Relation of renormalized meson mass to bare mass and cutoff parameter in scalar electrodynamics

The renormaiized mass $m$ of a scalar meson is related to the bare mass $m_0$, the charge, and the cutoff parameter A in the so-called “three-gamma” or $(\alpha L)^n$-approximation. It is shown that if one goes beyond standard perturbation theory in scalar electrodynamics, the divergence of the meson selfenergy is transformed from quadratic into linear. A nonzero solution for the meson mass $m$ is obtained for a vanishing bare mass. The Duffin–Kemmer formalism is used.