The Invisible Renormalon

Abstract

We study the structure of renormalons in the Heavy Quark Effective Theory, by expanding the heavy quark propagator in powers of $1/m_Q$. We demonstrate that the way in which renormalons appear depends on the regularisation scheme used to define the effective theory. In order to investigate the relation between ultraviolet renormalons and power divergences of matrix elements of higher-dimensional operators in the heavy quark expansion, we perform calculations in dimensional regularisation and in three different cut-off regularisation schemes. In the case of the kinetic energy operator, we find that the leading ultraviolet renormalon which corresponds to a quadratic divergence, is absent in all but one (the lattice) regularisation scheme. The nature of this ``invisible renormalon'' remains unclear.

20 pages LaTeX, 1 figure available as separate eps file

References in corpus (24)

• Heavy Quark Symmetry
• On the Viability of Lattice Perturbation Theory
• 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
• Reparameterisation Invariance Constraints on Heavy Particle Effective Field Theories
• Differential Distributions in Semileptonic Decays of the Heavy Flavors in QCD
• 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
• Operator Product Expansion for Inclusive Semileptonic Decays in Heavy Quark Effective Field Theory
• Scale Setting in QCD and the Momentum Flow in Feynman Diagrams
• Heavy Quark Expansion for the Inclusive Decay $\bar{B}\to \tau \bar{\nu }X$
• The Residual Mass Term in the Heavy Quark Effective Theory
• Bloch-Nordsieck cancellations beyond logarithms in heavy particle decays
• Cancellation of Renormalon Ambiguities in the Heavy Quark Effective Theory
• Renormalons in Effective Field Theories
• Extracting $|V_{bc}|$, $m_c$ and $m_b$ from Inclusive $D$ and $B$ Decays
• Renormalons and the Heavy Quark Effective Theory
• Phenomenological Constraints on $\bar{\Lambda }$ and ${\lambda }_1$
• Consistency and lattice renormalization of the effective theory for heavy quarks
• A new formulation of the effective theory for heavy particles

Cited by in corpus (18)

• Renormalons
• Treating the b quark distribution function with reliable uncertainties
• Factorization and Shape-Function Effects in Inclusive B-Meson Decays
• Theory of Charmless Inclusive B Decays and the Extraction of V_{ub}
• Renormalization-Group Improved Calculation of the B->Xs+gamma Branching Ratio
• On The Difficulty of Computing Higher-Twist Corrections
• Advanced Predictions for Moments of the B->X_s+gamma Photon Spectrum
• Order alpha_s^2 beta_0 Correction to the Charged Lepton Spectrum in b \to c \ell \barν_\ell decays
• Two-Loop Relations for Heavy-Quark Parameters in the Shape-Function Scheme
• A High-Statistics Lattice Calculation of ${\lambda }_1$ and ${\lambda }_2$ in the $B$ meson
• Exploring the Invisible Renormalon: Renormalization of the Heavy-Quark Kinetic Energy
• Radiative and semi-leptonic B-meson decay spectra: Sudakov resummation beyond logarithmic accuracy and the pole mass
• Asymptotics of QCD Factorization in Exclusive Hadronic Decays of B Mesons
• Spin-Flip Interactions and the Puzzle of psi's Polarization at Tevatron
• The photon energy spectrum in $B\to X_s\gamma$ at N${}^3$LL${}^{\prime }$
• Alternative Treatment of the Quark Mass in the Heavy Quark Expansion
• Soft-Collinear Factorization and Sudakov Resummation of Heavy Meson Decay Amplitudes with Effective Field Theories
• Theory of Inclusive B Decays