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The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method offers a…

High Energy Physics - Phenomenology · Physics 2009-11-07 M. Caffo , H. Czyz , E. Remiddi

We evaluate the master integrals for the two-loop, planar box-diagrams contributing to the elastic scattering of muons and electrons at next-to-next-to leading-order in QED. We adopt the method of differential equations and the Magnus…

High Energy Physics - Phenomenology · Physics 2022-10-13 Pierpaolo Mastrolia , Massimo Passera , Amedeo Primo , Ulrich Schubert

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…

High Energy Physics - Phenomenology · Physics 2009-11-07 S. Laporta

We obtain a simple relation between massless and massive scattering amplitudes in gauge theories in the limit where all kinematic invariants are large compared to particle masses. We use this relation to derive the two-loop QED corrections…

High Energy Physics - Phenomenology · Physics 2009-11-13 Thomas Becher , Kirill Melnikov

The calculation of the two-loop corrections to the three jet production rate and to event shapes in electron-positron annihilation requires the computation of a number of up to now unknown two-loop four-point master integrals with one…

High Energy Physics - Phenomenology · Physics 2008-11-26 T. Gehrmann , E. Remiddi

We present the computation of a full set of planar five-point two-loop master integrals with one external mass. These integrals are an important ingredient for two-loop scattering amplitudes for two-jet-associated W-boson production at…

High Energy Physics - Phenomenology · Physics 2020-12-30 S. Abreu , H. Ita , F. Moriello , B. Page , W. Tschernow , M. Zeng

The method of Mellin-Barnes representation is used to calculate dimensionally regularized massive on-shell double box Feynman diagrams contributing to Bhabha scattering at two loops.

High Energy Physics - Phenomenology · Physics 2009-11-10 G. Heinrich , V. A. Smirnov

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

We carry out a systematic investigation of all the 2-loop integrals occurring in the electron vertex in QED in the continuous $D$-dimensional regularization scheme, for on-shell electrons, momentum transfer $t=-Q^2$ and finite squared…

High Energy Physics - Phenomenology · Physics 2008-11-26 R. Bonciani , P. Mastrolia , E. Remiddi

We derive the two-loop corrections to Bhabha scattering from heavy fermions using dispersion relations. The double-box contributions are expressed by three kernel functions. Convoluting the perturbative kernels with fermionic threshold…

High Energy Physics - Phenomenology · Physics 2008-12-30 S. Actis , M. Czakon , J. Gluza , T. Riemann

We compute the differential equations for the two remaining integral topologies contributing to the leading colour two-loop amplitudes for $pp \rightarrow t\bar{t}j$. We derive differential equations for the master integrals by solving the…

High Energy Physics - Phenomenology · Physics 2024-05-01 Simon Badger , Matteo Becchetti , Nicolò Giraudo , Simone Zoia

The aim of this paper is to describe a Matlab toolbox, called $\mu$-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in $\mu$-diff…

Mathematical Software · Computer Science 2015-05-20 Bertrand Thierry , Xavier Antoine , Chokri Chniti , Hasan Alzubaidi

We present the two-loop virtual QED corrections to e^+ e^- to mu^+ mu^- and Bhabha scattering in dimensional regularization. The results are expressed in terms of polylogarithms. The form of the infrared divergences agrees with previous…

High Energy Physics - Phenomenology · Physics 2010-11-15 Z. Bern , L. Dixon , A. Ghinculov

The system of 4 differential equations in the external invariant satisfied by the 4 master integrals of the general massive 2-loop sunrise self-mass diagram is solved by the Runge-Kutta method in the complex plane. The method, whose…

High Energy Physics - Phenomenology · Physics 2009-11-07 M. Caffo , H. Czyz , E. Remiddi

I obtain identities satisfied by the 3-loop self-energy master integrals with four or five propagators with generic masses, including the derivatives with respect to each of the squared masses and the external momentum invariant. These…

High Energy Physics - Phenomenology · Physics 2023-03-29 Stephen P. Martin

The planar two-loop scalar Feynman integrals contributing to the massive NNLO QCD corrections for $W$-boson pair production via quark-antiquark annihilation can be classified into three family branches, each of which is reduced to a…

High Energy Physics - Phenomenology · Physics 2024-09-16 Wen-Jie He , Ren-You Zhang , Liang Han , Yi Jiang , Zhe Li , Xiao-Feng Wang , Shu-Xiang Li , Pan-Feng Li , Qing-hai Wang

The master differential equations in the external square momentum p^2 for the master integrals of the two-loop sunrise graph, in n-continuous dimensions and for arbitrary values of the internal masses, are derived. The equations are then…

High Energy Physics - Theory · Physics 2010-04-06 M. Caffo , H. Czyz , S. Laporta , E. Remiddi

We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be…

High Energy Physics - Phenomenology · Physics 2018-10-24 Long-Bin Chen , Jian Wang

We evaluate, in the high-energy limit, $s\gg|t|\gg m^2\gg\lambda^2$, the sum of amplitudes corresponding to a class of Feynman diagrams describing two-loop virtual photonic corrections to Bhabha scattering. The diagrams considered are box…

High Energy Physics - Phenomenology · Physics 2009-10-22 Göran Fäldt , Per Osland

Theoretical predictions for Bhabha scattering at the two-loop level require the inclusion of hadronic vacuum polarization in the photon propagator. We present predictions for the contributions from reducible amplitudes which are…

High Energy Physics - Phenomenology · Physics 2008-11-26 Johann H. Kühn , Sandro Uccirati