The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red

Abstract

Gauge invariance and soft limits can be enough to determine the analytic structure of scattering amplitudes in certain theories. This prompts the question of how gauge invariance is connected to analytic structure in more general theories. Here we focus on QED in background plane waves. We show that imposing gauge invariance introduces new virtuality poles into internal momenta on which amplitudes factorise into a series of terms. Each term is gauge invariant, has a different analytic structure in external momenta, and exhibits a hard/soft factorisation. The introduced poles are dictated by infra-red behaviour, which allows us to extend our results to scalar Yukawa theory. The background is treated non-perturbatively throughout.

A preprint version of the article is available at ArXiv.

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Correspondence to Alexander J. MacLeod.

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Ilderton, A., MacLeod, A.J. The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red. J. High Energ. Phys. 2020, 78 (2020). https://doi.org/10.1007/JHEP04(2020)078

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Keywords

  • Gauge Symmetry
  • Scattering Amplitudes