Laurent series expansion of sunrise-type diagrams using configuration space techniques

Groote, S.; Körner, Jürgen; Пивоваров, А. А.

doi:10.1140/epjc/s2004-01974-2

Cited by 13 publications

(14 citation statements)

References 60 publications

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“…For n = 3, however, the numerator factorintegral is no longer reducible [137]. The problem of irreducible numerator factors has a straightforward solution in configuration space by the integration-by-parts technique [141]. The starting expression involving the non-trivial numerator factor (k 1 · k 2 ) (or any other scalar product of linear independent inner moments) corresponds toΠ *…”

Section: Irreducible Numerator: Three-loop Vacuum Bubble Casementioning

confidence: 99%

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

2007

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We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases of their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology with an irreducible loop addition.

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Section: Irreducible Numerator: Three-loop Vacuum Bubble Casementioning

confidence: 99%

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

2007

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“…The goal of this paper is to study the first SFI examples of Feynman integrals with numerators and correspondingly to extend the SFI equation system and to study some of its solutions. For some of the other works on the topic of Feynman diagrams with numerators, see [16][17][18][19][20][21][22][23][24].…”

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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“…For a complete discussion of basketball integrals in dimensional regularization, see ref. [37]. -0.00031675 -0.00036476 -0.00032547 -0.00014179 1.063 * φ 21 0.0075590 0.0023970 -0.0033645 0.00069377 - * φ 22 -0.0025197 -0.00079883 0.0011212 -0.00023111 - * φ 31 0.0036091 0.0031005 -0.00069559 -0.00088573 - * φ 32 -0.0012030 -0.0026312 0.0043532 -0.0011224 - * φ 33 0.0 0.00053248 -0.0013736 0.00047246 - Table 3: The fit coefficients allowing to estimate the functions φ ij ,φ ij in the range 0.0 ≤ am 3 ≤ 1.0, according to Eq.…”

Section: Appendix C the 3-loop Basketball In Lattice Regularizationmentioning

confidence: 99%

Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

Renzo¹,

Laine²,

Schröder³

et al. 2008

J. High Energy Phys.

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The pressure of QCD admits at high temperatures a factorization into purely perturbative contributions from "hard" thermal momenta, and slowly convergent as well as nonperturbative contributions from "soft" thermal momenta. The latter can be related to various effective gluon condensates in a dimensionally reduced effective field theory, and measured there through lattice simulations. Practical measurements of one of the relevant condensates have suffered, however, from difficulties in extrapolating convincingly to the continuum limit. In order to gain insight on this problem, we employ Numerical Stochastic Perturbation Theory to estimate the problematic condensate up to 4-loop order in lattice perturbation theory. Our results seem to confirm the presence of "large" discretization effects, going like a ln(1/a), where a is the lattice spacing. For definite conclusions, however, it would be helpful to repeat the corresponding part of our study with standard lattice perturbation theory techniques.

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Laurent series expansion of sunrise-type diagrams using configuration space techniques

Cited by 13 publications

References 60 publications

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

On the evaluation of a certain class of Feynman diagrams in x-space: Sunrise-type topologies at any loop order

Numerator seagull and extended Symmetries of Feynman Integrals

Four-loop lattice-regularized vacuum energy density of the three-dimensional SU(3) + adjoint Higgs theory

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