Universality, the QCD critical and tricritical point, and the quark number susceptibility

The quark number susceptibility near the QCD critical end point (CEP), the tricritical point (TCP) and the $O\left(4\right)\mathrm{}$ critical line at finite temperature and quark chemical potential are investigated. Based on the universality argument and numerical model calculations we propose the possibility that the hidden tricritical point strongly affects the critical phenomena around the critical end-point. We make a semiquantitative study of the quark number susceptibility near CEP or TCP for several quark masses on the basis of the Cornwall-Jackiw-Tomboulis potential for QCD in the improved-ladder approximation. The results show that the susceptibility is enhanced in a wide region around the CEP, inside which the critical exponent gradually changes from that of the CEP to that of the TCP, indicating a crossover of different universality classes.