Baryon-Size Dependent Location of QCD Critical Point

The physics regarding the existence of the critical end point (CEP) on the QCD phase boundary still remains unclear and its precise location is quite uncertain. In this paper we propose that the hard-core size of the baryons used in the description of the hot and dense hadron gas (HG) plays a decisive role in the existence of CEP. Here we construct a deconfining phase transition using Gibbs' equilibrium conditions after using a quasiparticle equation of state (EOS) for QCD plasma and excluded-volume EOS for the HG. We find that the first order transition results only when we assign a hard-core size to each baryon in the description of HG and the phase boundary thus obtained terminates at CEP beyond which a cross-over region occurs. The mean field approach for the HG lends support to this finding where unless we include an excluded-volume effect in the approach, CEP does not materialize on the QCD boundary. This investigation provides an intuitive reasoning regarding the origin of CEP and the cross-over transition on the QCD phase boundary.