Persistence of the EOS excess under consistent mesonic corrections

Determine whether the static equation-of-state slope excess found in the homogeneous quark mean-field nonlocal Nambu–Jona-Lasinio model persists after incorporating consistent mesonic fluctuations, including their thermal and field-response contributions and vacuum matching at the same order.

Background

The paper analyzes thermodynamic stability using only the quark determinant and a homogeneous scalar mean field; thermal meson populations and mesonic fluctuations are omitted. For the nominal quartic-exponent kernel fit, the authors rigorously find positive entropy and heat capacity for every positive temperature, but also find that the static ratio dP/dε=s/C_V exceeds unity on a finite temperature interval.

The paper notes that vacuum pion matching does not itself add a thermal pion gas and that an illustrative ideal-pion contribution substantially changes the slope ratio in the relevant temperature range. However, this illustration does not include scalar feedback, consistent fluctuation corrections, or refitting. The unresolved problem is therefore to determine whether the mean-field equation-of-state excess survives a systematic mesonic treatment performed consistently at the same order.