Numerator seagull and extended Symmetries of Feynman Integrals
Abstract 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....
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2021-01-01
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Online Access: | https://doi.org/10.1007/JHEP01(2021)165 |
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doaj-0eac62ce4a44433880431ce601563df52021-01-31T12:13:17ZengSpringerOpenJournal of High Energy Physics1029-84792021-01-012021112810.1007/JHEP01(2021)165Numerator seagull and extended Symmetries of Feynman IntegralsBarak Kol0Amit Schiller1Ruth Shir2Racah Institute of Physics, The Hebrew University of JerusalemRacah Institute of Physics, The Hebrew University of JerusalemRacah Institute of Physics, The Hebrew University of JerusalemAbstract 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.https://doi.org/10.1007/JHEP01(2021)165Perturbative QCDScattering AmplitudesQuark Masses and SM Parameters |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Barak Kol Amit Schiller Ruth Shir |
spellingShingle |
Barak Kol Amit Schiller Ruth Shir Numerator seagull and extended Symmetries of Feynman Integrals Journal of High Energy Physics Perturbative QCD Scattering Amplitudes Quark Masses and SM Parameters |
author_facet |
Barak Kol Amit Schiller Ruth Shir |
author_sort |
Barak Kol |
title |
Numerator seagull and extended Symmetries of Feynman Integrals |
title_short |
Numerator seagull and extended Symmetries of Feynman Integrals |
title_full |
Numerator seagull and extended Symmetries of Feynman Integrals |
title_fullStr |
Numerator seagull and extended Symmetries of Feynman Integrals |
title_full_unstemmed |
Numerator seagull and extended Symmetries of Feynman Integrals |
title_sort |
numerator seagull and extended symmetries of feynman integrals |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2021-01-01 |
description |
Abstract 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. |
topic |
Perturbative QCD Scattering Amplitudes Quark Masses and SM Parameters |
url |
https://doi.org/10.1007/JHEP01(2021)165 |
work_keys_str_mv |
AT barakkol numeratorseagullandextendedsymmetriesoffeynmanintegrals AT amitschiller numeratorseagullandextendedsymmetriesoffeynmanintegrals AT ruthshir numeratorseagullandextendedsymmetriesoffeynmanintegrals |
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