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We propose that the concept of multidimensional residues can be used to directly extracting the coefficients of scalar master integrals (with single propagators only) from one-loop Feynman integrals with generic power of propagators. Unlike…

High Energy Physics - Theory · Physics 2011-12-20 Jian-Hui Zhang

We advertise intersection theory for generalised hypergeometric functions as a means of evaluating Mellin-Barnes representations. As an example, we study two-parameter representations of the off-shell one- and two-loop box graphs in exactly…

High Energy Physics - Theory · Physics 2025-04-17 Burkhard Eden

Among the unitarity cuts of massless 4-loop propagators two classes have remained unknown until recently: 2-loop 3-particle cuts, and 1-loop 4-particle cuts. In this article we shall discuss the calculation that completes the master…

High Energy Physics - Phenomenology · Physics 2019-12-16 Vitaly Magerya , Andrey Pikelner

We present a method to calculate the $x$--space expressions of massless or massive operator matrix elements in QCD and QED containing local composite operator insertions, depending on the discrete Mellin index $N$, directly, without…

High Energy Physics - Phenomenology · Physics 2023-07-05 A. Behring , J. Blümlein , K. Schönwald

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…

High Energy Physics - Phenomenology · Physics 2026-03-24 Andrei I. Davydychev , Pablo Navarrete , York Schröder

We compute epsilon-expansions around 4 dimensions of a complete set of master integrals for momentum space five-loop massless propagator integrals in dimensional regularization, up to and including the first order with contributions of…

High Energy Physics - Phenomenology · Physics 2021-10-04 Alessandro Georgoudis , Vasco Gonçalves , Erik Panzer , Raul Pereira , Alexander V. Smirnov , Vladimir A. Smirnov

The dimensionally regularized massless double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with non-zero q^2=p_1^2, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for…

High Energy Physics - Phenomenology · Physics 2008-11-26 V. A. Smirnov

This paper provides details of the massless three-loop three-point integrals calculation at the symmetric point. Our work aimed to extend known two-loop results for such integrals to the three-loop level. Obtained results can find their…

High Energy Physics - Phenomenology · Physics 2021-06-17 Andrey Pikelner

Unitarity cut method has been proved to be very useful in the computation of one-loop integrals. In this paper, we generalize the method to the situation where the powers of propagators in the denominator are larger than one in general. We…

High Energy Physics - Theory · Physics 2021-08-18 Bo Feng , Hongbin Wang

The class of the two-loop massless crossed boxes, with light-like external legs, is the final unresolved issue in the program of computing the scattering amplitudes of 2 --> 2 massless particles at next-to-next-to-leading order. In this…

High Energy Physics - Phenomenology · Physics 2009-10-31 C. Anastasiou , T. Gehrmann , C. Oleari , E. Remiddi , J. B. Tausk

A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…

High Energy Physics - Phenomenology · Physics 2007-05-23 Stefan Bekavac

We complete the calculation of master integrals for massless three-loop form factors by computing the previously-unknown three diagrams with nine propagators in dimensional regularisation. Each of the integrals yields a six-fold…

High Energy Physics - Phenomenology · Physics 2009-07-24 G. Heinrich , T. Huber , D. A. Kosower , V. A. Smirnov

A short review of the method for the tensor reduction of Feynman integrals based on recurrence relations with respect to space-time dimension d- is given. A solution of the difference equation with respect to d for the n - point one-loop…

High Energy Physics - Phenomenology · Physics 2009-11-07 O. V. Tarasov

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically…

High Energy Physics - Phenomenology · Physics 2008-11-26 V. A. Smirnov

We describe methods for evaluating one-loop integrals in $4-2\e$ dimensions. We give a recursion relation that expresses the scalar $n$-point integral as a cyclicly symmetric combination of $(n-1)$-point integrals. The computation of such…

High Energy Physics - Phenomenology · Physics 2008-11-26 Z. Bern , L. Dixon , D. A. Kosower

Higher order coefficients of the inverse mass expansion of one-loop effective actions are obtained from a one-dimensional path integral representation. For the case of a massive scalar loop in the background of both a scalar potential and a…

High Energy Physics - Theory · Physics 2009-10-30 D. Fliegner , P. Haberl , M. G. Schmidt , C. Schubert

Negative dimensional integration method (NDIM) is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and…

High Energy Physics - Theory · Physics 2008-11-26 Alfredo T. Suzuki , Alexandre G. de M. Schmidt

In this paper, we extend previous work on scalar $\phi^4$ theory using the Source Galerkin method. This approach is based on finding solutions $Z[J]$ to the lattice functional equations for field theories in the presence of an external…

High Energy Physics - Theory · Physics 2009-10-28 John W. Lawson , G. S. Guralnik

Various of the single scale quantities in massless and massive QCD up to 3-loop order can be expressed by iterative integrals over certain classes of alphabets, from the harmonic polylogarithms to root-valued alphabets. Examples are the…

High Energy Physics - Phenomenology · Physics 2017-11-28 J. Ablinger , A. Behring , J. Blümlein , A. De Freitas , E. Imamoglu , M. van Hoeij A. von Manteuffel , C. G. Raab , C. -S. Radu , C. Schneider

We consider solutions of the massless scalar wave equation $\Box_g\psi=0$ on a fixed Rindler background and show polynomial decay of the energy flux related to the Rindler observers near null infinity and to local observers near the Rindler…

General Relativity and Quantum Cosmology · Physics 2024-04-18 Anne Franzen , Yafet Sanchez Sanchez