Subleading soft dressings for QED scattering states

Abstract

We study soft emission in QED during scattering of Faddeev-Kulish dressed states. The incoming and outgoing charged particles are accompanied by coherent clouds of soft photons with energies below a characteristic infrared scale $E_d$. We focus on explicit processes that allow the dependence of the soft factors on the hard particles' momenta and total angular momenta to be displayed clearly. We argue that the dressings remove the infrared divergences in hard amplitudes order by order in perturbation theory, effectively regulating the contributions from virtual soft photons at the scale $E_d$. Essentially, the Faddeev-Kulish hard amplitudes become equivalent to the infrared-finite part of the corresponding Fock-basis amplitudes. Finally, tree-level soft-photon emission is found to be suppressed once the dressings are extended to subleading order in the soft-momentum expansion, as prescribed in recent work by Choi and Akhoury.

Figures (7)

• Figure 1:
• Figure 2:
• Figure 4: Diagrams depicting single soft-photon emission during a generic QED scattering process. The interactions are collectively represented by the blob. Diagrams (a) and (b) describe soft-photon emission from outgoing and incoming charged particles, respectively, while diagram (c) corresponds to soft-photon emission from a virtual charged particle.
• Figure 5: A schematic representation of the cancellation of virtual infrared divergences against real soft infrared divergences at the level of inclusive rates. Representative examples of Feynman diagrams depicting Compton scattering are used.
• Figure 6: Pictorial representation of the replacement of $n$ incoming charged particle state by the corresponding dressed state in a generic QED scattering process. An analogous replacement can be applied for the $m$ outgoing charged particle state, which has not been displayed in full.