where B is the MIT bag constant. The bag constant is assigned to be approximately B 1 / 4 ≈ 200 MeV. The constraint of Hagedorn mass threshold becomes The asymptotic density of states for the micro-canonical ensemble with large blob energy W is calculated by taking the inverse Laplace transform for the grand canonical ensemble. The inverse Laplace transform for large W is evaluated using the steepest descent method, The straightforward calculation leads to the following micro-canonical ensemble, where The saddle point of the Laplace transform is found In the standard MIT bag model, the bag’s mass and volume are given by the following relations The density of states for the continuous high-lying mass spectrum is given by calculating the canonical ensemble and its transformation to the micro-canonical ensemble. The con- tinuous high-lying mass spectral densities for the color-singlet-state orthogonal, unitary and 29 m = W + BV, m = 4 BV, W = 3 $_{4}$m, V = m 4 $_{B}$, ( 3˜ a (0) q ¯ $_{qg}$V W 3 ) 1 / 4 = 3 4 ( ˜ a (0) q ¯ qg B ) 1 / 4 m. (105) β = 1 W [ 3˜ a (0) q ¯ $_{qg}$V W 3 ] 1 / $^{4}$. (104) C ⋆ = 1 $_{2}$√$_{2}$$_{π}$ C ( 3˜ a (0) q ¯ qg ˜ a (2) q ¯ qg ) α − 1 / 2 . (103) Z$_{qqg}$ ( W, V ) = C ⋆ 1 W [ ( 3˜ a (0) q ¯ $_{qg}$V W 3 ) 1 / 4 ] − ( α − 1) exp [ 4 3 ( 3˜ a (0) q ¯ $_{qg}$V W 3 ) 1 / 4 ] , (102) Z$_{qqg}$ ( W, V ) = 1 2 πi ∫ β$_{0}$ + i ∞ β$_{0}$ − i ∞ dβe $^{βW}$Z$_{qqg}$ ( β, V ) = 1 2 πi β$_{0}$ + i ∞ β$_{0}$ − i ∞ dβ [ C ( ˜ a (2) q ¯ qg V β 3 ) − α + 1 2 e βW + V β $_{3}$˜ a (0) q ¯ qg ] . (101) m$_{threshold}$ ≥ 4 ( α − 1 2 ) ( B ˜ a (0) $_{qqg}$) 1 / 4 . (100)