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where C$_{1}$ and C$_{2}$ are certain linear combinations of ¯ y$_{1}$ , ¯ y$_{2}$ and ¯ y$_{3}$ . Applying the same procedure as that in section 3 with the correction in Eq. (4.5), we obtain the masses of ρ meson and ω meson as 

The quadratic term for ( V$_{B}$$_{+}$, V$_{B}$$_{−}$ ) is obtained as 

<img src='content_image/373288.jpg'>

<img src='content_image/373289.jpg'>

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The masses of “vector” bosons with J P = 1 + are obtained by diagonalizing the mass matrix in Eq. (4.8). We can see that the mixing between V$_{B}$$_{+}$ and V$_{B}$$_{−}$ is related with the mass difference between m$_{ρ}$ and m$_{ω}$ as 

<img src='content_image/373291.jpg'>

Equations (4.6), (4.7) and (4.8) show that the corrections to the masses from O ( p $^{4}$) terms include the factor of sin θ , which is zero for µ$_{B}$ < M$_{π}$ . Then, the O ( p $^{4}$) corrections appear only for µ$_{B}$ > M$_{π}$ , where the U (1)$_{B}$ is spontaneously broken. It should be noticed that two 

