Spectral properties of $\rho$ meson in a magnetic field

We calculate the rho meson mass in a weak magnetic field using effective $\rho \pi \pi$ interaction. It is seen that both ${\rho }^0$ and ${\rho }^{\pm }$ masses decrease with the magnetic field in vacuum. $\rho$ meson dispersion relation has been calculated and shown to be different for ${\rho }^0$ and ${\rho }^{\pm }$. We also calculate the $\rho \pi \pi$ decay width and spectral functions of ${\rho }^0$ and ${\rho }^{\pm }$. The width is seen to decrease with $eB$ and the spectral functions become narrower.