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Related papers: Some Exact Results for Two-Loop Diagrams with Thre…

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Negative dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method simultaneously gives solutions in different regions of…

High Energy Physics - Theory · Physics 2007-05-23 Alfredo T. Suzuki , Alexandre G. M. Schmidt

A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…

High Energy Physics - Phenomenology · Physics 2016-04-14 Johannes Bluemlein , Khiem Hong Phan , Tord Riemann

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only…

Exactly Solvable and Integrable Systems · Physics 2026-05-05 Tim Zolkin , Sergei Nagaitsev , Ivan Morozov , Sergei Kladov

A method of calculating Feynman diagrams from their small momentum expansion [1] is extended to diagrams with zero mass thresholds. We start from the asymptotic expansion in large masses [2] (applied to the case when all $M_i^2$ are large…

High Energy Physics - Phenomenology · Physics 2015-06-25 J. Fleischer , V. A. Smirnov , O. V. Tarasov

We describe the calculation of all planar master integrals that are needed for the computation of NNLO QCD corrections to the production of two off-shell vector bosons in hadron collisions. The most complicated representatives of integrals…

High Energy Physics - Phenomenology · Physics 2015-06-18 Johannes M. Henn , Kirill Melnikov , Vladimir A. Smirnov

I present a Mathematica package designed for manipulations and evaluations of triple-K integrals and conformal correlation functions in momentum space. Additionally, the program provides tools for evaluation of a large class of 2- and…

High Energy Physics - Theory · Physics 2020-08-26 Adam Bzowski

Area preserving maps provide the simplest and most accurate means to visualize and quantify the behavior of nonlinear systems. Convenience of the mapping equations of motion for investigation of transition to chaotic behavior in dynamics of…

chao-dyn · Physics 2007-05-23 B. Kaulakys

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

We calculate all three-loop, five-point, massless planar Feynman integral families in the dimensional regularization scheme. This is a new milestone in Feynman integral computations. The analysis covers four distinct families of Feynman…

High Energy Physics - Phenomenology · Physics 2025-12-22 Dmitry Chicherin , Yu Wu , Zihao Wu , Yongqun Xu , Shun-Qing Zhang , Yang Zhang

Feynman diagrams are a pictorial way of describing integrals predicting possible outcomes of interactions of subatomic particles in the context of quantum field physics. It is highly desirable to have an intrinsic mathematical…

Representation Theory · Mathematics 2016-11-02 Matvei Libine

Generalized-unitarity calculations of two-loop amplitudes are performed by expanding the amplitude in a basis of master integrals and then determining the coefficients by taking a number of generalized cuts. In this paper, we present a…

High Energy Physics - Phenomenology · Physics 2025-05-08 Simon Caron-Huot , Kasper J. Larsen

Vladimir Shpilrain and Jie-Tai Yu have asked for an effective algorithm to decide if two elements of C[x,y] are related by an automorphism of C[x,y]. We describe here an efficient algorithm that decides this question and finds the…

Algebraic Geometry · Mathematics 2007-05-23 Walter D. Neumann , Penelope G. Wightwick

We compute the complete set of two-loop master integrals for the scattering of four massless particles and a massive one. Our results are ready for phenomenological applications, removing a major obstacle to the computation of complete…

High Energy Physics - Phenomenology · Physics 2024-05-03 Samuel Abreu , Dmitry Chicherin , Harald Ita , Ben Page , Vasily Sotnikov , Wladimir Tschernow , Simone Zoia

Loop integration results have been obtained using numerical integration and extrapolation. An extrapolation to the limit is performed with respect to a parameter in the integrand which tends to zero. Results are given for a non-scalar…

High Energy Physics - Phenomenology · Physics 2009-11-10 E. de Doncker , Y. Shimizu , J. Fujimoto , F. Yuasa , K. Kaugars , L. Cucos , J. Van Voorst

In this work, we calculate two-loop six-point planar massless Feynman integrals at higher orders in the dimensional regulator $\epsilon$, corresponding to higher transcendental weights. In previous works, these integrals were calculated up…

High Energy Physics - Phenomenology · Physics 2026-04-03 Yuanche Liu , Antonela Matijašić , Tiziano Peraro , Yingxuan Xu , Zihua Yang , Yang Zhang

We study several multiscale one-loop five-point families of Feynman integrals. More specifically, we employ the Simplified Differential Equations approach to obtain results in terms of Goncharov polylogarithms of up to transcendental weight…

High Energy Physics - Phenomenology · Physics 2021-09-14 Nikolaos Syrrakos

We consider a dual representation of an effective three-dimensional Polyakov loop model for the SU(3) theory at nonzero real chemical potential. This representation is free of the sign problem and can be used for numeric Monte-Carlo…

High Energy Physics - Lattice · Physics 2021-12-02 Oleg Borisenko , Volodymyr Chelnokov , Emanuele Mendicelli , Alessandro Papa

The approach of direct integration of the three-dimensional Faddeev equations with respect to the breakup T-matrix in momentum space for three bodies of different masses is presented. The Faddeev equations are written out explicitly without…

Quantum Physics · Physics 2025-02-03 Mikhail Egorov

Modern particle physics is increasingly becoming a precision science that relies on advanced theoretical predictions for the analysis and interpretation of experimental results. The planned physics program at the LHC and future colliders…

High Energy Physics - Phenomenology · Physics 2023-01-04 Ievgen Dubovyk , Ayres Freitas , Janusz Gluza , Krzysztof Grzanka , Martijn Hidding , Johann Usovitsch

We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of $n$- and $(n-1)$-point scalar integrals that are finite in the limit of vanishing…

High Energy Physics - Phenomenology · Physics 2008-11-26 J. M. Campbell , E. W. N. Glover , D. J. Miller