Stringy confinement of light quarks

Abstract

Linear confining potentials, independent of spin, and conserving chirality are found from the non-perturbative extension of the light front QCD. The V qq potential in baryons is obtained from V q q in mesons by multiplying V q q by 1 2 ( 8 9 ) 2 ≈ 0.4 . In any light meson V q q (r)=λr , λ=(0.13±0.03)GeV 2, if the gluon and quark condensates are 〈|( α s/ π): G μν a G a μν :|〉=(360±20 MeV) 4, 〈| α s : ψψ:|〉=−(240 MeV) 3 , and Λ=150 MeV. For p 2⩽ m p 2 the running quark mass is frozen at the pole value m p= m( p 2=m p 2=331 MeV. Inside mesons, q and q , with an average momentum equal to m p, move in the meson rest frame with velocity 0.7 c, and are “connected” by a string with tension equal to (0.17±0.03) GeV 2. The slope α′ of Regge trajectories, the quark and gluon condensates, and the frozen coupling constant α s= α s( p 2= m p 2) obey by the relation α′〈|(α s /π):G μν aG a μν:|〉=( 16 9π )(3πα s 2) − 1 3 (〈| α s : ψψ:|〉) 2 3 giving α′=(1.0±0.2) GeV −2.