Relativistic Heavy Quarks on the Lattice

Abstract

Lattice QCD should allow quantitative predictions for the heavy quark physics from first principles. Up to now, however, most approaches have based on the nonrelativistic effective theory, with which the continuum limit can not be taken in principle. In this paper we investigate feasibility of relativistic approaches to the heavy quark physics in lattice QCD. We first examine validity of the idea that the use of the anisotropic lattice could be advantageous to control the $m_Q a$ corrections. Our perturbative calculation, however, reveals that this is not true. We instead propose a new relativistic approach to handle heavy quarks on the isotropic lattice. We explain how power corrections of $m_Q a$ can be avoided and remaining uncertainties are reduced to be of order $(a\Lambda_{QCD})^2$.Comment: 39 pages, 8 figure as eps-fil

A perturbative determination of mass dependent O(a) improvement coefficients in a relativistic heavy quark action

“…Although ν (1) , r (1) s , c (1) E and c (1) B should be determined free from the infrared divergence, we have to deal with it in the process of calculations. Following the method employed in Ref.…”

“…[3], it is sufficient for us to improve each on-shell quark-quark-gluon vertex individually. To determine the one-loop coefficients c (1) E and c (1) B we need six types of diagrams shown in Fig. 9.…”

“…9. We first consider to calculate c (1) B . Without the space-time symmetry the general form of the off-shell vertex function at the one-loop level is written as…”

“…Figure 10 shows the quark mass dependences of c (1) B /c (0) B for the plaquette and the Iwasaki gauge actions. We find relatively modest quark mass dependences for both cases.…”

“…To control this large m Q a corrections a new relativistic approach is proposed from the view point of the on-shell O(a) improvement program [1]. The generic quark action is given by…”