Relativistic heavy quarks on the lattice

Lattice QCD is expected to provide the opportunity of precise evaluation for weak matrix elements associated with B mesons from first principles. The main obstacle on the way is the systematic errors originating from large mba errors. At present this difficulty is avoided in most cases by employing the nonrelativistic approaches[1,2]. On the other hand, the use of anisotropic lattice[3] has a fascinating feature to allow us to take the continuum limit. However, there exists a theoretical concern whether or notmQas errors could revive perturbatively or nonperturbatively even after they are removed classically. Unfortunately, our one-loop calculation of the quark self energy strongly suggests that radiative corrections allow the revival of mQas errors. Having found that the anisotropic lattice is not theoretically advantageous over the isotropic one, we propose a new relativistic way to deal with the heavy quarks on the isotropic lattice. Cutoff effects in the heavy quark system are discussed by applying the on-shell improvement program[4,5] to the finite mQa case. We show that a proper adjustment of four parameters in the quark action reduces the remaining cutoff effects to be O((aΛQCD) ). We also demonstrate a determination of the four parameters at the tree-level from the on-shell quark-quark scattering amplitude. In this report we present the salient points in our work[6]. 2. ANISOTROPIC LATTICE