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 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) ), 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 42 β = 1 W [ 3˜ a (0) $_{qqg}$V W 3 ] 1 4 , = [ ˜ a (0) $_{qqg}$/B ] 1 4 . (158) ˜ a (0) qq ( σ ) ∣ σ =0 = ˜ a (0) qq = (2 J + 1) N$_{c}$ N$_{f}$ ∑ q [ 7 π 2 360 + 1 12 ( µ$_{q}$ T ) 2 + 1 24 π 2 ( µ$_{q}$ T ) 4 ] . (157) ˜ a (0) qq ( σ ) = (2 J + 1) N$_{c}$ 1 2 π 2 N$_{f}$ ∑ q ∫ ∞ 0 dx x 2 × ln [ 1 + 2 cosh ( µ$_{q}$ T ) e − √ x $^{2}$+ ( βm ∗ $_{q}$( σ ) 2 + e − 2 √ x $^{2}$+ ( βm ∗ $_{q}$( σ ) 2 ] , = (2 J + 1) N$_{c}$ 1 3 π 2 N$_{f}$ ∑ q ∫ ∞ 0 dx x 4 √ x 2 + ( βm ∗ $_{q}$( σ ) ) 2 × e − √ x $^{2}$+ ( βm ∗ $_{q}$( σ ) 2 [ e − √ x $^{2}$+ βm ∗ $_{q}$( σ ) 2 + cosh ( µ$_{q}$ T ) ] [ 1 + 2 cosh ( µ$_{q}$ T ) e − √ x $^{2}$+ ( βm ∗ $_{q}$( σ ) 2 + e − 2 √ x $^{2}$+ βm ∗ $_{q}$( σ ) 2 ] . (156) ˜ a (0) qqg ( σ ) = ˜ a (0) qq ( σ ) + ˜ a (0) g , (155) b ( σ ) = 1 B 1 / 4 [ ˜ a (0) qqg ( σ ) ] 1 / 4 . (154)