Numerator seagull and extended Symmetries of Feynman Integrals

Barak Kol, Amit Schiller, Ruth Shir*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The Symmetries of Feynman Integrals (SFI) method is extended for the first time to incorporate an irreducible numerator. This is done in the context of the so-called vacuum and propagator seagull diagrams, which have 3 and 2 loops, respectively, and both have a single irreducible numerator. For this purpose, an extended version of SFI (xSFI) is developed. For the seagull diagrams with general masses, the SFI equation system is found to extend by two additional equations. The first is a recursion equation in the numerator power, which has an alternative form as a differential equation for the generating function. The second equation applies only to the propagator seagull and does not involve the numerator. We solve the equation system in two cases: over the singular locus and in a certain 3 scale sector where we obtain novel closed-form evaluations and epsilon expansions, thereby extending previous results for the numerator-free case.

Original languageAmerican English
Article number165
JournalJournal of High Energy Physics
Issue number1
StatePublished - Jan 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s).


  • Perturbative QCD
  • Quark Masses and SM Parameters
  • Scattering Amplitudes


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