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Radiation Reaction by Massive Particles and Its Non-Analytic Behavior

We derive a massive analog of the ALD (Abraham, Lorentz and 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 non-analytic behavior as a function of the mass M of the radiation field and both expansions with respect of M and 1/M are generally invalid. Hence the massive ALD 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.