Nc−1 Gluons Quarks Symmetry breaking HTL(thermal excitation) Symmetry breaking HTL(thermal excitation) SU(Nc) SU(Nc) O(Nc) O(Nc) O(Nc) U(1) FIG. 5: (Color online) The Hagedorn’s bag internal symmetry breaking from SU ( N$_{c}$ ) to O ( N$_{c}$ ) and eventually to U (1) N$_{c}$ − 1 in the dilute and hot nuclear matter. The quarks are represented by colored circles while the gluons are shown by short wavy lines. The hard thermal loop is expected to generate degenerate/non-degenerate gluon’s Debye masses with vanishing/non-vanishing adjoint (mean-) fields ˆ A a depending on the medium. This mechanism is responsible for the symmetry transmutation in order to reduce to the constituent quark-gluon self-interactions and basically to maintain the quark confinement. The liberated gluons acquire finite masses ( m 2 D ∝ g $^{2}$T $^{2}$) due to the Higgs phenomenon. In the present calculation, the liberated gluons are practically treated as an ideal gas of massless particles. 70