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 \( {B}^{-}\to \left({\mu}^{-},{\tau}^{-}\right)\overline{\nu}\left(\gamma \right) \) in differential and integrated form as a function of the photon energy cut-off \( {E}_{\gamma}^{\textrm{cut}} \). 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 \( {\left.{E}_{\gamma}^{\textrm{cut}}\right|}_{\mu } \) > 0.18(3) GeV and is subdominant for the tau channel even when fully inclusive.
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Acknowledgments
RZ is supported by an STFC Consolidated Grant, ST/P0000630/1. We are grateful to Will Barter and Franz Muheim for discussions. In addition we acknowledge Saad Nabeebaccus for useful discussions and comments on the manuscript. Many loop computations are performed with the FeynCalc package [94, 95] and Package-X [96].
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Rowe, M., Zwicky, R. Structure-dependent QED in \( {B}^{-}\to {\ell}^{-}\overline{\nu}\left(\gamma \right) \). J. High Energ. Phys. 2024, 249 (2024). https://doi.org/10.1007/JHEP07(2024)249
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DOI: https://doi.org/10.1007/JHEP07(2024)249