Quark confinement in a constituent quark model

Abstract

On the level of an effective quark theory, we define confinement by the absence of quark anti-quark thresholds in correlation functions. We then propose a confining Nambu-Jona-Lasinio-type model. The confinement is implemented in analogy to Anderson localization in condensed matter systems. We study the model's phase structure as well as its behavior under extreme conditions, i.e. high temperature and/or high density. * Supported in part by DFG under contracts La-932/1 − 1/2.

Analytic structure of meson propagators in the proper-time regularized Nambu-Jona-Lasinio model

“…Recently Langfeld and Rho [26] analyzed a confining Nambu-Jona-Lasinio-like model in which the pion propagator has, in addition to the physical pole, complex singularities located similarly to our case. In fact, complex singularities appear frequently in model descriptions of confinement (for a review see [27]).…”

Erratum: Schwinger-Dyson approach to color superconductivity in dense QCD [Phys. Rev. D61, 056001 (2000)]

“…[6,17,21,24]. In this paper, however, we pay special attention to the effect of the unscreened magnetic modes of gluons.…”

“…Recently, interest in the study of the color superconducting phase considerably increased [7][8][9][12][13][14][15][16][17][18][19][20][21][22]. The renewed interest was triggered by the observation that the necessary attractive interaction could be exclusively due to the instanton effects [7][8][9].…”

Quark confinement in a random background Gross-Neveu model

“…An average of all orientations O of the background field G ab , transforming as G ′ = O T GO with O being a 3 ×3 orthogonal matrix, is understood in (1) to restore global SU(2) color symmetry. From [8] we expect that these randomness leads to the confinement of quarks. In order to explore ground state properties of the model, it is convenient to study the effective potential U of the (Euclidean) condensate, since a non-vanishing value signals the spontaneous breakdown of chiral symmetry.…”

“…They successfully describe the mechanism of the spontaneous breakdown of chiral symmetry and the physics of the light mesons, but inherently suffer from a non-confinement of the quarks [7]. Recently, an effective quark model was proposed which incorporates the quark confinement in a sense that quark anti-quark thresholds are absent in (mesonic) Green's functions [8]. The main ingredient in this model is an effective low energy four quark interaction mediated by a random gluonic background field.…”