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Spectral properties of $ρ$ meson in a magnetic field

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