TY - JOUR

T1 - An improved model of color confinement

AU - Zwanziger, Daniel

PY - 2010

Y1 - 2010

N2 - We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jbμ (x) = Hb μ cos(k · x), where Hb μ is, by analogy with spin models, an external "magnetic" field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volumeWk(H)/V and the average magnetization m(k,H) = 1 V ¶Wk(H) ¶H vanish in the limit of constant external field k!0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) 6=0, at k =0. This would imply a non-analyticity inWk(H) at k =0. We present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.

AB - We consider the free energy W[J] = Wk(H) of QCD coupled to an external source Jbμ (x) = Hb μ cos(k · x), where Hb μ is, by analogy with spin models, an external "magnetic" field with a color index that is modulated by a plane wave. We report an optimal bound on Wk(H) and an exact asymptotic expression for Wk(H) at large H. They imply confinement of color in the sense that the free energy per unit volumeWk(H)/V and the average magnetization m(k,H) = 1 V ¶Wk(H) ¶H vanish in the limit of constant external field k!0. Recent lattice data indicate a gluon propagator D(k) which is non-zero, D(0) 6=0, at k =0. This would imply a non-analyticity inWk(H) at k =0. We present a model that is consistent with the new results and exhibits (non)-analytic behavior. Direct numerical tests of the bounds are proposed.

UR - http://www.scopus.com/inward/record.url?scp=84868702814&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84868702814&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84868702814

JO - Proceedings of Science

JF - Proceedings of Science

SN - 1824-8039

T2 - Workshop on the Many Faces of QCD, FacesQCD 2010

Y2 - 1 November 2010 through 5 November 2010

ER -