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A recently proposed scheme for numerical evaluation of Feynman diagrams is extended to cover all two-loop two-point functions with arbitrary internal and external masses. The adopted algorithm is a modification of the one proposed by F. V.…

High Energy Physics - Phenomenology · Physics 2009-11-07 G. Passarino , S. Uccirati

The method of the large mass expansion (LME) is investigated for selfenergy and vertex functions in two-loop order. It has the technical advantage that in many cases the expansion coefficients can be expressed analytically. As long as only…

High Energy Physics - Phenomenology · Physics 2009-09-25 J. Fleischer , A. V. Kotikov , O. L. Veretin

A new scheme for the numerical evaluation of the one-loop self-energy correction to all orders in Z \alpha is presented. The scheme proposed inherits the attractive features of the standard potential-expansion method but yields a…

Atomic Physics · Physics 2009-11-11 Vladimir A. Yerokhin , Krzysztof Pachucki , Vladimir M. Shabaev

By use of the threshold expansion we develop an algorithm for analytical evaluation, within dimensional regularization, of arbitrary terms in the expansion of the (two-loop) sunset diagram with general masses m_1, m_2 and m_3 near its…

High Energy Physics - Phenomenology · Physics 2010-11-15 A. I. Davydychev , V. A. Smirnov

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 2011-04-15 L. Avdeev , J. Fleischer , M. Yu. Kalmykov , M. Tentyukov

An efficient method to calculate tadpole diagrams is proposed. Its capability is demonstrated by analytically evaluating two four-loop tadpole diagrams of current interest in the literature, including their $O(\epsilon)$ terms in…

High Energy Physics - Phenomenology · Physics 2009-11-11 Bernd A. Kniehl , Anatoly V. Kotikov

The method suggested by Lowell Brown for calculating multi-particle threshold amplitudes is extended to the one-loop level in scalar theories with broken reflection symmetry. A result for the threshold amplitude for multiparticle production…

High Energy Physics - Phenomenology · Physics 2009-10-22 B. H. Smith

We report a method for the evaluation of the one-loop self-energy, to all orders in the external binding field, using a Gaussian basis set expansion. This choice of basis is motivated by its widespread use in molecular calculations. For a…

Quantum Physics · Physics 2025-04-14 Dávid Ferenc , Maen Salman , Trond Saue

We give an algorithm for obtaining expansions of massive two-loop Feynman graphs in powers of the external momentum around a finite, nonzero value of the momentum. This is based on our general two-loop formalism to reduce massive two-loop…

High Energy Physics - Phenomenology · Physics 2009-10-31 A. Ghinculov , Y. P. Yao

New method of calculation of master integrals using differential equations and asymptotical expansion is presented. This method leads to the results exact in space-time dimension $D$ having the form of the convergent power series. As an…

High Energy Physics - Phenomenology · Physics 2009-11-11 A. V. Bogdan , R. N. Lee

Recently presented explicit formulae for asymptotic expansions of Feynman diagrams in the Sudakov limit are applied to typical two-loop diagrams. For a diagram with one non-zero mass these formulae provide an algorithm for analytical…

High Energy Physics - Phenomenology · Physics 2009-10-30 V. A. Smirnov

We present a review of the Bielefeld-Dubna activities on the multiloop calculations. In the first part a C-program DIANA (DIagram ANAlyser) for the automation of Feynman diagram evaluations is presented, in the second part various…

High Energy Physics - Phenomenology · Physics 2011-04-15 J. Fleischer , M. Tentyukov , O. L. Veretin

It is shown that the technique recently suggested by Lowell Brown for summing the tree graphs at threshold can be extended to calculate the loop effects. Explicit result is derived for the sum of one-loop graphs for the amplitude of…

High Energy Physics - Phenomenology · Physics 2009-12-30 M. B. Voloshin

Hard thermal loops describe how soft gauge fields are screened and damped in hot plasmas. As such they are used to calculate transport coefficients, Sphaleron rates, equations of state, and particle production. However, most calculations…

High Energy Physics - Phenomenology · Physics 2023-07-12 Andreas Ekstedt

The differential equation method is applied to evaluate analytically two-loop vertex Feynman diagrams. Three on-shell infrared divergent planar two-loop diagrams with zero thresholds contributing to the processes Z --> bb bar (for zero b…

High Energy Physics - Phenomenology · Physics 2009-10-30 J. Fleischer , A. V. Kotikov , O. L. Veretin

For certain dimensionally-regulated massive two- and three-loop propagator-type diagrams the higher order epsilon-expansion is constructed.

High Energy Physics - Phenomenology · Physics 2010-04-05 M. Yu. Kalmykov

We apply differential equations technique to the calculation of the one-loop massless diagram with one offshell legs. Using reduction to $\epsilon$-form, we managed to obtain a simple one-fold integral representation exact in space-time…

High Energy Physics - Phenomenology · Physics 2017-02-15 Mikhail G. Kozlov

Calculations of the two-loop electron self-energy for the $n = 1$ and $n = 2$ states of hydrogen-like ions are reported, performed to all orders in the nuclear binding strength parameter $Z\alpha$ (where $Z$ is the nuclear charge number and…

Atomic Physics · Physics 2025-09-12 V. A. Yerokhin , Z. Harman , C. H. Keitel

Loop diagram calculations typically rely on reduction to a finite set of master integrals in $4 - 2\epsilon$ dimensions. It has been shown that for any problem, the masters can be chosen so that their coefficients are finite as $\epsilon…

High Energy Physics - Phenomenology · Physics 2022-04-06 Stephen P. Martin

Three-loop vertex diagrams in HQET needed for sum rules for B^0 - \bar{B}^0 mixing are considered. They depend on two residual energies. An algorithm of reduction of these diagrams to master integrals has been constructed. All master…

High Energy Physics - Phenomenology · Physics 2014-11-18 Andrey G. Grozin , Roman N. Lee