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We present a grapical way to describe invariants and covariants in the (4 dim) general relativity. This makes us free from the complexity of suffixes . Two new off-shell relations between (mass)$\ast\ast 6$\ invariants are obtained. These…

High Energy Physics - Theory · Physics 2010-04-06 Shoichi Ichinose

We present a method to compute the Laurent expansion of the two-loop sunrise integral with equal non-zero masses to arbitrary order in the dimensional regularisation $\varepsilon$. This is done by introducing a class of functions…

High Energy Physics - Phenomenology · Physics 2016-04-20 Luise Adams , Christian Bogner , Stefan Weinzierl

We calculate the two-mass three-loop contributions to the unpolarized and polarized massive operator matrix elements $\tilde{A}_{Qg}^{(3)}$ and $\Delta \tilde{A}_{Qg}^{(3)}$ in $x$-space for a general mass ratio by using a semi-analytic…

High Energy Physics - Phenomenology · Physics 2025-10-13 J. Ablinger , J. Blümlein , A. De Freitas , A. von Manteuffel , C. Schneider , K. Schönwald

We use dimensional regularization to evaluate quantum mechanical path integrals in arbitrary curved spaces on an infinite time interval. We perform 3-loop calculations in Riemann normal coordinates, and 2-loop calculations in general…

High Energy Physics - Theory · Physics 2009-10-31 F. Bastianelli , O. Corradini , P. van Nieuwenhuizen

An algorithm to construct analytic approximations to two-loop diagrams describing their behaviour at small non-zero thresholds is discussed. For some special cases (involving two different-scale mass parameters), several terms of the…

High Energy Physics - Phenomenology · Physics 2015-06-25 F. A. Berends , A. I. Davydychev , V. A. Smirnov

Two-loop multi-leg form factors in off-shell kinematics require knowledge of planar and nonplanar double box Feynman diagrams with massless internal propagators. These are complicated functions of Mandelstam variables and external particle…

High Energy Physics - Theory · Physics 2024-02-29 A. V. Belitsky , V. A. Smirnov

We discuss a practical approach to compute master integrals entering physical quantities which depend on one parameter. As an example we consider four-loop QCD corrections to the relation between a heavy quark mass defined in the…

High Energy Physics - Phenomenology · Physics 2021-10-11 Matteo Fael , Fabian Lange , Kay Schönwald , Matthias Steinhauser

We consider the most general two-loop massless correlator $I(n_1,n_2,n_3,n_4,n_5; x,y;D)$ of two composite vertices with the Bjorken fractions $x$ and $y$ for arbitrary indices $\{n_i\}$ and space-time dimension $D$; this correlator is…

High Energy Physics - Theory · Physics 2022-06-16 S. V. Mikhailov , N. Volchanskiy

The program package XLOOPS calculates massive one- and two-loop Feynman diagrams. It consists of five parts: i) a graphical user interface ii) routines for generating diagrams from particle input iii) procedures for calculating one-loop…

High Energy Physics - Phenomenology · Physics 2011-02-11 L. Brücher , J. Franzkowski , A. Frink , D. Kreimer

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 Symmetries of Feynman Integrals method (SFI) associates a natural Lie group with any diagram, depending only on its topology. The group acts on parameter space and the method determines the integral's dependence within group orbits.…

High Energy Physics - Theory · Physics 2018-07-20 Barak Kol

As a generalization of a previous work [Phys. Rev. D. {\bf 59}, 105014 (1999)], we compute analytically a class of three-loop vacuum diagrams with two {\em arbitrarily} different mass scales. We use a decomposition algorithm in which the…

High Energy Physics - Phenomenology · Physics 2008-11-26 J. -M. Chung , B. K. Chung

We present a simple method which simplifies the evaluation of the on-shell multiple box diagrams reducing them to triangle type ones. For the $L$-loop diagram one gets the expression in terms of Feynman parameters with $2L$-fold…

High Energy Physics - Theory · Physics 2015-06-18 D. I. Kazakov

We present an algorithm to evaluate multiloop Feynman integrals with an arbitrary number of internal massive lines, with the masses being in general complex-valued, and its implementation in the \textsc{Mathematica} package…

High Energy Physics - Phenomenology · Physics 2022-10-24 Tommaso Armadillo , Roberto Bonciani , Simone Devoto , Narayan Rana , Alessandro Vicini

We report on recent results on the two-mass corrections for massive operator matrix elements at 2- and 3-loop orders in QCD. These corrections form the building blocks of the variable flavor number scheme. Due to the similar values of the…

High Energy Physics - Phenomenology · Physics 2018-07-23 J. Ablinger , J. Blümlein , A. De Freitas , A. Goedicke , C. Schneider , K. Schönwald

A method to calculate two-loop self-energy diagrams of the Standard Model is demonstrated. A direct physical application is the calculation of the two-loop electroweak contribution to the anomalous magnetic moment of the muon…

High Energy Physics - Phenomenology · Physics 2009-10-30 L. Avdeev , J. Fleischer , M. Yu. Kalmykov , M. N. Tentyukov

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the…

High Energy Physics - Phenomenology · Physics 2009-11-10 R. Bonciani , P. Mastrolia , E. Remiddi

We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell)…

High Energy Physics - Phenomenology · Physics 2014-11-17 Natalia I. Ussyukina , Andrei I. Davydychev

Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…

Mathematical Physics · Physics 2020-09-03 Juuso Österman

We report on the three-loop unpolarized and polarized massive operator matrix elements, with single- and two-mass corrections, and the associated deep-inelastic massive Wilson coefficients in the region $Q^2 \gg m_Q^2$, the calculation of…

High Energy Physics - Phenomenology · Physics 2026-02-12 J. Ablinger , A. Behring , J. Blümlein , A. De Freitas , A. von Manteuffel , C. Schneider , K. Schönwald