Relativistic Heavy Quark Effective Action

Details Relativistic Heavy Quark Effective Action Relativistic Heavy Quark Effective Action

2006-08-08

arxiv.org/abs/hep-lat/0608006v1

Phys.Rev.D76:074505,2007

Physics

High Energy Physics

High Energy Physics - Lattice

40 pages, 1 figure

Scientific paper

10.1103/PhysRevD.76.074505

We study the fermion action needed to accurately describe the low energy physics of systems including heavy quarks in lattice QCD even when the heavy fermion mass $m$ is on the order of, or larger than, the inverse lattice spacing: $m \ge 1/a$. We carry out an expansion through first order in $|\vec p| a$ (where $\vec p$ is the heavy quark momentum) and all orders in $ma$, refining the analysis of the Fermilab and Tsukuba groups. We demonstrate that the spectrum of heavy quark bound states can be determined accurately through $|\vec p| a$ and $(ma)^n$ for arbitrary exponent $n$ by using a lattice action containing only three unknown coefficients: $m_0$, $\zeta$ and $c_P$ (a generalization of $c_{SW}$), which are functions of $ma$. In a companion paper, we show how these three coefficients can be precisely determined using non-perturbative techniques.

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