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

TL;DR

This paper derives how the QCD coupling constant varies in the presence of a constant SU(3) chromo-electric field, revealing dependence on two invariants and providing insights for high-energy collider phenomena.

Contribution

It introduces a novel solution to the renormalization group equation in QCD with a chromo-electric field, showing the coupling depends on two invariants instead of one.

Findings

QCD coupling depends on two invariants C_1 and C_2 in a chromo-electric field.

Derived the eta function from the one-loop effective action.

Potential applications in studying hadron formation and quark-gluon plasma.

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.