content_image/330830.jpg content_image/330829.jpg content_image/330828.jpg content_image/330827.jpg content_image/330826.jpg content_image/330825.jpg
The mixed-grand canonical ensemble for the matter of chiral Hagedorn states reads 

<img src='content_image/330830.jpg'>

The total grand potential density for the chiral Hagedorn matter in the presence of the chiral field is given by 

<img src='content_image/330829.jpg'>

The chiral Hagedorn’s grand potential density ( i.e. the first term on the right hand side of Eq.(149) ) is given as follows, 

<img src='content_image/330828.jpg'>

The chiral potential U ( σ ) ( i.e. the second term on the right hand side of Eq.(149) ) can be introduced by a phenomenological one in the following way 

<img src='content_image/330827.jpg'>

where the cubic and quartic terms represent the scalar self-interactions and they were pro- posed by Boguta and Bodmer [66]. In the simplest approximation, the cubic and quartic terms are neglected by taking c$_{2}$ = 0 and c$_{3}$ = 0 and this corresponds to the Walecka-like models. The value of the mean field σ is determined by calculating the extremum (i.e. minimum) of the total grand potential density, namely, 

<img src='content_image/330826.jpg'>

In order to calculate the chiral Hagedorn’s grand potential density that is given in Eq.(150), the high-lying mass spectral density for chiral Hagedorn states is rewritten in the following way 

<img src='content_image/330825.jpg'>

