Quark-quark-gluon vertex for heavy quarks up to order 1/m^5

Abstract

Instead of the often used Foldy-Wouthuysen-Tani (FWT) transformation in non-relativistic quantum chromodynamics (NRQCD), we take a more general relation between the relativistic and non-relativistic on-shell spinors to recalculate the quark-quark-gluon vertex for heavy quarks. In comparison with the previous result using FWT, the recalculated coefficients in the NRQCD Lagrangian are different at order $1/m^3$ and new at order $1/m^4$ and $1/m^5$, where $m$ is the heavy quark mass.