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In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried…

High Energy Physics - Phenomenology · Physics 2011-09-21 F. Yuasa , T. Ishikawa , Y. Kurihara , J. Fujimoto , Y. Shimizu , N. Hamaguchi , E. de Doncker , K. Kato

This article is devoted problems of electromagnetic interaction in curved spacetime. Such problems exist, in particular, when we investigate electromagnetic quantum processes near black holes. The generalization of reduction formalism…

High Energy Physics - Theory · Physics 2017-10-17 Yuriy Ostapov

I describe a mathematical framework for the efficient processing of the very large sets of Feynman diagrams contributing to the scattering of many particles. I reexpress the established numerical methods for the recursive construction of…

High Energy Physics - Phenomenology · Physics 2023-07-21 Thorsten Ohl

We describe a method to numerically compute multi-loop integrals, depending on one dimensionless parameter $x$ and the dimension $d$, in the whole kinematic range of $x$. The method is based on differential equations, which, however, do not…

High Energy Physics - Phenomenology · Physics 2021-10-13 Matteo Fael , Fabian Lange , Kay Schönwald , Matthias Steinhauser

We calculate the two-loop virtual, UV renormalized corrections at order \alpha^4 (N_F=1) in QED to the Bhabha scattering differential cross section, for arbitrary values of the squared c.m. energy s and momentum transfer t, and on-shell…

High Energy Physics - Phenomenology · Physics 2009-11-10 R. Bonciani , A. Ferroglia , P. Mastrolia , E. Remiddi , J. J. van der Bij

By employing the differential equations, we compute analytically the elliptic sectors of two-loop master integrals appearing in the NNLO QCD corrections to CP-even heavy quarkonium exclusive production and decays, which turns out to be the…

High Energy Physics - Phenomenology · Physics 2018-05-23 Long-Bin Chen , Jun Jiang , Cong-Feng Qiao

We describe a first attempt to calculate scalar 2-loop box-functions with arbitrary internal masses, applying a novel method proposed in hep-ph/9407234. Four of the eight integrals are accessible to integration by means of the residue…

High Energy Physics - Phenomenology · Physics 2011-09-13 R. Kreckel , D. Kreimer , K. Schilcher

We calculate fragmentation functions for a b-quark to fragment into color-singlet P-wave bound states $\bar c b$ in the Heavy Quark Effective Theory with the exact account of $O(1/m_b)$ corrections. We demonstrate an agreement of the…

High Energy Physics - Phenomenology · Physics 2011-03-02 A. P. Martynenko , V. A. Saleev

We present a set of algebraic functions for evaluating the coefficients of the scalar integral basis of a general one-loop amplitude. The functions are derived from unitarity cuts, but the complete cut-integral procedure has been carried…

High Energy Physics - Phenomenology · Physics 2008-11-26 Ruth Britto , Bo Feng

The two-loop radiative photonic corrections to the Bhabha scattering are computed in the leading order of the small electron mass expansion up to nonlogarithmic term. After including the soft photon bremsstrahlung we obtain the infrared…

High Energy Physics - Phenomenology · Physics 2009-11-11 A. A. Penin

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

We evaluate analytically all previously unknown nonplanar master integrals for massless five-particle scattering at two loops, using the differential equations method. A canonical form of the differential equations is obtained by…

High Energy Physics - Phenomenology · Physics 2020-09-23 D. Chicherin , T. Gehrmann , J. M. Henn , P. Wasser , Y. Zhang , S. Zoia

The luminosity measurement at the projected International Linear $e^+e^-$ Collider ILC is planned to be performed with forward Bhabha scattering with an accuracy of the order of $10^{-4}$. A theoretical prediction of the differential…

High Energy Physics - Phenomenology · Physics 2009-11-11 J. Fleischer , J. Gluza , A. Lorca , T. Riemann

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…

High Energy Physics - Phenomenology · Physics 2015-06-03 F. Yuasa , E. de Doncker , N. Hamaguchi , T. Ishikawa , K. Kato , Y. Kurihara , J. Fujimoto , Y. Shimizu

A computational algorithm for the exact equations representing the scattering coefficients of an infinite grating of insulating dielectric circular cylinders associated with obliquely incident vertically polarized plane electromagnetic…

Mathematical Physics · Physics 2007-11-02 Omer Kavaklioglu , Baruch Schneider

Several new relationships between hypergeometric functions are found by comparing results for Feynman integrals calculated using different methods. A new expression for the one-loop propagator-type integral with arbitrary masses and…

Mathematical Physics · Physics 2015-05-30 Bernd A. Kniehl , Oleg V. Tarasov

By employing the method of differential equations, we compute the various types of two-loop master integrals involved in CP-even heavy quarkonium exclusive production and decays. All the integrals presented in this paper can be casted into…

High Energy Physics - Phenomenology · Physics 2017-06-28 Long-Bin Chen , Yi Liang , Cong-Feng Qiao

We present a complete set of one-loop matrix elements relevant for the hadroproduction of heavy quarks in next-to-leading order employing dimensional regularization to isolate ultraviolet and soft divergences. All results of the…

High Energy Physics - Phenomenology · Physics 2014-11-17 J. G. Korner , Z. Merebashvili

We present the analytic computation of all the planar master integrals which contribute to the two-loop scattering amplitudes for Higgs$\to 3$ partons, with full heavy-quark mass dependence. These are relevant for the NNLO corrections to…

High Energy Physics - Phenomenology · Physics 2017-02-01 Roberto Bonciani , Vittorio Del Duca , Hjalte Frellesvig , Johannes M. Henn , Francesco Moriello , Vladimir A. Smirnov

We study the applicability of the Z-Sum approach to multi-loop calculations with massive particles in perturbative quantum field theory. We systematically analyze the case of one-loop scalar integrals, which represent the building blocks of…

High Energy Physics - Phenomenology · Physics 2015-05-28 Paulo A. Rottmann , Laura Reina