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Related papers: Techniques for Calculating two-loop Diagrams

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We introduce dynamical versions of loop (or Dyson-Schwinger) equations for large families of two--dimensional interacting particle systems, including Dyson Brownian motion, Nonintersecting Bernoulli/Poisson random walks, $\beta$--corners…

Probability · Mathematics 2024-03-07 Vadim Gorin , Jiaoyang Huang

Recent developments in the field of automatic computation of Feynman diagrams using asymptotic expansions are reviewed. The hadronic decay rate of the Z-boson is taken as an example for their physical application.

High Energy Physics - Phenomenology · Physics 2011-07-19 Robert Harlander

We calculate the two-loop QCD corrections to $gg \to ZZ$ involving a closed top-quark loop. We present a new method to systematically construct linear combinations of Feynman integrals with a convergent parametric representation, where we…

High Energy Physics - Phenomenology · Physics 2021-06-16 Bakul Agarwal , Stephen P. Jones , Andreas von Manteuffel

We discuss a progress in calculations of Feynman integrals based on the Gegenbauer Polynomial Technique and the Differential Equation Method. We demonstrate the results for a class of two-point two-loop diagrams and the evaluation of most…

High Energy Physics - Phenomenology · Physics 2007-05-23 A. V. Kotikov

Decay amplitude of $H \to \gamma Z$ process via one $W$ loop in the unitary gauge is presented. The divergent integrals including those of high divergence orders typical of unitary gauge are arranged to cancel to get the electromagnetic…

High Energy Physics - Phenomenology · Physics 2023-06-21 Shi-Yuan Li

A FORM based package (ON-SHELL2) for the calculation of two loop self-energy diagrams with one nonzero mass in internal lines and the external momentum on the same mass shell is elaborated. The algorithm, based on recurrence relations…

High Energy Physics - Phenomenology · Physics 2014-11-17 J. Fleischer , M. Yu. Kalmykov

Two-loop massive Feynman integrals for $\phi^4$ field-theoretical model with long-range correlated disorder are considered. Massive integrals for the vertex function $\Gamma^{(4)}$ including two or three massless propagators for generic…

Statistical Mechanics · Physics 2015-04-01 M. Dudka

We calculate two-loop massive master integrals for $e^{+}e^{-}\rightarrow2\gamma$ in terms of generalized power series with respect to electron mass. The coefficients of this series are expressed via Goncharov's polylogarithms. Our approach…

High Energy Physics - Phenomenology · Physics 2024-10-07 Roman N. Lee , Vyacheslav A. Stotsky

I study the Feynman integrals needed to compute two-loop self-energy functions for general masses and external momenta. A convenient basis for these functions consists of the four integrals obtained at the end of Tarasov's recurrence…

High Energy Physics - Phenomenology · Physics 2014-11-17 Stephen P. Martin

We compute the full set of two-loop Feynman integrals appearing in massless two-loop four-point functions with two off-shell legs with the same invariant mass. These integrals allow to determine the two-loop corrections to the amplitudes…

High Energy Physics - Phenomenology · Physics 2014-06-13 Thomas Gehrmann , Andreas von Manteuffel , Lorenzo Tancredi , Erich Weihs

In the paper, we obtain an expression for a two-loop master-diagram by using the Mellin$-$Barnes transformation. In the two-dimensional case we managed to factorize the answer and write it as a bilinear combination of hypergeometric…

High Energy Physics - Theory · Physics 2023-10-05 S. E. Derkachev , A. V. Ivanov , L. A. Shumilov

The $tW\bar{b}$ production contributes to the real corrections to the $tW$ cross section. It would interfere with the top quark pair production, causing difficulties in a clear definition of the $tW{\bar b}$ events. The subtraction of the…

High Energy Physics - Phenomenology · Physics 2025-04-01 Liang Dong , Hai Tao Li , Zheng-Yu Li , Jian Wang

The method of regions, which provides a systematic approach for computing Feynman integrals involving multiple kinematic scales, proposes that a Feynman integral can be approximated and even reproduced by summing over integrals expanded in…

High Energy Physics - Phenomenology · Physics 2024-10-01 Yao Ma

Feynman diagrams may be evaluated by Mellin-Barnes representations of their Feynman parameter integrals in d=4-2\eps dimensions. Recently, the Mathematica toolkit AMBRE has been developed for the automatic derivation of such representations…

High Energy Physics - Phenomenology · Physics 2009-04-16 J. Gluza , F. Haas , K. Kajda , T. Riemann

Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to have an intrinsic mathematical…

Representation Theory · Mathematics 2016-11-02 Matvei Libine

The dual-fermion approach provides a formally exact prescription for calculating properties of a correlated electron system in terms of a diagrammatic expansion around dynamical mean-field theory (DMFT). Most practical implementations,…

Strongly Correlated Electrons · Physics 2017-08-02 Jan Gukelberger , Evgeny Kozik , Hartmut Hafermann

An approach for an effective computer evaluation of one-loop multi-leg diagrams is proposed. It's main feature is the combined use of several systems - DIANA, FORM and MAPLE. As an application we consider the one-loop correction to Higgs…

High Energy Physics - Phenomenology · Physics 2009-11-07 F. Jegerlehner , O. Tarasov

Some of the difficulties faced when calculating multi-loop amplitudes with several mass scales are reviewed. We then focus on one particular difficulty, the evaluation of the Feynman integrals, and introduce the program pySecDec which can…

High Energy Physics - Phenomenology · Physics 2018-06-08 S. P. Jones , B. Ruijl

We discuss some of the problems that may occur in the calculation of complicated Feynman diagrams. These include the group independent evaluation of color factors, and the summation techniques that are needed for the expansion of diagrams…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. A. M. Vermaseren

We review some recent additions to the tool-chest of techniques for finding compact integrand representations of multiloop gauge-theory amplitudes - including non-planar contributions - applicable for N=4 super-Yang-Mills in four and higher…

High Energy Physics - Theory · Physics 2015-05-27 John Joseph M. Carrasco , Henrik Johansson