Evaluation of particle--anti-particle scaled correlation within effective models

Correlations and fluctuations of physical quantities are known to play an important role in phase transitions and critical phenomena. In recent years some experimental attempts were made in the scope of the Beam Energy Scan program to locate a possible critical point in the QCD phase diagram. In this work we use the Nambu--Jona-Lasinio model to investigate the off-diagonal quark susceptibility, which is related to the quark--anti-quark scaled correlation at the mean field level. We show that this correlation has a significant peak near the critical point and, therefore, may be a useful quantity to measure in experiment. We further study the effects of a repulsive vector coupling, which reduces the strength of the scaled correlation near the critical point.