Radiation reaction by massive particles and its nonanalytic behavior

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We derive a massive analog of the Abraham-Lorentz-Dirac equation, i.e., the equation of motion of a relativistic charged particle with a radiation reaction term induced by emissions of massive fields. We show that the radiation reaction term has a nonanalytic behavior as a function of the mass $M$ of the radiation field and that both expansions with respect to $M$ and $1/M$ are generally invalid. Hence the massive Abraham-Lorentz-Dirac equation cannot be written as a local equation with derivative expansions. We especially investigate the radiation reaction in three specific motions: uniform acceleration, a circular motion, and a scattering process.