### Abstract

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.

Original language | English (US) |
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Title of host publication | Proceedings of Science |

State | Published - 2010 |

Event | Workshop on the Many Faces of QCD, FacesQCD 2010 - Gent, Belgium Duration: Nov 1 2010 → Nov 5 2010 |

### Other

Other | Workshop on the Many Faces of QCD, FacesQCD 2010 |
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Country | Belgium |

City | Gent |

Period | 11/1/10 → 11/5/10 |

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### ASJC Scopus subject areas

- General

### Cite this

*Proceedings of Science*

**An improved model of color confinement.** / Zwanziger, Daniel.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of Science.*Workshop on the Many Faces of QCD, FacesQCD 2010, Gent, Belgium, 11/1/10.

}

TY - GEN

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 contribution

AN - SCOPUS:84868702814

BT - Proceedings of Science

ER -