Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

Abstract Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or correlator web, which is a set of skeleton diagrams built with connected gluon correlators, and we computed the mixing matrices for all Cwebs connecting four or five Wilson lines at four loops. Here we complete the evaluation of four-loop mixing matrices, presenting the results for all Cwebs connecting two and three Wilson lines. We observe that the conjuctured column sum rule is obeyed by all the mixing matrices that appear at four-loops. We also show how low-dimensional mixing matrices can be uniquely determined from their known combinatorial properties, and provide some all-order results for selected classes of mixing matrices. Our results complete the required colour building blocks for the calculation of the soft anomalous dimension matrix at four-loop order.

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Master integrals for bipartite cuts of three-loop photon self energy

Journal of High Energy Physics ◽

10.1007/jhep04(2021)177 ◽

2021 ◽

Vol 2021 (4) ◽

Author(s):

R. N. Lee ◽

A. I. Onishchenko

Keyword(s):

Spectral Density ◽

High Energy ◽

Elliptic Integrals ◽

Iterated Integrals ◽

Self Energy ◽

Complete Elliptic Integrals ◽

The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

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On two supercongruences of double binomial sums

Periodica Mathematica Hungarica ◽

10.1007/s10998-020-00377-4 ◽

2021 ◽

Author(s):

Long Li ◽

Ji-Cai Liu

Keyword(s):

Binomial Sums

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Bold Feynman Diagrams and the Luttinger–Ward Formalism via Gibbs Measures: Perturbative Approach

Archive for Rational Mechanics and Analysis ◽

10.1007/s00205-021-01692-x ◽

2021 ◽

Author(s):

Lin Lin ◽

Michael Lindsey

Keyword(s):

Gibbs Measures ◽

Feynman Diagrams ◽

Perturbative Approach

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Stochastic computation of g − 2 in QED

Journal of High Energy Physics ◽

10.1007/jhep05(2021)119 ◽

2021 ◽

Vol 2021 (5) ◽

Author(s):

Ryuichiro Kitano ◽

Hiromasa Takaura ◽

Shoji Hashimoto

Keyword(s):

Perturbation Theory ◽

Numerical Computation ◽

Magnetic Moment ◽

Anomalous Magnetic Moment ◽

Stochastic Perturbation ◽

Higher Order ◽

Feynman Diagrams ◽

Perturbative Series ◽

Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

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