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In the context of standard MIT bag model (see for instance Eq.(105)), the exponential term, namely, b ( σ ) reads 

Furthermore, the function ˜ a (0) qqg ( σ ) with the chiral field background is determined as follows 

where the chiral quark-antiquark term reads 

The gluon term remains intact and is given by ˜ a (0) g = (2 J +1) N$_{adj}$ ( π 2 90 ) . The term ˜ a (0) qq ( σ ) ∣ σ =0 with zero chiral field background is reduced to 

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The saddle point β is calculated by iteration with respect to the chiral mean field σ . The first iteration in the context of the MIT bag model leads to ( see also Eq.(104) ), 

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The mass spectral exponent α that appears in the mass spectral density that is given in Eq.(153) is determined by Eq.(87). It is reduced to α = 3 , 9 2 and 15 2 for the orthogonal, uni- tary and symplectic Hagedorn states, respectively. It becomes α = 3 2 for U (1) N$_{c}$ =3 Hagedorn 

