Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2006-01-29
JHEP0603:067,2006
Physics
High Energy Physics
High Energy Physics - Theory
20 pages, 7 figures
Scientific paper
10.1088/1126-6708/2006/03/067
We study the competing effects of gluon self-coupling and their interactions with quarks in a baryon, using the very simple setting of a hermitian 1-matrix model with action tr A^4 - log det(nu + A^2). The logarithmic term comes from integrating out N quarks. The model is a caricature of 2d QCD coupled to adjoint scalars, which are the transversely polarized gluons in a dimensional reduction. nu is a dimensionless ratio of quark mass to coupling constant. The model interpolates between gluons in the vacuum (nu=infinity), gluons weakly coupled to heavy quarks (large nu) and strongly coupled to light quarks in a baryon (nu to 0). It's solution in the large-N limit exhibits a phase transition from a weakly coupled 1-cut phase to a strongly coupled 2-cut phase as nu is decreased below nu_c = 0.27. Free energy and correlation functions are discontinuous in their third and second derivatives at nu_c. The transition to a two-cut phase forces eigenvalues of A away from zero, making glue-ring correlations grow as nu is decreased. In particular, they are enhanced in a baryon compared to the vacuum. This investigation is motivated by a desire to understand why half the proton's momentum is contributed by gluons.
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