We find a general expression for the one-loop self-energy function of neutral $rho$-meson due to $pi^+pi^-$ intermediate state in a background magnetic field, valid for arbitrary magnitudes of the field. The pion propagator used in this expression is given by Schwinger, which depends on a proper-time parameter. Restricting to weak fields, we calculate the decay rate $Gamma(rho^0 rightarrow pi^+ +pi^-)$, which changes negligibly from the vacuum value.
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