Vacuum seagull: Evaluating a three-loop Feynman diagram with three mass scales

Burda, Philipp; Kol, Barak; Shir, Ruth

doi:10.1103/physrevd.96.125013

Cited by 10 publications

(24 citation statements)

References 28 publications

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“…By now, SFI was further developed and numerous diagrams have been analyzed within it [8][9][10][11][12][13][14][15]. Even though these diagrams are relatively basic, the analysis achieved new results including the value of the seagull diagram (to be discussed below) in a 3 mass scale sector and the value of the kite diagram (2-loop 2-leg) throughout its singular locus.…”

Section: Jhep01(2021)165mentioning

confidence: 99%

Numerator seagull and extended Symmetries of Feynman Integrals

Kol

Schiller

Shir

2021

J. High Energ. Phys.

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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.

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Section: Jhep01(2021)165mentioning

confidence: 99%

Numerator seagull and extended Symmetries of Feynman Integrals

Kol

Schiller

Shir

2021

J. High Energ. Phys.

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“…[54]- [73] found a variety of important special analytical cases that have been incorporated into 3VIL.…”

Section: Conventions and Setupmentioning

confidence: 99%

Effective potential at three loops

Martin

2017

Phys. Rev. D

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I present the effective potential at three-loop order for a general renormalizable theory, using the \MSbar renormalization scheme and Landau gauge fixing. As applications and illustrative points of reference, the results are specialized to the supersymmetric Wess-Zumino model and to the Standard Model. In each case, renormalization group scale invariance provides a consistency check. In the Wess-Zumino model, the required vanishing of the minimum vacuum energy yields an additional check. For the Standard Model, I carry out the resummation of Goldstone boson contributions, which provides yet more opportunities for non-trivial checks, and obtain the minimization condition for the Higgs vacuum expectation value at full three-loop order. An infrared divergence due to doubled photon propagators appears in the three-loop Standard Model effective potential, but it does not affect the minimization condition or physical observables and can be eliminated by resummation.Comment: 48 pages, 8 ancillary file

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“…Analytic calculation of Feynman diagrams with several mass scales is a challenge, but it is important for higher loop corrections to Standard Model/Core Theory 1 observables involving several different particles, and it is of intrinsic interest to Quantum Field Theory. The Symmetries of Feynman Integrals method (SFI) [2], see also developments in [3][4][5][6][7][8], reduces the diagram to its value at some allowed and more convenient base point in parameter space, namely the space X of masses and kinematical invariants, plus a line integral in X over simpler diagrams (with one edge contracted).…”

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confidence: 99%

The propagator seagull: general evaluation of a two loop diagram

Kol

Shir

2019

J. High Energ. Phys.

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We study a two loop diagram of propagator type with general parameters through the Symmetries of Feynman Integrals (SFI) method. We present the SFI group and equation system, the group invariant in parameter space and a general representation as a line integral over simpler diagrams. We present close form expressions for three sectors, each with three or four energy scales, for any spacetime dimension d as well as the expansion. We determine the singular locus and the diagram's value on it. arXiv:1809.05040v3 [hep-th] 19 May 2019 ∂ 2 O 3 I(M 2 , m 2 t, m 2 4 , p 2 ) = J bubble (1, 1; M 2 , m 2 4 , p 2 )J tad (2; m 2 t) (5.37) with J tad and J bubble defined in (A.1) and (A.2) and given explicitly by J bubble (1, 1; M 2 , m 2 4 , p 2 ) = i 1−d π d/2 (−m 2 4 )

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Vacuum seagull: Evaluating a three-loop Feynman diagram with three mass scales

Cited by 10 publications

References 28 publications

Numerator seagull and extended Symmetries of Feynman Integrals

Numerator seagull and extended Symmetries of Feynman Integrals

Effective potential at three loops

The propagator seagull: general evaluation of a two loop diagram

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