相关论文: On evaluation of two-loop self-energy diagram with…

Problems occurring in physically important non-trivial examples of loop calculations are discussed. A procedure of deriving expansions of two-loop self-energy diagrams with different masses is constructed. The cases of small and large…

The $\epsilon$-expansion of several two-loop self-energy diagrams with different thresholds and one mass are calculated. On-shell results are reduced to multiple binomial sums which values are presented in analytical form.

For a large class of two-loop selfenergy- and vertex-type diagrams with only one non-zero mass ($M$) and the vertices also with only one non-zero external momentum squared ($q^2$) the first few expansion coefficients are calculated by the…

For two-loop two-point diagrams with arbitrary masses, an algorithm to derive the asymptotic expansion at large external momentum squared is constructed. By using a general theorem on asymptotic expansions of Feynman diagrams, the…

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…

The differential equations for the 2-loop sunrise graph, at equal masses but arbitrary momentum transfer, are used for the analytic evaluation of the coefficients of its Laurent-expansion in the continuous dimension $d$.

Motivated by the precision results in the electroweak theory studies of two-loopFeynman diagrams are performed. Specifically this paper gives a contribution to the knowledge of massive two-loop self-energy diagrams in arbitrary and…

I describe a method to calculate a class of three-loop selfenergy diagrams for arbitrary internal masses and external momentum. This method combines analytical results and numerical integration, and is suitable for implementation in a…

This class of diagrams has numerous applications. Many interesting results have been obtained for it.

The master differential equations in the external square momentum p^2 for the master integrals of the two-loop sunrise graph, in n-continuous dimensions and for arbitrary values of the internal masses, are derived. The equations are then…

We derive new convergent series representations for the two-loop sunset diagram with three different propagator masses m1, m2 and m3 and external momentum p by techniques of analytic continuation on a well-known triple series that…

The scalar two-loop self-energy master diagram is studied in the case of arbitrary masses. Analytical results in terms of Lauricella- and Appell-functions are presented for the imaginary part. By using the dispersion relation a…

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…

The behaviour of two-loop two-point diagrams at non-zero thresholds corresponding to two-particle cuts is analyzed. The masses involved in a cut and the external momentum are assumed to be small as compared to some of the other masses of…

An algorithm is constructed to derive a small momentum expansion for two-loop two-point diagrams in all cases where, due to the presence of physical thresholds, there are singularities at zero external momentum. The coefficients of this…

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…

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…

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions…

Evaluation of three- and four-point diagrams with massless internal particles and arbitrary external momenta is considered. Exact results for some two-loop diagrams (planar and non-planar three-point contributions and the "double box"…

In all mass cases needed for quark and gluon self-energies, the two-loop master diagram is expanded at large and small $q^2$, in $d$ dimensions, using identities derived from integration by parts. Expansions are given, in terms of…