  By including the strong isospin symmetry breaking effects and the
electromagnetic contributions between the pseudoscalar mesons, we calculate the
phase shifts of the $P$-wave $\pi\pi$ and $K\pi$ scattering up to
$\mathcal{O}(p^4)$ in the framework of the SU(3) chiral perturbation theory
(ChPT) and coupled channel inverse amplitude method. We re-fit the low energy
constants with the present meson-meson scattering data and derive the mass
differences for the charged and neutral iso-multiplets of $\rho$ and $K^{*}$.
Our results show that the mass difference between $\rho^\pm$ and $\rho^0$ is
very small while the mass difference between the charged and neutral $K^*$ can
reach a relatively large value of $m_{K^{*0}}-m_{K^{*+}}= 2.91^{+1.43}_{-1.41}$
MeV. This full one-loop ChPT calculation would shed some light towards a better
understanding of the long-standing puzzle about the $K^*$ mass splitting.
