Andrei I. Davydychev

Massive Feynman diagrams and inverse binomial sums

Abstract When calculating higher terms of the ɛ -expansion of massive Feynman diagrams, one needs to evaluate particular cases of multiple inverse binomial sums. These sums are related to the derivatives of certain hypergeometric functions with respect to their parameters. Exploring this connection and using it together with an approach based on generating functions, we analytically calculate a number of such infinite sums, for an arbitrary value of the argument which corresponds to an arbitrary value of the off-shell external momentum. In such a way, we find a number of new results for physically important Feynman diagrams. Considered examples include two-loop two- and three-point diagrams, as well as three-loop vacuum diagrams with two different masses. The results are presented in terms of generalized polylogarithmic functions. As a physical example, higher-order terms of the ɛ -expansion of the polarization function of the neutral gauge bosons are constructed.

An approach to the evaluation of three- and four-point ladder diagrams

Abstract An approach to the calculation of ladder graphs with three and four external lines is considered (in the case of massless internal particles and arbitrary external momenta). Simple formulae for reducing four-point diagrams to three-point vertices are derived. Exact results for diagrams up to the two-loop level are obtained in terms of polylogarithms.

A simple formula for reducing Feynman diagrams to scalar integrals

Abstract An explicit general formula is obtained which makes it possible to reduce tensor Feynman integrals (corresponding to arbitrary one-loop N -point diagrams) to scalar integrals.

New results for the ε-expansion of certain one-, two- and three-loop Feynman diagrams

Abstract For certain dimensionally-regulated one-, two- and three-loop diagrams, problems of constructing the e -expansion and the analytic continuation of the results are studied. In some examples, an arbitrary term of the e -expansion can be calculated. For more complicated cases, only a few higher terms in e are obtained. Apart from the one-loop two- and three-point diagrams, the examples include two-loop (mainly on-shell) propagator-type diagrams and three-loop vacuum diagrams. As a by-product, some new relations involving Clausen function, generalized log-sine integrals and certain Euler–Zagier sums are established, and some useful results for the hypergeometric functions of argument 1 4 are presented.

Explicit results for all orders of the ɛ expansion of certain massive and massless diagrams

An arbitrary term of the

Some exact results for N point massive Feynman integrals

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General results for massive N‐point Feynman diagrams with different masses

expansion of a dimensionally regulated off-shell massless one-loop three-point Feynman diagram is expressed in terms of log-sine integrals related to the polylogarithms. Using a magic connection between these diagrams and two-loop massive vacuum diagrams, the

Threshold and pseudothreshold values of the sunset diagram

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Some remarks on the ϵ-expansion of dimensionally regulated Feynman diagrams

expansion of the latter is also obtained, for arbitrary values of the masses. The problem of analytic continuation is also discussed.

Threshold expansion of the sunset diagram

By using the Mellin–Barnes representation for massive denominators, some exact results for classes of one‐loop N‐point massive Feynman integrals are obtained for arbitrary values of the line indices (the powers of denominators) and of the space‐time dimension. A representation for corresponding massless integral is also derived.