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We present a systematic method to factorise singularities using non-linear mappings. As a first application of the method the fully differential NNLO calculation of the partial decay width of a Higgs boson into Bottom-quarks is presented.

High Energy Physics - Phenomenology · Physics 2012-01-04 Franz Herzog

In a series of papers we have developed the method of iterated sector decomposition for the calculation of infrared divergent multi-loop integrals. Here we apply it to phase space integrals to calculate a contribution to the double real…

High Energy Physics - Phenomenology · Physics 2009-11-10 T. Binoth , G. Heinrich

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 compare the phase space slicing and dipole subtraction methods in the computation of the inclusive and differential next-to-leading order cross sections for heavy quark production in the simple process gamma^* -> Q Qbar. For the phase…

High Energy Physics - Phenomenology · Physics 2008-11-26 Tim Oliver Eynck , Eric Laenen , Lukas Phaf , Stefan Weinzierl

We discuss a practical approach to compute master integrals entering physical quantities which depend on one parameter. As an example we consider four-loop QCD corrections to the relation between a heavy quark mass defined in the…

High Energy Physics - Phenomenology · Physics 2021-10-11 Matteo Fael , Fabian Lange , Kay Schönwald , Matthias Steinhauser

Splitting methods have emerged as powerful tools to address complex problems by decomposing them into smaller solvable components. In this work, we develop a general approach to forward-backward splitting methods for solving monotone…

Optimization and Control · Mathematics 2026-04-20 Minh N. Dao , Matthew K. Tam , Thang D. Truong

The techniques of integration by parts and differential reduction differ in the counting of master integrals. This is illustrated using as an example the two-loop sunset diagram with on-shell kinematics. A new algebraic relation between the…

Mathematical Physics · Physics 2011-08-09 Mikhail Yu. Kalmykov , Bernd A. Kniehl

Integration by parts is used to reduce scalar Feynman integrals to master integrals.

High Energy Physics - Phenomenology · Physics 2015-03-19 A. G. Grozin

We present an algorithm which allows to solve analytically linear systems of differential equations which factorize to first order. The solution is given in terms of iterated integrals over an alphabet where its structure is implied by the…

High Energy Physics - Phenomenology · Physics 2018-12-19 J. Ablinger , J. Blümlein , P. Marquard , N. Rana , C. Schneider

In this article we give the details on the analytic calculation of the master integrals for the planar double box integral relevant to top-pair production with a closed top loop. We show that these integrals can be computed systematically…

High Energy Physics - Phenomenology · Physics 2018-11-14 Luise Adams , Ekta Chaubey , Stefan Weinzierl

We apply the differential equation technique to the calculation of the one-loop massless diagram with five onshell legs. Using the reduction to $\epsilon$-form, we manage to obtain a simple one-fold integral representation exact in…

High Energy Physics - Phenomenology · Physics 2016-03-23 Mikhail G. Kozlov , Roman N. Lee

An equation containing a fractional power of an elliptic operator of second order is studied for Dirichlet boundary conditions. Finite difference approximations in space are employed. The proposed numerical algorithm is based on solving an…

Numerical Analysis · Computer Science 2015-05-18 Petr N. Vabishchevich

We describe the analytic calculation of the master integrals required to compute the two-mass three-loop corrections to the $\rho$ parameter. In particular, we present the calculation of the master integrals for which the corresponding…

High Energy Physics - Phenomenology · Physics 2018-07-17 J. Blümlein , A. De Freitas , M. van Hoeij , E. Imamoglu , P. Marquard , C. Schneider

A very simple and accurate numerical method which is applicable to systems of differentio-integral equations with quite general boundary conditions has been devised. Although the basic idea of this method stems from the Keller Box method,…

Fluid Dynamics · Physics 2014-09-30 Jian-Jun Shu , Graham Wilks

Loop amplitudes are conveniently expressed in terms of master integrals whose coefficients carry the process dependent information. Similarly before integration, the loop integrands may be expressed as a linear combination of propagator…

High Energy Physics - Theory · Physics 2016-12-28 Harald Ita

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 employ a procedure that enables us to calculate the excess free energies for a finite Ising cylinder with domain walls analytically. This procedure transparently covers all possible configurations of the domain walls under given boundary…

Statistical Mechanics · Physics 2025-06-23 Alessio Squarcini , Piotr Nowakowski , Douglas B. Abraham , Anna Maciołek

Master equations are probably the most fundamental equations for anyone working in quantum optics in the presence of dissipation. In this context it is then incredibly useful to have efficient ways of coding and simulating such equations in…

Quantum Physics · Physics 2015-04-23 Carlos Navarrete-Benlloch

We present the analytic computation of the master integrals associated to certain two-loop non-planar topologies, which are needed to complete the evaluation of the last two color coefficients for the top-pair production in the…

High Energy Physics - Phenomenology · Physics 2019-12-13 Matteo Becchetti , Roberto Bonciani , Valerio Casconi , Andrea Ferroglia , Simone Lavacca , Andreas von Manteuffel

We extend the antenna subtraction method to include hadron fragmentation processes up to next-to-next-to-leading order (NNLO) in QCD in $e^+e^-$ collisions. To handle collinear singularities associated with the fragmentation process, we…

High Energy Physics - Phenomenology · Physics 2022-11-09 Thomas Gehrmann , Giovanni Stagnitto