QED factorization of two-body non-leptonic and semi-leptonic B to charm decays

• Published in: The journal of high energy physics 2021-10, Vol.2021 (10), p.1-23, Article 223
• Main Authors: Beneke, Martin, Böer, Philipp, Finauri, Gael, Vos, K. Keri
• Format: Article
• Language: English
• Subjects: Amplitudes; Charm (particle physics); Classical and Quantum Gravitation; Decay rate; Elementary Particles; Factorization; High energy physics; Leptons; Light; Physics; Physics and Astronomy; QCD Phenomenology; Quantum chromodynamics; Quantum electrodynamics; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Quarks; Regular Article - Theoretical Physics; Relativity Theory; String Theory
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP10(2021)223

A bstract The QCD × QED factorization is studied for two-body non-leptonic and semi-leptonic B decays with heavy-light final states. These non-leptonic decays, like B ¯ s 0 → D s + π − and B ¯ d 0 → D + K − , are among the theoretically cleanest non-leptonic decays as penguin loops do not contribute and colour-suppressed tree amplitudes are suppressed in the heavy-quark limit or even completely absent. Advancing the theoretical calculations of such decays requires therefore also a careful analysis of QED effects. Including QED effects does not alter the general structure of factorization which is analogous for both semi-leptonic and non-leptonic decays. For the latter, we express our result as a correction of the tree amplitude coefficient a 1 . At the amplitude level, we find QED effects at the sub-percent level, which is of the same order as the QCD uncertainty. We discuss the phenomenological implications of adding QED effects in light of discrepancies observed between theory and experimental data, for ratios of non-leptonic over semi-leptonic decay rates. At the level of the rate, ultrasoft photon effects can produce a correction up to a few percent, requiring a careful treatment of such effects in the experimental analyses.