A Closer Look at Gluons 3
A Closer Look at Gluons 1 Chapter 6 ACLOSER LOOK AT GLUONS Sadataka Furui* (formerly) Teikyo University, Graduate School of Science and Engineering Utsunomiya, Tochigi, Japan Abstract: Gluons are strong interaction gauge fields which interact between quarks, i.e. constituents of baryons and mesons. Interaction of matters is phenomenologically described by gauge theory of strong, electromagnetic, weak and gravitational interactions. In electro- weak theory, left handed leptons lL and neutrino νL, right handed leptons lR and left handed quarks u , d and right handed quarks u , d follow SU(2) U(1) symmetry. Charge of L L R R × leptons and quarks define hypercharge Y , and via Higgs mechanism SU(2) U(1) L × Y symmetry forms U(1)em symmetry. Presence of J P = 3/2+ baryons, or N ∗++ uuu suggests a new degree of free- ∼ dom “color” for quarks, which follows SU(3) symmetry group. Hence the gluon fields are expressed as a where a = 1, 2, , 8 specify the color SU(3) bases, and µ are 4- Aµ · · · dimensional space-time coordinates. The quantum electrodynamics was extended to quan- tum chromo dynamics (QCD). Since ∂µ a is not a free field, the gauge theory requires Aµ ghosts that compensates unphysical degrees of freedom of gluons. Gluons, ghosts, leptons and quarks are related by Becchi-Rouet-Stora -Tyuitin (BRST) transformation of electro- weak and strong interaction of the U(1) SU(2) SU(3) symmetric Faddeev-Popov × × Lagrangian. In order to describe Hadron dynamics properly, embedding of 4-dimensional space to 5-dimensional space was tried in lattice simulations, and in light front holographic QCD (LFHQCD) approach in which conformally symmetric light-front dynamics without ghost are embedded in AdS5, and a parameter that fixes a mass scale was chosen from the Prin- ciple of Maximum Conformality.
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