Renormalized sum rules for structure functions of heavy mesons decays

Abstract

We consider properties of the structure functions of inclusive heavy meson decays $B\to X_c$ and treat the $c$ quark mass as a free parameter. We show that in two extreme cases of heavy and light $c$ quark the structure functions of heavy--heavy and heavy--light transitions are given by a Fourier transform of the matrix elements of Wilson lines containing a time--like and a light--like segment, correspondingly. Using the renormalization properties of Wilson lines we find the dependence of the structure functions on the factorization scale, the structure function of heavy--heavy transition is renormalized multiplicatively while that of heavy-light transition obeys the GLAP--type evolution equation. We propose a generalization of the sum rules for the moments of the structure functions (Bjorken, Voloshin, and the ``third'' sum rules) with a soft exponential factorization cut--off, which correctly incorporates both perturbative and nonperturbative effects. We analyze nonperturbative corrections by first considering infrared renormalon contributions to the Wilson lines. Uncertainties induced by the leading renormalon pole at $u=\frac{1}{2}$ are exactly cancelled by the similar uncertainty in the heavy quark pole mass. The leading nonperturbative corrections associated with the next renormalon at $u=1$ are parameterized by the matrix element ${\mu }_{\pi }^2$ which is proportional to the heavy quark kinetic energy.

20 pages, LaTeX style

References in corpus (17)

• QCD Predictions for Lepton Spectra in Inclusive Heavy Flavour Decays
• Inclusive Semileptonic B and Polarized Lambda_b Decays from QCD
• Nonperturbative Corrections to Inclusive Beauty and Charm Decays: QCD versus Phenomenological Models
• Heavy Quark Effective Theory beyond Perturbation Theory: Renormalons, the Pole Mass and the Residual Mass Term
• The Pole Mass of The Heavy Quark. Perturbation Theory and Beyond
• Structure functions for large $x$ and renormalization of Wilson loops
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• 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
• Nonperturbative Contributions to the Inclusive Rare Decays $B\to X_s\gamma$ and $B\to X_s{\ell }^{+}{\ell }^{-}$
• QCD-Based Interpretation of the Lepton Spectrum in Inclusive $\bar{B}\to X_u\ell \bar{\nu }$ Decays
• Sum Rules for Heavy Flavor Transitions in the SV Limit
• Infrared factorization in inclusive B meson decays
• Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays
• Resummation of Nonperturbative Corrections to the Lepton Spectrum in Inclusive $B\to X\ell \bar{\nu }$ Decays
• Gauge Invariance and Anomalous Dimensions of a Light-Cone Wilson Loop in Light-Like Axial Gauge
• How to Measure Kinetic Energy of the Heavy Quark Inside B Mesons?

Cited by in corpus (35)

• Summing Sudakov logarithms in B -> X_s + gamma in effective field theory
• Asymptotics of Heavy-Meson Form Factors
• Heavy-to-Light Form Factors in the Final Hadron Large Energy Limit of QCD
• Precision Corrections to Dispersive Bounds on Form Factors
• Factorization and Shape-Function Effects in Inclusive B-Meson Decays
• The B-Meson Distribution Amplitude in QCD
• 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
• Event shapes in e+e- annihilation and deep inelastic scattering
• Collinear effective theory at subleading order and its application to heavy-light currents
• Renormalization-Group Improved Calculation of the B->Xs+gamma Branching Ratio
• 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
• High Power n of m_b in Beauty Widths and n=5 -> oo Limit
• Effective Predictions of Event Shapes: Factorized, Resummed, and Gapped Angularity Distributions
• Evolution of the Light Cone Distribution Function for a Heavy Quark
• Consistent Factorization of Jet Observables in Exclusive Multijet Cross-Sections
• NNLO corrections to B --> X_u l nu in the shape-function region
• On the quark distribution in an on-shell heavy quark and its all-order relations with the perturbative fragmentation function
• The structure function of semi-inclusive heavy flavour decays in field theory
• Renormalisation of heavy-light light ray operators
• One Interesting New Sum Rule Extending Bjorken's to order {1/m_Q}
• Systematic Parametrization of the Leading $B$-meson Light-Cone Distribution Amplitude
• Corrections to the Bjorken and Voloshin sum rules
• Refactorisation in subleading $\bar{B}\to X_s\gamma$
• Semileptonic inclusive heavy meson decay: duality in a nonrelativistic potential model in the Shifman-Voloshin limit
• Evolution equation for the B-meson distribution amplitude in the heavy-quark effective theory in coordinate space
• More Conservation Laws and Sum Rules in the Heavy Quark Limit
• Isgur-Wise functions and unitary representations of the Lorentz group : the baryon case j = 0
• Perturbative Corrections to a Sum Rule for the Heavy Quark Kinetic Energy
• Subleading form factors at order 1/m_Q in terms of leading quantities using the non-forward amplitude in HQET
• Sum rules of Bjorken-Uraltsev type in the Bakamjian-Thomas relativistic quark model
• Soft-Collinear Factorization and Sudakov Resummation of Heavy Meson Decay Amplitudes with Effective Field Theories
• Progress in computing inclusive B decay spectra
• The Large Energy Expansion for B Decays: Soft Collinear Effective Theory
• The Simplest B Decay, Precisely
• Non-Universal Effects in Semi-Inclusive B Decays