Structure-dependent QED in B−→ℓ−ν¯γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}^{-}\ o {\\ell}^{-}\\overline{\ u}\\left(\\gamma \\right) $$\\end{document}

Abstract

Based on explicitly gauge invariant interpolating operators we compute complete next-leading order QED-corrections for leptonic decays. These are sizeable since the helicity-suppression in V-A interactions allows for structure-dependent collinear logs. We have explicitly checked that these logs are absent for helicity-unsuppressed Yukawa-type transitions. Based on B → γ form factors we present the rates for B−→μ−τ−ν¯γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {B}^{-}\ o \\left({\\mu}^{-},{\ au}^{-}\\right)\\overline{\ u}\\left(\\gamma \\right) $$\\end{document} in differential and integrated form as a function of the photon energy cut-off Eγcut\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {E}_{\\gamma}^{\ extrm{cut}} $$\\end{document}. The effect of the virtual structure-dependent corrections are approximately +5% and +3% for the μ- and τ-channel respectively. The structure dependence of the real radiation exceeds that of the virtual one for Eγcutμ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\left.{E}_{\\gamma}^{\ extrm{cut}}\\right|}_{\\mu } $$\\end{document}> 0.18(3) GeV and is subdominant for the tau channel even when fully inclusive.