Consistency and lattice renormalization of the effective theory for heavy quarks

Abstract

The effective theory describing infinite mass particles with a given velocity, has a great interest in heavy flavor physics. It has the unpleasant characteristic that the energy spectrum is unbounded from below; this fact is the source of the problems in the formulation of the euclidean theory. In this paper we present an analysis of the euclidean effective theory, that is rather complete and has positive conclusions. A proof of the consistency of the euclidean theory is presented and a technique for the evaluation of the amplitudes in perturbation theory is described. We compute also the one-loop renormalization constants of the lattice effective theory and of the heavy-heavy current that is needed for the determination of the Isgur-Wise function. A variety of effects related to the explicit breaking of the Lorentz symmetry of lattice regularization is demonstrated. The most peculiar phenomenon is that the heavy quark velocity receives a finite renormalization. Finally, we compute the lattice-continuum renormalization constant of the Isgur-Wise current. It is needed for the conversion of the values of the matrix elements computed with the lattice effective theory, to the values in the full theory.

28 pages, Latex version 2.09, SISSA 56/93/EP

Cited by in corpus (20)

• Large-Momentum Effective Theory
• TMD Soft Function from Large-Momentum Effective Theory
• Renormalons and the Heavy Quark Effective Theory
• Lattice Heavy Quark Effective Theory and the Isgur-Wise function
• Moving NRQCD for heavy-to-light form factors on the lattice
• The structure function of semi-inclusive heavy flavour decays in field theory
• The Invisible Renormalon
• Heavy-light mesons in the epsilon-regime
• Matching of the Shape Function
• Perturbative renormalization for static and domain-wall bilinears and four-fermion operators with improved gauge actions
• Semileptonic Decays: an Update Down Under
• Next-to-leading resummed coefficient function for the shape function
• Non-Perturbative Evaluation of the Physical Classical Velocity in the Lattice Heavy Quark Effective Theory
• Renormalization of the Lattice HQET Isgur-Wise Function
• Lattice HQET Calculation of the Isgur-Wise Function
• Renormalization of the effective theory for heavy quarks at small velocity
• Non-Perturbative Renormalization of the Lattice Heavy Quark Classical Velocity
• Assorted weak matrix elements involving the bottom quark
• B meson form factors from HQET simulations
• Revisiting the time-ordering issue of TMD soft factors: causality, coordinate space analyticity and new equalities