9 FIG. 1: µ$_{B}$ -dependence of the VEV ˜ ω in unit of M$_{π}$ as a function of µ$_{B}$/M$_{π}$ . Substituting this into V$_{potential}$ , we have This is equivalent to the potential term of the chiral Lagrangian for NG bosons analyzed in Ref. [3]. Then, the value of ξ (˜ π ) which minimizes the potential is obtained as where X 5 is given in Eqs. (B.6) and (B.7) and the VEV ˜ π 5 is determined as with B This means that there is a condensation of the baryonic-NG boson with J P = 0 + and U (1)$_{B}$ symmetry is broken spontaneously for µ$_{B}$ > M$_{π}$ . By substituting this VEV into Eq. (3.6), the VEV of the “vector” boson fields ˜ V α 0 is determined as This implies that the time component of ω meson (see Table II) has a VEV for any µ$_{B}$ , as in the ordinary three-color QCD. In FIG. 1, we plot the µ$_{B}$ -dependence of ˜ ω = ˜ V 4 0 . This shows that the ˜ ω increases with µ$_{B}$ for µ$_{B}$ < M$_{π}$ while it decreases for µ$_{B}$ > M$_{π}$ . ˜ V α 0 =    √$_{2}$$_{µ}$$_{B}$ cos θ, ( α = 4 ) , 0 , ( α = 4 ) . (3.11) θ = 0 , (for 0 < µ$_{B}$ < M$_{π}$ ) , cos θ = M π µ 2 , (for µ$_{B}$ > M$_{π}$ ) . (3.10) ˜ π 5 = √$_{2}$$_{f}$$_{π}$$_{θ,}$ (3.9) ξ (˜ π ) = e i ˜ π $^{5}$X5 (3.8) V$_{potential}$ ∣ ˜ V 0 = − f 2 π 4 tr [ µ 2 B 4 { ξ $^{†}$(˜ π ) Bξ (˜ π ) − ξ (˜ π ) Bξ $^{†}$(˜ π ) } 2 + M 2 π { ξ $^{2}$(˜ π ) ¯ Σ ˆ M + (h.c) } ] . (3.7)