Gauge dependence and matching procedure of a nonrelativistic QED-QCD boundstate formalism - art. no. 105001

A nonrelativistic bound state formalism used in contemporary calculations i s investigated. It is known that the effective Hamiltonian of the bound sta te system depends on the choice of gauge. We obtain the transformation char ge Q of the Hamiltonian for an arbitrary infinitesimal change of gauge, by which gauge independence of the mass spectrum and gauge dependences of the bound state wave functions are dictated. We give formal arguments based on the BRST symmetry supplemented by power countings of Coulomb singularities of diagrams. For illustration, (1) we calculate Q up to O(1/c) and (2) we e xamine the gauge dependences of diagrams for a decay of a q (q) over bar bo und state up to O(1/c) and show that cumbersome gauge cancellations can be circumvented by directly calculating Q. As an application we point out that the present calculations of the top quark momentum distribution in the t ( t) over bar threshold region are gauge dependent. We also show the possibil ities for incorrect calculations of physical quantities of bound states whe n the on-shell matching procedure is employed. We give a proof of a justifi cation for the use of the equation of motion to simplify the form of a loca l NRQCD Lagrangian. The formalism developed in this work will provide usefu l cross-checks in computations involving NRQED or NRQCD bound states.