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Instead of the often used Foldy-Wouthuysen-Tani (FWT) transformation innon-relativistic quantum chromodynamics (NRQCD), we take a more generalrelation between the relativistic and non-relativistic on-shell spinors torecalculate the quark-quark-gluon vertex for heavy quarks. In comparison withthe previous result using FWT, the recalculated coefficients in the NRQCDLagrangian 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.

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