FIG. 5: µ$_{B}$ -dependences of the “vector” boson masses. The curves on the left figure are for the ρ and ω mesons and those on the right figure are for baryonic and anti-baryonic “vector” bosons. We use M$_{V}$ /M$_{π}$ = 5 / 4, C$_{1}$ = 1, C$_{2}$ = 2 and g = 1 to make the curves. boson masses for C$_{1}$ = 0 and C$_{2}$ = 1 together with M$_{V}$ /M$_{π}$ = 5 / 4 and g = 1 in FIG. 4. We choose the value C$_{2}$ = 1 to reproduce the decreasing masses of ρ and ω mesons in the lattice data [7] for µ$_{B}$ > M$_{π}$ . We obtain the result that m$_{V}$$_{B}$$_{+}$ increases and m$_{V}$$_{B}$$_{−}$ decreases with increasing µ$_{B}$ for µ$_{B}$ > M$_{π}$ . The lattice analysis [7] shows that m$_{V}$$_{B}$$_{+}$ is almost stable against the change of µ$_{B}$ , which does not agree with the result of the present analysis. Though any clear signal for m$_{V}$$_{B}$$_{−}$ is not observed. We investigate the effect of C$_{1}$ term to m$_{V}$$_{B}$$_{+}$ and m$_{V}$$_{B}$$_{−}$ in Eq. (4.8). This term causes a mixing between V$_{B}$$_{+}$ and V$_{B}$$_{−}$ , and makes m$_{V}$$_{B}$$_{+}$ ( m$_{V}$$_{B}$$_{−}$ ) smaller (larger). At the same time, the C$_{1}$ term produces the mass difference between the ρ and ω mesons (see Eq. (4.9)): The positive C$_{1}$ gives the positive correction to m$_{ρ}$ and the negative one to m$_{ω}$ , and the negative C$_{1}$ gives the negative correction to m$_{ρ}$ and the positive one to m$_{ω}$ . As an example, we plot the µ$_{B}$ -dependence of the “vector” boson masses for C$_{1}$ = 1 and C$_{2}$ = 2 together with M$_{V}$ /M$_{π}$ = 5 / 4 and g = 1 in FIG. 5. We set C$_{2}$ − C$_{1}$ = 1 to reproduce the decreasing mass of ρ meson in the lattice data [7], and C$_{1}$ = 1 to produce 10% decreasing of m$_{V}$$_{B}$$_{+}$ at µ$_{B}$/M$_{π}$ = 1 . 5. Left panel of FIG. 5 shows that the splitting between m$_{ρ}$ and m$_{ω}$ is large: m$_{ω}$ is about half of m$_{ρ}$ at µ$_{B}$/M$_{π}$ = 1 . 5. Thus, our model cannot simultaneously reproduce the µ$_{B}$ -dependences of m$_{ρ}$ , m$_{ω}$ and m$_{V}$$_{B}$$_{+}$ in the lattice data [7]. For relatively heavy π s, we expect that the masses of “axial-vector” bosons are smaller than M$_{V}$ + M$_{π}$ which is the largest value of “vector” boson masses in the present analysis, so that we cannot neglect the “axial-vector” bosons. When we include the “axial-vector”