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Infrared behavior of the photon yield in nonlinear Compton scattering

Antonino Di Piazza1,2,* and Giulio Audagnotto1,3,†

  • *Contact author: a.dipiazza@rochester.edu
  • †Contact author: giulio.audagnotto@unito.it
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Phys. Rev. D 114, 076024 – Published 23 October, 2026

DOI: https://doi.org/10.1103/854z-dc2g

Abstract

Nonlinear Compton scattering is the process of emission of a single photon by a charge driven by an intense laser field. Here, we study the infrared behavior of the photon yield emitted via nonlinear Compton scattering. We first consider the idealized case of an electron in the presence of a plane wave and derive an analytical expression of the total yield in the form of a double integral over the laser phase. As it is known, the total yield is finite in the experimentally common case of a plane wave laser field without a dc component whereas it diverges logarithmically in the complementary case of so-called unipolar fields. The divergence is found here to correspond to the longer-and-longer formation lengths of emitted photons with lower-and-lower frequency. Interestingly, we also find that the corrections to the Volkov states stemming from the fact that the field is unipolar cancel out in the computation of the probability of nonlinear Compton scattering, which is in agreement with the fact that in the classical limit the expression of the photon yield is independent of whether the plane wave is unipolar or not. Then, we pass to the more realistic case of an electron in a tightly focused laser beam by assuming that the electron is ultrarelativistic. In this case we determine analytically the classical angular distribution of the yield of photons with an energy larger than a fixed value ℏωm as a double integral over the electron’s trajectory. Indeed, in the case of a focused laser beam the electron does typically undergo a net acceleration and it is therefore appropriate to fix a lower bound to avoid the infrared divergence. After obtaining also the corresponding quantum expression of the angular distribution of the photon yield within the quasiclassical approximation, we determine analytically the leading-order quantum correction, which scales as ℏωm/ϵ, where ϵ is the initial electron energy. Considerations on the experimental feasibility of the found results in the latter situations are also presented.

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Phys. Rev. D 114, 076024– Published 23 October, 2026
  • Received 22 May 2026
  • Accepted 30 July 2026
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