Radiative leptonic decays ofBmesons in QCD

We compute the form factors parametrizing radiative leptonic decays of heavy mesons $B^{+}\to \gamma e^{+}\nu$ for photon energies much larger than ${\Lambda }_{\mathrm{QCD}},$ 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 $\Lambda {/E}_{\gamma }.$ The leading term in this expansion displays an additional spin symmetry manifested in the equality of form factors of vector and axial vector 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 $\left[\right({\alpha }_s/\pi ){\log }^2{(2E}_{\gamma }/\Lambda ){]}^n$ are resummed to all orders. As an application we present a method for determining the CKM matrix element $|V_{\mathrm{ub}}|$ from a comparison of photon spectra in B and D radiative leptonic decays.