonperturbative input to CKM phenomenology, while highlighting the role of higher-twist corrections and the complementarity with low-energy approaches.

Abstract

We compute the form factors parametrizing radiative leptonic decays of heavy mesons B^+\toγe^+νfor photon energies much larger than Λ_{QCD}, where perturbative QCD methods for exclusive processes can be combined with the heavy quark effective theory. The form factors can be reliably obtained in this region in an expansion in powers of Λ/E_γ. The leading term in this expansion displays an additional spin symmetry manifested in the equality of form factors of vector and axial currents. The leading twist form factors can be written as the convolution of the B meson light-cone wave function with a hard scattering amplitude, which is explicitly calculated to one-loop order. The Sudakov double logarithms of the form (\frac{α_s}π\log^2\frac{2E_γ}Λ)^n are resummed to all orders. As an application we present a method for determining the CKM matrix element |V_{ub}| from a comparison of photon spectra in B and D radiative leptonic decays.

Figures (4)

• Figure 1: Leading order diagrams contributing to the radiative leptonic decay $B^+\to W\gamma$. The double line denotes the heavy quark $b$, the zigzag line the W boson and the wiggly line a photon.
• Figure 2: One-loop corrections to the radiative leptonic decay $B^+\to W\gamma$. The curly line represents a gluon. The quark wave function renormalization corrections are not shown.
• Figure 3: Typical leading twist form factors $f_i(E_\gamma)$$(i=V,A)$ for $B\to \gamma e\nu$ decays. The continuous line shows the tree-level result, the dotted line includes one-loop corrections to the hard scattering amplitude, and the dashed line includes the resummed Sudakov form factor truncated with a cut-off at $(k_+)_{min}= \Lambda_{QCD}$. We use $\alpha_s(m_b)=0.3$ and $a=0.36$ GeV, $\omega=0.2$ GeV, corresponding to $\bar{\Lambda}=0.35$ GeV.
• Figure 4: The photon spectrum in $B^+\to\gamma e^+\nu$ normalized to the pure muonic leptonic decay rate. The continuous line represents the tree-level result, assuming $R=3$ GeV$^{-1}$. The dotted line includes the effects of the one-loop strong correction (only the logarithms) with $\alpha_s(m_b)=0.3$, and the dashed line includes the resummed Sudakov logs. The same parameters are used for the light-cone $B$ wave function as in Fig. 3.