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Analytic structure of nonperturbative quark propagators and meson processes

The analytic structure of certain Ansaetze for quark propagators in the non-perturbative regime of QCD is investigated. When choosing physically motivated parametrization of the momentum-dependent dressed quark mass function M(p^2), with definite analytic structure, it is highly nontrivial to predict and control the analytic structure of the corresponding nonperturbative quark propagator. The issue of the Wick rotation relating the Minkowski-space and Euclidean-space formulations is also highly nontrivial in the nonperturbative case. A propagator form allowing the Wick rotation and enabling equivalent calculations in Minkowski and Euclidean spaces is presented. In spite of its simplicity, this model yields good qualitative and semi-quantitative description of some pseudoscalar meson processes. Extension to finite densities and temperatures is possible.

analytic; propagator; quark; nonperturbative; QCD

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