Multi-parton contributions to $\bar{B}\to X_s\gamma$ at NLO

Abstract

Many contributions to the decay rate of the inclusive radiative $\bar{B}\to X_s\gamma$ transition have been calculated to NNLO in QCD during the past decades. However, there are still a few unknown contributions from multi-parton final states which are formally NLO. In the present work, we compute those four-body $b\to sq\bar{q}\gamma$ contributions at NLO in QCD which need to be supplemented by the five-body $b\to sq\bar{q}g\gamma$ bremsstrahlung. This calculation formally completes the purely perturbative contributions to $\bar{B}\to X_s\gamma$ at NLO. Our results are obtained by applying modern techniques of integral reduction and evaluation of master integrals. In particular, the analytic integration over the four and five-particle phase space in the presence of a cut on the photon energy turns out to be technically involved. We give our results completely analytically in terms of multiple polylogarithms, including the dependence on the collinear logarithms which arise from the mass-regularisation of collinear divergences. The numerical impact of multi-parton corrections on the $\bar{B}\to X_s\gamma$ decay rate turns out to be small, owing to a partial cancellation between LO and NLO contributions.

40 pages, 11 figures, 1 table. v2: Minor modifications, matches published version

References in corpus (14)

• Updated NNLO QCD predictions for the weak radiative B-meson decays
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Feynman Diagrams and Differential Equations
• Reducing differential equations for multiloop master integrals
• Fully differential NLO predictions for the rare muon decay
• Chromomagnetic Dipole-Operator Corrections in Bbar -> X_sgamma at O(beta_0 alpha_s^2)
• An observation on Feynman diagrams with axial anomalous subgraphs in dimensional regularization with an anticommuting ${\gamma }_5$
• Dark matter decay through gravity portals
• Next-to-leading order prediction for the decay $\mu \to e(e^{+}{e}^{-})\nu \bar{\nu }$
• Cutting massless four-loop propagators
• A Procedure g5anchor to Anchor ${\gamma }_5$ in Feynman Diagrams for the Standard Model
• Specific three-loop contributions to $b\to s\gamma$ associated with the current-current operators
• The Q_{1,2}-Q_7 interference contributions to b -> s gamma at O(alpha_s^2) for the physical value of m_c
• Renormalisation group evolution of the shape function $g_{17}$ in $\bar{B}\to X_s\gamma$ and $\bar{B}\to X_s{\ell }^{+}{\ell }^{-}$ at subleading power