Renormalization Group Equation and QCD Coupling Constant in the Presence of SU(3) Chromo-Electric Field

Abstract

We solve renormalization group equation in QCD in the presence of SU(3) constant chromo-electric field E^a with arbitrary color index a=1,2,...8 and find that the QCD coupling constant \alpha_s depends on two independent casimir/gauge invariants C_1=[E^aE^a] and C_2=[d_{abc}E^aE^bE^c]^2 instead of one gauge invariant C_1=[E^aE^a]. The \beta function is derived from the one-loop effective action. This coupling constant may be useful to study hadron formation from color flux tubes/strings at high energy colliders and to study quark-gluon plasma formation at RHIC and LHC.