Renormalization group equation and QCD coupling constant in the presence of SU(3) chromo-electric field

• Published in: The European physical journal. C, Particles and fields Particles and fields, 2009-11, Vol.64 (1), p.73-79, Article 73
• Main Author: Nayak, Gouranga C.
• Format: Article
• Language: English
• Subjects: Astronomy; Astrophysics and Cosmology; Color; Coupling; Electric fields; Elementary Particles; Exact sciences and technology; Flux; Gages; Gauges; Gluons; Hadrons; Heavy Ions; Invariants; Joining; Large Hadron Collider; Mathematical analysis; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quark-gluon plasma; Regular Article - Theoretical Physics; String Theory; Strings; The physics of elementary particles and fields; Tubes
• ISSN: 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-009-1119-7

We solve the renormalization group equation in QCD in the presence of a SU(3) constant chromo-electric field E a with arbitrary color index a =1,2,…,8 and find that the QCD coupling constant α s depends on two independent Casimir/gauge invariants C 1 =[ E a E a ] and C 2 =[ d abc E a E b E c ] 2 instead of one gauge invariant C 1 =[ E a E a ]. The β 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.