  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.
