The photon energy spectrum in $B\to X_s\gamma$ at N${}^3$LL${}^{\prime }$

Abstract

We present predictions for the photon energy spectrum in inclusive $B\to X_s\gamma$ decays mediated by the electromagnetic penguin operator $O_7$ to N${}^3$LL${}^{\prime }$. We use soft-collinear effective theory (SCET) to resum the singular contributions in the peak region at large photon energy. In the tail region the resummed predictions are matched to fixed order at N${}^3$LO, where we include the known fixed-order contributions for $O_7$ up to $\mathcal{O}({\alpha }_s^2)$. We develop a method to suitably parametrize the still unknown $\mathcal{O}({\alpha }_s^3)$ nonsingular corrections in terms of theory nuisance parameters, whose variations provide an estimate of the associated theory uncertainty. In this context, we also study different ways to treat higher-order cross terms in the matching. Another important aspect of our analysis is the short-distance scheme used for the $b$-quark mass $m_b$. We find that in the present context, the 1$S$ mass scheme, which was previously used up to 2-loop order, fails to work at 3-loop order, because the mass scheme enters at a soft scale much smaller than $m_b$ here, for which the 1$S$ scheme was not devised. Using instead the MSR mass scheme with $R\sim 1\mathrm{GeV}$, we obtain stable results with good perturbative convergence up to N${}^3$LL${}^{\prime }$.

arXiv comment12 figures, 35 pages + appendix

References in corpus (39)

• An effective field theory for collinear and soft gluons: heavy to light decays
• Soft-Collinear Factorization in Effective Field Theory
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• The four-loop beta-function in Quantum Chromodynamics
• The three-loop QCD $\beta$-function and anomalous dimensions
• The Four-Loop QCD Beta-Function and Anomalous Dimensions
• Updated NNLO QCD predictions for the weak radiative B-meson decays
• Weak Radiative Decays of the B Meson and Bounds on $M_{H^{\pm }}$ in the Two-Higgs-Doublet Model
• On the Motion of Heavy Quarks inside Hadrons: Universal Distributions and Inclusive Decays
• Analysis of the Photon Spectrum in Inclusive $B\to X_s\gamma$ Decays
• Treating the b quark distribution function with reliable uncertainties
• Factorization and Shape-Function Effects in Inclusive B-Meson Decays
• QCD-Based Interpretation of the Lepton Spectrum in Inclusive $\bar{B}\to X_u\ell \bar{\nu }$ Decays
• Top Jets in the Peak Region: Factorization Analysis with NLL Resummation
• B decay and the Upsilon mass
• Toward a NNLO calculation of the B-->X_s+gamma decay rate with a cut on photon energy: II. Two-loop result for the jet function
• Cusp and collinear anomalous dimensions in four-loop QCD from form factors
• B decays in the upsilon expansion
• Infrared factorization in inclusive B meson decays
• Renormalization-Group Improved Calculation of the B->Xs+gamma Branching Ratio
• Infrared Renormalization Group Flow for Heavy Quark Masses
• Top Quark Pair Production close to Threshold: Top Mass, Width and Momentum Distribution
• Toward a NNLO calculation of the B-->X_s gamma decay rate with a cut on photon energy: I. Two-loop result for the soft function
• The Residual Mass Term in the Heavy Quark Effective Theory
• Higher Order $1/m$ Corrections at Zero Recoil
• Top Quark Mass Calibration for Monte Carlo Event Generators
• Non-Abelian Dipole Radiation and the Heavy Quark Expansion
• The photon energy spectrum in B-> X_s + γin perturbative QCD through O(α_s^2)
• The Three-loop Quark Jet Function
• Evolution of the Light Cone Distribution Function for a Heavy Quark
• Magnetic dipole operator contributions to the photon energy spectrum in anti-B -> X(s) gamma at O(alpha(s)^2)
• The MSR Mass and the $\mathcal{O}({\Lambda }_{\mathrm{QCD}})$ Renormalon Sum Rule
• Radiative B decay spectrum: DGE at NNLO
• Higher-Order Sudakov Resummation in Coupled Gauge Theories
• Exploring the Invisible Renormalon: Renormalization of the Heavy-Quark Kinetic Energy
• Three-loop soft function for heavy-to-light quark decays
• The Invisible Renormalon
• Complete O(alpha_s^2) Corrections to Zero-Recoil Sum Rules for B-->D* Transitions
• Analytic results for Sudakov form factors in QCD

Cited by in corpus (2)

• Robust estimates of theoretical uncertainties at fixed-order in perturbation theory
• The Q_{1,2}-Q_7 interference contributions to b -> s gamma at O(alpha_s^2) for the physical value of m_c