the effective potential is the decisive term in determining the process of the symmetry trans- mutation (or breaking) [67, 68]. The gluon polarization tensor in the HTL approximation is found [69] Π$_{µν}$ a $^{$^{′}$a}$( p$_{0}$, ⃗ p ) = ( m 2 D ) a $^{′}$a [ − δ 0 $_{µ}$δ 0 ν + p$_{0}$ ∫ d Ω$_{k}$ 4 π ˆ k$_{µ}$ ˆ k$_{ν}$ p$_{0}$ − ˆ k · ⃗ p ] , = ( m 2 D ) $^{a}$δ a $^{′}$a [ − δ 0 $_{µ}$δ 0 ν + p$_{0}$ ∫ d Ω$_{k}$ 4 π ˆ k$_{µ}$ ˆ k$_{ν}$ p$_{0}$ − ˆ k · ⃗ p ] . (164) The information that is needed to understand the Higgs mechanism and symmetry breaking is decoded implicitly in the gluon Debye mass(es). The Debye mass is found as follows where while the real gluonic part reads Eq.(165) hints some information about the possible symmetry breaking processes. There is ( N 2 c − N$_{c}$ ) non-degenerate masses and ( N$_{c}$ − 1) degenerate masses. It is naively to conjecture that ˆ A a ∝ µ$_{C}$ a ≡ ( µ$_{C}$$_{A}$ − µ$_{C}$$_{B}$ ) where a = ( AB ) ︸ ︷︷ ︸$^{.}$ This means that the N 2 c − N$_{c}$ non- degenerate masses correspond the non-vanishing values ˆ A a with A = B while the N$_{c}$ − 1 degenerate masses correspond ˆ A a = 0 with A = B . Hence the N 2 c − N$_{c}$ non-degenerate masses are simply the Higgs masses which are generated by breaking the symmetry SU ( N$_{c}$ ) while the N$_{c}$ − 1 degenerate masses are the elements of the resultant new symmetry U (1) N$_{c}$ − $^{1}$. These masses in one (Hard-thermal) loop correction are of order m$_{D}$ ∼ g T . Depending on the higher order interaction ( ˆ A a µ ) n> 2 which appear in Eq.(163) and its modification 55 ( m 2 D ( G ) ) b = ( AB ) ︸ ︷︷ ︸ → ℜ e ( m 2 D ( G ) ) b = ( AB ) ︸ ︷︷ ︸ , = g 2 π 2 [ π 2 3 T 2 − 1 2 ( µ$_{C}$ b ) 2 ] , = g 2 π 2 π 2 3 T 2 − 1 2 µ$_{C}$$_{A}$ − µ$_{C}$$_{B}$ ) 2 ] . (167) ( m 2 D ( Q ) ) i = 2 g 2 π 2 N$_{f}$ ∑ Q =1 [ π 2 6 T 2 + 1 2 ( µ$_{Q}$ + µ$_{C}$$_{i}$ ) 2 ] , (166) ( m 2 D ) a $^{′}$a = ( m 2 D ) a δ a $^{$^{′}$a}$, = [( m 2 D ( Q ) ) a + ( m 2 D ( G ) ) a ] δ a $^{$^{′}$a}$, = [ t a ′ $_{ij}$t a ji ( m 2 D ( Q ) ) i + T a ′ $_{cb}$T a bc ( m 2 D ( G ) ) b ] δ a $^{$^{′}$a}$, (165)