Heavy and Light Quarks with Lattice Chiral Fermions

TL;DR

This paper investigates the use of lattice chiral fermions, specifically overlap fermions, for both heavy and light quarks, demonstrating small discretization errors and extending the viable mass range for accurate calculations in lattice QCD.

Contribution

It shows that lattice chiral fermions can be effectively used for heavy and light quarks without mass-dependent tuning, with errors comparable to or smaller than improved Wilson actions.

Findings

Errors in dispersion relations are small for $O(m^2a^2)$ terms.

The applicable $ma$ range can be extended to ~0.56 with only 5% error.

The generalized Gell-Mann-Oakes-Renner relation helps determine finite $ma$ errors.

Abstract

The feasibility of using lattice chiral fermions which are free of $O(a)$ errors for both the heavy and light quarks is examined. The fact that the effective quark propagators in these fermions have the same form as that in the continuum with the quark mass being only an additive parameter to a chirally symmetric antihermitian Dirac operator is highlighted. This implies that there is no distinction between the heavy and light quarks and no mass dependent tuning of the action or operators as long as the discretization error $O(m^2 a^2)$ is negligible. Using the overlap fermion, we find that the $O(m^2a^2)$ (and $O(ma^2)$) errors in the dispersion relations of the pseudoscalar and vector mesons and the renormalization of the axial-vector current and scalar density are small. This suggests that the applicable range of $ma$ may be extended to $\sim 0.56$ with only 5% error, which is a factor of $\sim 2.4$ larger than that of the improved Wilson action. We show that the generalized Gell-Mann-Oakes-Renner relation with unequal masses can be utilized to determine the finite $ma$ errors in the renormalization of the matrix elements for the heavy-light decay constants and semileptonic decay constants of the B/D meson.