Exploring the Invisible Renormalon: Renormalization of the Heavy-Quark Kinetic Energy

Abstract

Using the virial theorem of the heavy-quark effective theory, we show that the mixing of the operator for the heavy-quark kinetic energy with the identity operator is forbidden at the one-loop order by Lorentz invariance. This explains why such a mixing was not observed in several one-loop calculations using regularization schemes with a Lorentz-invariant UV regulator, and why no UV renormalon singularity was found in the matrix elements of the kinetic operator in the bubble approximation (the ``invisible renormalon''). On the other hand, we show that the mixing is not protected in general by any symmetry, and it indeed occurs at the two-loop order. This implies that the parameter ${\lambda }_1^H$ of the heavy-quark effective theory is not directly a physical quantity, but requires a non-perturbative subtraction.

13 pages, 3 figures

References in corpus (5)

• Implications of the $B\to X\ell {\bar{\nu }}_{\ell }$ lepton spectrum for heavy quark physics
• B Decays and CP Violation
• On The Difficulty of Computing Higher-Twist Corrections
• Perturbative corrections to zero recoil inclusive $B$ decay sum rules
• On the $b-$ Quark Kinetic Energy in the ${\Lambda }_b$

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• The bottom quark mass from the ${\rm Y}(1S)$ system at NNNLO
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• Two-Loop Relations for Heavy-Quark Parameters in the Shape-Function Scheme
• Relations between Heavy-light Meson and Quark Masses
• Calculation of binding energies and masses of quarkonia in analytic QCD models
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• UV contributions to energy of a static quark-antiquark pair in large ${\beta }_0$ approximation
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