Journal of High Energy Physics (Mar 2022)

Integrands of less-supersymmetric Yang-Mills at one loop

  • Jacob L. Bourjaily,
  • Enrico Herrmann,
  • Cameron Langer,
  • Kokkimidis Patatoukos,
  • Jaroslav Trnka,
  • Minshan Zheng

DOI
https://doi.org/10.1007/JHEP03(2022)126
Journal volume & issue
Vol. 2022, no. 3
pp. 1 – 41

Abstract

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Abstract We construct a prescriptive, bubble power-counting basis of one-loop integrands suitable for representing amplitude integrands in less-supersymmetric (1 ≤ N $$ \mathcal{N} $$ ≤ 4) Yang-Mills theory. With the exception of massless bubbles, all integrands have unambiguous, leading singularities as coefficients defined in field theory; for the massless bubbles on external legs, we find two natural choices which lead to different integrands that highlight distinct aspects of field theory. For concreteness, we give the all-multiplicity integrands for MHV amplitudes, and the split-helicity amplitude integrand for six-particle NMHV. The basis we construct is mostly pure and is divided into to separately UV- and IR-finite sectors of fixed transcendental weight, resulting in UV- and IR-finite ratio functions of n-particle helicity amplitudes.

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