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(ǫ) terms in D = 4 − 2ǫ space-time dimensions.

We investigate Feynman diagrams which are calculable in terms of generalized one-loop functions, and explore how the presence or absence of transcendentals in their counterterms reflects the entanglement of link diagrams constructed from them.

The MSSM is extended to the $U(1)_X$SSM, whose local gauge group $SU(3)_C \times SU(2)_L U(1)_Y U(1)_X$. To obtain we add new superfields MSSM, namely: three Higgs singlets $\hat{\eta},~\hat{\bar{\eta}},~\hat{S}$ and right-handed neutrinos $\hat{\nu}_i$. It can give light neutrino tiny mass at tree level through seesaw mechanism. study of contribution two-loop diagrams MDM muon under $U(1)_X$SS...

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 1 2 (g − 2) µ. Presently we confine ourselves to a " toy " model with only µ, γ and a scalar particle (Higgs). The algorithm is implemented as a package of computer progra...

In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving 3 distinct masses. A proof is devised, though it cannot be accounted as a derivation; rather it certifies that an Ansatz found by PSLQ satisfies a more easily derived pair of partial differential equations. The resul...

The computation of higher order processes very often involves a large number of diagrams. In addition, it is in general not possible to solve the occurring integrals explicitly and expansions in small quantities have to be performed. This makes it necessary to automate the calculations as much as possible. A program package will be described which generates automatically the Feynman diagrams, m...

Abstract. The Bethe approximation is a successful method for approximating partition functions of probabilistic models associated with a graph. Recently, Chertkov and Chernyak derived an interesting formula called “Loop Series Expansion”, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labelled by subgraphs called gen...

In a recent paper [1] a new powerful method to calculate Feynman diagrams was proposed. It consists in setting up a Taylor series expansion in the external momenta squared. The Taylor coefficients are obtained from the original diagram by differentiation and putting the external momenta equal to zero. It was demonstrated that by a certain conformal mapping and subsequent resummation by means of...

Aims. We describe various expansion schemes that can be used to study gravitational clustering. Obtained from the equations of motion or their path-integral formulation, they provide several perturbative expansions that are organized in a different fashion or involve different partial resummations. We focus on the two-point and three-point correlation functions, but these methods also apply to ...

The use of Mellin-Barnes integrals became a widespread technique for calculating Feynman diagrams throughout the last years [ 1], in particular to calculate double and triple box-diagrams. In Ref. [ 2], it was possible to expand the scalar two-loop two-point function in all orders in the dimensional regularization parameter ε, using additionally the gluing operation of Feynman diagrams, defined...