Scalar-pseudoscalar meson masses in nonlocal effective QCD at finite temperature

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Abstract
The Schwinger-Dyson equation for the quark propagator and the Bethe-Salpeter equations for the quark-meson vertex functions are derived within nonlocal effective QCD in the quark sector using functional integral techniques at finite temperature. We apply the approach for separable instantaneous interactions and derive mass formulas for the scalar and pseudoscalar mesons. The pion mass obeys the Goldstone theorem. The sigma meson mass is lowered when the interaction kernel is not constant. The temperature behavior of the constituent quark mass and the scalar as well as pseudoscalar meson masses is obtained from a self-consistent numerical solution to the coupled set of Schwinger-Dyson and Bethe-Salpeter equations. We present a systematic investigation of the modification of the chiral transition phenomena due to the choice of the form factor of the effective interaction. The standard Nambu–Jona-Lasinio model is discussed as a particular case of nonlocal separable interaction.