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

The massless sunrise diagram with an arbitrary number of loops is calculated in a simple but formal manner. The result is then verified by rigorous mathematical treatment. Pitfalls in the calculation with distributions are highlighted and…

In this paper, we consider the two-loop sunset diagram with two different masses, m and M, at spacelike virtuality q^2 = -m^2. We find explicit representations for the master integrals and an analytic result through O(epsilon) in…

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…

We derive expressions for the phase-space of a particle of momentum $p$ decaying into $N$ particles, that are valid for any number of dimensions. These are the imaginary parts of so-called `sunset' diagrams, which we also obtain. The…

The differential equation in the external invariant p^2 satisfied by the master integral of the general massive 2-loop 4-denominator self-mass diagram is exploited and the expansion of the master integral at p^2=0 is obtained analytically.…

We determine the numerical values of scalar multi-loop two-vertex Feynman diagrams, the generalized sunset diagrams, by integrating all but the longitudinal momenta analytically. For the longitudinal momenta we introduce one collective…

A set of recurrence relations for on-shell two-loop self-energy diagrams with one mass is presented, which allows to reduce the diagrams with arbitrary indices (powers of scalar propagators) to a set of the master integrals. The SHELL2…

I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…

The one-loop HQET heavy-heavy vertex diagram with arbitrary powers of all three denominators and arbitrary residual energies is investigated. Various particular cases in which the result becomes simpler are considered.

We study the sunset graph defined as the scalar two-point self-energy at two-loop order. We evaluate the sunset integral for all identical internal masses in two dimensions. We give two calculations for the sunset amplitude; one based on an…

We consider two loop sunset diagrams with two mass scales m and M at the threshold and pseudotreshold that cannot be treated by earlier published formula. The complete reduction to master integrals is given. The master integrals are…

Explicit general formulae for the tensor reduction of two-loop massive vacuum diagrams are presented. The problem of calculating the corresponding coefficients is shown to be equivalent to the problem of constructing differential operators…

We consider the two-loop self-mass sunrise amplitude with two equal masses $M$ and the external invariant equal to the square of the third mass $m$ in the usual $d$-continuous dimensional regularization. We write a second order differential…

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…

The threshold behavior of the master amplitudes for two loop sunrise self-mass graph is studied by solving the system of differential equations, which they satisfy. The expansion at the threshold of the master amplitudes is obtained…

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.…

A recently proposed method of calculating scalar two-loop propagator and vertex functions with massive particles is illustrated with simple examples. A double integral representation is derived with the example of a propagator function. An…

I present results for the two-loop self-energy functions for scalars in a general renormalizable field theory, using mass-independent renormalization schemes based on dimensional regularization and dimensional reduction. The results are…

Detailed description of the calculation of the 2-loop self-energy for a scalar particle is presented. By employing a simple sector decomposition method, the ultraviolet divergent part is efficiently separated from the finite part. The…

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…