Chiral symmetry breaking in the truncated Coulomb Gauge II. Non-confining power law potentials

In this paper we study the breaking of chiral symmetry with non-confining power-like potentials. The region of allowed exponents is identified and, after the previous study of confining (positive exponent) potentials, we now specialize in shorter range non-confining potentials, with a negative exponent. These non-confining potentials are close to the Coulomb potential, and they are also relevant as corrections to the linear confinement, and as models for the quark potential at the deconfinement transition. The mass-gap equation is constructed and solved, and the quarks mass, the chiral angle and the quark energy are calculated analytically with a exponent expansion in the neighbourhood of the Coulomb potential. It is demonstrated that chiral symmetry breaking occurs, but only the chiral invariant false vacuum and a second non-trivial vacuum exist. Moreover chiral symmetry breaking is led by the UV part of the potential, with no IR enhancement of the quark mass. Thus the breaking of chiral symmetry driven by non-confining potentials differs from the one lead by confining potentials.Comment: 8 pages, 3 figure

Circumventing the axial anomalies and the strong CP problem

Many meson processes are related to the U_A(1) axial anomaly, present in the Feynman graphs where fermion loops connect axial vertices with vector vertices. However, the coupling of pseudoscalar mesons to quarks does not have to be formulated via axial vertices. The pseudoscalar coupling is also possible, and this approach is especially natural on the level of the quark substructure of hadrons. In this paper we point out the advantages of calculating these processes using (instead of the anomalous graphs) the graphs where axial vertices are replaced by pseudoscalar vertices. We elaborate especially the case of the processes related to the Abelian axial anomaly of QED, but we speculate that it seems possible that effects of the non-Abelian axial anomaly of QCD can be accounted for in an analogous way.Comment: 13 pages, some typos corrected, published in Prof. D. Tadic's memorial issue of Fizika B, expanded version of hep-ph/051212

A UA(1)U_A(1) symmetry restoration scenario supported by the generalized Witten-Veneziano relation and its analytic solution

The Witten-Veneziano relation, or, alternatively, its generalization proposed by Shore, facilitates understanding and describing the complex of eta and eta' mesons. We present an analytic, closed-form solution to Shore's equations which gives results on the eta-eta' complex in full agreement with results previously obtained numerically. Although the Witten-Veneziano relation and Shore's equations are related, the ways they were previously used in the context of dynamical models to calculate eta and eta' properties, were rather different. However, with the analytic solution, the calculation can be formulated similarly to the approach through the Witten-Veneziano relation, and with some conceptual improvements. In the process, one strengthens the arguments in favor of a possible relation between the U_A(1) and SU_A(3) chiral symmetry breaking and restoration. To test this scenario, the experiments such as those at RHIC, NICA and FAIR, which extend the RHIC (and LHC) high-temperature scans also to the finite-density parts of the QCD phase diagram, should pay particular attention to the signatures from the eta'-eta complex indicating the symmetry restoration.Comment: elsarticle style, 6 page

Nucleon strangeness as the response to a strangeness-sensitive probe in a class of hadron models

On top of its valence quarks, the full nucleon ground state may contain appreciable admixture of s-\bar{s} pairs already at small momentum transfers. This paper discusses strangeness in the mean-field type of nucleon models, and exemplifies this by explicit calculations in the MIT bag model enriched by the presence of instantons. We calculate the instanton contribution to the strangeness in the MIT bag (on top of the standard contribution to strangeness found in that model). Although we do it in an essentially perturbative way, we present a detailed derivation of the formula expressing nucleon matrix elements of bilinear strange quark operators, in terms of a model valence nucleon state and interactions producing quark-antiquark fluctuations on top of that valence state. We do it in detail to clarify our argument that in the context of the mean-field type of quark models (where a Fock state expansion exists and where the nucleon state can be constructed out of single-quark states), the resulting formula acquires a significance beyond perturbation theory.The derivation combines the usage of the evolution operator containing a strangeness source, and Feynman-Hellmann theorem.Comment: LaTeX2e, 34 pages, 4 figures (included