Perturbative study of anisotropic lattice actions for heavy quarks

Abstract

The anisotropic lattice fermion actions are investigated with the one-loop perturbative calculations aiming at constructing a formulation for heavy quark with controlled systematic uncertainties.For the heavy-light systems at rest the anisotropic lattice with small temporal lattice spacing a t suppresses the discretization error by a power of a t m Q for a heavy quark of mass m Q . We discuss the issue of large discretization errors, which scales as a s m Q with a s the spatial lattice spacing. By performing one-loop calculations of the speed-of-light renormalization for several possible lattice actions in the limit of a t → 0, we show that one can eliminate the large systematic error on the anisotropic lattice.

Nonperturbative study of the action parameters for anisotropic-lattice quarks

“…These expressions are consistent with those obtained in Ref. [6] for the sD34 action and in Ref. [24] for the Fermilab action on an isotropic lattice.…”

“…Section III compares this action with the sD34 action proposed in Ref. [6] and details some analytic results. Results from a study of the dispersion relations and the mass-dependence of the speed of light are described in Sec.…”

A Numerical Study of Improved Quark Actions on Anisotropic Lattices

“…We have also tried another (conventional) way of extracting the Z parameters, namely by using only the zero-momentum point and the lowest non-vanishing momentum point (n = (0, 0, 1) in this case). This is what has been done in the literature by many authors [12,24,25,26]. We find that the Z parameters are always better determined by using linear fits with more momentum points as compared with only two lowest momentum points.…”

“…However, in order to take full advantage of the improved quark action on anisotropic lattices, some parameters in the action have to be determined, either perturbatively or non-perturbatively, in order to gain as much improvement as possible. Some numerical studies of these parameters have already appeared in the literature [23,12,24,25,26]. The anisotropic quark actions used in these studies fall into two categories.…”

Dynamical QCD simulations on anisotropic lattices

“…The advantages of simulations with anisotropic lattices are well understood and the method has been used for precision determinations of an extensive range of quantities in the quenched approximation to QCD [1][2][3][4][5][6]. In general a 3 1 anisotropy is employed where the lattice spacing in the temporal direction, a t , is made fine while keeping the spatial lattice spacing a s relatively coarse.…”