TY - JOUR

T1 - Numerator seagull and extended Symmetries of Feynman Integrals

AU - Kol, Barak

AU - Schiller, Amit

AU - Shir, Ruth

N1 - Publisher Copyright:
© 2021, The Author(s).

PY - 2021/1

Y1 - 2021/1

N2 - 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.

AB - 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.

KW - Perturbative QCD

KW - Quark Masses and SM Parameters

KW - Scattering Amplitudes

UR - http://www.scopus.com/inward/record.url?scp=85100218136&partnerID=8YFLogxK

U2 - 10.1007/JHEP01(2021)165

DO - 10.1007/JHEP01(2021)165

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AN - SCOPUS:85100218136

SN - 1126-6708

VL - 2021

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 1

M1 - 165

ER -