Non-Perturbative Evaluation of the Physical Classical Velocity in the Lattice Heavy Quark Effective Theory

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Abstract
In the lattice formulation of the Heavy Quark Effective Theory, the value of the classical velocity v, as defined through the separation of the 4-momentum of a heavy quark into a part proportional to the heavy quark mass and a residual part which remains finite in the heavy quark limit (P = Mv + p) is different from its value as it appears in the bare heavy quark propagator (S(p) = 1/vp). The origin of the difference, which is effectively a lattice-induced renormalization, is the reduction of Lorentz (or O(4)) invariance to (hyper)-cubic invariance. The renormalization is finite and depends specifically on the form of the discretization of the reduced heavy quark Dirac equation. For the Forward Time - Centered Space discretization, we compute this renormalization non-perturbatively, using an ensemble of lattices at beta = 6.1 provided by the Fermilab ACP-MAPS Collaboration. The calculation makes crucial use of a variationally optimized smeared operator for creating composite heavy-light mesons. It has the property that its propagator achieves an asymptotic plateau in just a few Euclidean time steps. For comparison, we also compute the shift perturbatively, to one loop in lattice perturbation theory. The non-perturbative calculation of the leading multiplicative shift in the classical velocity is considerably different from the one-loop estimate, and indicates that for the above parameters, v is reduced by about 10-13%.

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