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Z. Batiz

Publications and source records attributed to Z. Batiz.

5 recordsLinked to original sources
arXiv2010

Chiral Symmetry Breaking and confinement in Minkowski space QED2+1

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Obtained complex fermion propagator exhibits confinement in the sense that it has no pole. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. Obvious invalidity of Wick rotation is briefly discussed. The infrared value of the dynamical mass is compared with other known approaches, e.g. with the standard Euclidean calculation.

hep-ph↗
arXiv2009

Confinement, Chiral Symmetry Breaking and complex mass in QED2+1 in Minkowski and Euclidean spaces

Without any analytical assumption we solve the ladder QED2+1 in Minkowski space. Further, we transform Greens functions to the Temporal Euclidean space, wherein we show that in the special case of ladder QED2+1 the solution is fully equivalent to the Minkowski one. The obtained complex fermion propagator exhibits confinement because of the lack of the pole at the real timelike $q^2$ axis.

hep-ph↗
arXiv2008

Quark Schwinger-Dyson equation in temporal Euclidean space

We present an elementary nonperturbative method to obtain Green's functions (GFs) for timelike momenta. We assume there are no singularities in the first and third quadrants of the complex plane of space momentum components and perform a 3d analogue of Wick rotation. This procedure defines Greens functions in a timelike Euclidean space. As an example we consider the quark propagator in QCD. While for weak coupling, this method is obviously equivalent to perturbation theory, for a realistic QCD coupling a complex part of the quark mass and renormalization wave function has been spontaneously generated even below the standard perturbative threshold. Therefore, our method favors a confinement mechanism based on the lack of real poles.

hep-ph↗
arXiv2003

Meson-Meson Interactions and Resonances in the 't Hooft Model

We studied meson-meson interactions using the 't Hooft model, which represents QCD in 1+1 dimensions and assumes a large number of colors ($N_c$). The dominant interactions in this large $N_c$ limit are generated by quark exchange. Our results show that QCD in 1+1 dimensions allows the realization of a constituent-type quark model for the mesons, and generates a scalar ``$σ$''-like meson-meson resonance, whose effective coupling and mass are determined by the underlying QCD dynamics. These results suggest an interpretation of the lightest scalar mesons as $q\bar{q} q \bar{q}$ systems.

nucl-th↗