Four-point function in general kinematics through geometrical splitting and reduction

It is shown how the geometrical splitting of N-point Feynman diagrams can be used to simplify the parametric integrals and reduce the number of variables in the occurring functions. As an example, a calculation of the dimensionally-regulated one-loop four-point function in general kinematics is presented.Comment: 8 pages, 9 figures, contribution for proceedings of ACAT 2017 (Seattle, USA, August 21-25, 2017). arXiv admin note: substantial text overlap with arXiv:1605.0482

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.Comment: 5 pages, 1 figure, presented at "Loops and Legs in Quantum Field Theory 2010", Woerlitz, Germany, April 201

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 K\"all\'en 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.Comment: 34 pages, 5 figures; v2: references adde

Geometrical methods in loop calculations and the three-point function

A geometrical way to calculate N-point Feynman diagrams is reviewed. As an example, the dimensionally-regulated three-point function is considered, including all orders of its epsilon-expansion. Analytical continuation to other regions of the kinematical variables is discussed.Comment: 6 pages, LaTeX, 3 eps figures, contribution to proceedings of ACAT2005 (Zeuthen, May 2005

New results for two-loop off-shell three-point diagrams

A number of exact results for two-loop three-point diagrams with massless internal particles and arbitrary (off-shell) external momenta are presented. Divergent contributions are calculated in the framework of dimensional regularization.Comment: 10 pages, 3 figures, standard LaTEX (PS-file is also available by anonymous FTP at node VSFYS1.FI.UIB.NO in subdirectory DAVYDYCHEV, the file BERGEN94-03.PS), Bergen Scientific/Technical Report No.1994-0

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.Comment: 10 pages + 4 figures, PostScript

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.Comment: 12 pages, latex, 3 figures, ps-file available at ftp://vsfys1.fi.uib.no/davydychev/bergen94-17.p

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

Abstract We investigate the structure of a particular class of massive vacuum Feynman integrals at two loops. This class enjoys the linear relation m1 + m2 = m3 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