Leading logarithms of the $b$ quark mass in inclusive $B\to X_s\gamma$ decay

Abstract

Part of the order ${\alpha }_s$ correction to the inclusive $B\to X_s\gamma$ photon spectrum is enhanced by $\log (m_b^2/m_s^2)$. We discuss its origin and sum the corrections proportional to $[{\alpha }_s\log (m_b^2/{\mu }^2){]}^n$ to all orders. These are the calculable leading logarithms in the parton fragmentation functions of a quark or gluon into a photon. Although the gluon fragmentation into a photon starts only at order ${\alpha }_s^2$, its contribution is of the same order as the $s$ quark's in the leading log sum. For not too small values of the photon energy, the resummation yields a moderate suppression. In the standard model, the coefficient of the operator whose matrix element gives rise to such terms is small. A measurement of the photon spectrum around $1$GeV would provide a theoretically clean determination of $C_8$, the Wilson coefficient of the $b\to sg$ operator.

12 pages revtex, 2 figures included

References in corpus (2)

• Two-loop mixing of dimension-five flavor-changing operators
• Moments of the photon spectrum in the inclusive $B\to X_s\gamma$ decay

Cited by in corpus (29)

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• Weak Radiative B-Meson Decay Beyond Leading Logarithms
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• Flavor Physics in the Quark Sector
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• Renormalization-Group Improved Calculation of the B->Xs+gamma Branching Ratio
• Towards B -> X_s gamma at the NNLO in QCD without interpolation in m_c
• Factorization at Subleading Power and Irreducible Uncertainties in $\bar{B}\to X_s\gamma$ Decay
• Bremsstrahlung corrections to the decay $b\to s\gamma$
• B, D and K decays
• Comment on nonperturbative effects in $B\to X_s\gamma$
• The B -> X_s gamma Photon Spectrum
• Enhanced Non-local Power Corrections to the B->X_s+gamma Decay Rate
• Completing the Calculation of BLM corrections to B -> Xs gamma
• Chromomagnetic Dipole-Operator Corrections in Bbar -> X_sgamma at O(beta_0 alpha_s^2)
• Large-m_c Asymptotic Behaviour of O(alpha_s^2) Corrections to B -> X_s gamma
• Tree-level contributions to B -> Xs gamma
• Reevaluating Uncertainties in $\bar{B}\to X_s\gamma$ Decay
• Precision Global Determination of the $B\to X_s\gamma$ Decay Rate
• Phase space analysis for three and four massive particles in final states
• Refactorisation in subleading $\bar{B}\to X_s\gamma$
• Tree-level contribution to \bar{B} -> X_d gamma using fragmentation functions
• Determination of the HQET Parameters from the $B\to X_s\gamma$ Decay
• Rare decays $\bar{B}\to X_{s(d)}\gamma$ at the NLO
• NLL QCD contribution of the Electromagnetic Dipole operator to B-> X_s gamma gamma
• NLL QCD contribution of the electromagnetic dipole operator to B -> X_s gamma gamma with a massive strange quark
• Light masses in short distance penguin loops
• (O_8, O_8) contribution to $\bar{B}\to X_s\gamma \gamma$ at O(α_s)
• Multi-parton contributions to $\bar{B}\to X_s\gamma$ at NLO