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Andrei I. Davydychev

Publications and source records attributed to Andrei I. Davydychev.

8 recordsLinked to original sources
arXiv2026

Factorizing two-loop vacuum sum-integrals

We derive analytic results for scalar massless bosonic vacuum sum-integrals at two loops. Building upon a recent factorization proof of massive two-loop vacuum integrals, we are able to solve the corresponding Matsubara sums and map the result onto one-loop structures, thereby proving factorization also in the sum-integral setting. Analytic results are provided for generic integer-valued propagator- and numerator-powers of the class of sum-integrals under consideration, allowing to eliminate them from any perturbative expansion, dramatically simplifying the evaluation of some observables encountered e.g. in hot QCD.

hep-ph↗
arXiv2022

Recursion-free solution for two-loop vacuum integrals with "collinear" masses

We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation $m_1+m_2=m_3$ between its three propagator masses, corresponding to zeros of the associated Källén function. Apart from having applications in thermal field theory, the integrals can be mapped onto one-loop three-point functions with collinear external momenta, suggesting the term "collinear" masses. We present a closed-form solution for these integrals, proving that they can always be factorized into products of one-loop cases, for all integer-valued propagator powers.

hep-ph↗
arXiv2016

Geometrical splitting and reduction of Feynman diagrams

A geometrical approach to the calculation of N-point Feynman diagrams is reviewed. It is shown that the geometrical splitting yields useful connections between Feynman integrals with different momenta and masses. It is demonstrated how these results can be used to reduce the number of variables in the occurring functions.

hep-th↗
arXiv2010

Exponential suppression with four legs and an infinity of loops

The L-loop 4-point ladder diagram of massless phi^3 theory is finite when all 4 legs are off-shell and is given in terms of polylogarithms with orders ranging from L to 2L. We obtain the exact solution of the linear Dyson-Schwinger equation that sums these ladder diagrams and show that this sum vanishes exponentially fast at strong coupling.

hep-th↗
arXiv1996

Some techniques for calculating two-loop diagrams

A brief overview of some recent publications related to the evaluation of two-loop Feynman diagrams is given. (Talk given at the International Symposium on Radiative Corrections CRAD96, Cracow, Poland, 1--5 August 1996)

hep-ph↗
arXiv1994

Two-loop three-point diagrams with irreducible numerators

We study the problem of calculating two-loop three-point diagrams with irreducible numerators (i.e. numerators which cannot be expressed in terms of the denominators). For the case of massless internal particles and arbitrary (off-shell) external momenta, exact results are obtained in terms of polylogarithms. We also consider the tensor decomposition of two-loop three-point diagrams, and show how it is connected with irreducible numerators.

hep-ph↗
arXiv1993

Two-loop renormalization group analysis of hadronic decays of a charged Higgs boson

We calculate next-to-leading QCD corrections to the decay $H^+ \to u\bar d$ for generic up and down quarks in the final state. A recently developed algorithm for evaluation of massive two-loop Feynman diagrams is employed to calculate renormalization constants of the charged Higgs boson. The origin and summation of large logarithmic corrections to the decay rate of the top quark into a lighter charged Higgs boson is also explained.

hep-ph↗