7 Building block P C HLS ˆ α ν ‖ (ΩΣ$_{c}$)ˆ α$_{‖}$$_{ν}$ (ΩΣ$_{c}$) − ˆ α νT ‖ h ˆ α ν $_{‖}$h † ˆ α ν ⊥ − (ΩΣ$_{c}$)ˆ α$_{⊥}$$_{ν}$ (ΩΣ$_{c}$) ˆ α νT ⊥ h ˆ α ν $_{⊥}$h † ˆ χ (ΩΣ$_{c}$)ˆ χ $^{†}$(ΩΣ$_{c}$ ) ˆ χ T h ˆ χh † G ν Ω G T ν Ω Σ$_{c}$ G $^{ν}$Σ$_{c}$ gG$_{ν}$g † + ig ( ∂$_{ν}$g $^{†}$) TABLE I: Transformation properties of the building blocks under parity ( P ), charge-conjugation ( C ), and HLS. Then the lowest order term invariant under the P transformation is given by where f$_{χ}$ is introduced to renormalize the quadratically divergent correction to this term [18]. In the present analysis, we introduced this parameter in such a way that the field ˆ χ does not get any renormalization effect. Finally, the HLS Lagrangian with leading order terms is given by In this section, we study the vacuum structure and examine the effects of nonzero chemical potential for the baryon number charge on the spectrum of “vector” bosons in the case of N$_{f}$ = 2. In Table II, we show the fields included in the present model together with their quantum numbers for the SU (2) “isospin” I $^{#3}$, the baryon number charge B #4 and the spin-parity J $^{P}$. The effect of chemical potential for the baryon number charge is introduced as the vacuum expectation value (VEV) of the external chiral gauge boson as 〈 G$_{ν}$ 〉 = δ$_{0}$$_{ν}$ µ$_{B}$ 2  $^{1}$ 0 0 − $_{1}$  = µ$_{B}$δ$_{0}$$_{ν}$ 2 B, (3.1) L = − 1 2 g $_{2}$tr[ V$_{νρ}$V $^{νρ}$] + f 2 $_{σ}$tr[ˆ α 2 ‖ $_{ν}$] + f 2 $_{π}$tr[ˆ α 2 ⊥ $_{ν}$] + f 2 χ 4 tr[ˆ χ + ˆ χ $^{†}$] . (2.30) f 2 χ 4 tr[ˆ χ + ˆ χ $^{†}$] . (2.29) 3. VACUUM STRUCTURE AND SPECTRUM OF “VECTOR” BOSONS AT NONZERO BARYON CHEMICAL POTENTIAL #3 For N$_{f}$ = 2 there exists an SU (2) flavor symmetry which we call the “isospin” symmetry. #4 We follow the convention of baryon number given in Ref. [3], which is different from the one in Ref. [7].