The toolbox of modern multi-loop calculations: novel analytic and semi-analytic techniques

Abstract

We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate their identification. Second, we present a practical solution to the problem of multi-loop analytical tensor reduction. Finally, we discuss the partial fractioning of polynomials with external linear relations between the variables. All algorithms have been tested and used in real calculations.

Talk given at ACAT 2011 conference in London, 5-9 September

Cited by in corpus (37)

• Reduze 2 - Distributed Feynman Integral Reduction
• Quark mass relations to four-loop order
• Presenting LiteRed: a tool for the Loop InTEgrals REDuction
• FIRE4, LiteRed and accompanying tools to solve integration by parts relations
• Ultraviolet Properties of N = 8 Supergravity at Five Loops
• FeynCalc 10: Do multiloop integrals dream of computer codes?
• FIESTA5: numerical high-performance Feynman integral evaluation
• Pentagon Functions for One-Mass Planar Scattering Amplitudes
• MultivariateApart: Generalized Partial Fractions
• The Three-loop Quark Jet Function
• Analytic Next-To-Leading Order Calculation of Energy-Energy Correlation in Gluon-Initiated Higgs Decays
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Matter dependence of the four-loop QCD cusp anomalous dimension: from small angles to all angles
• $\text{tapir}$: A tool for topologies, amplitudes, partial fraction decomposition and input for reductions
• Two-loop leading colour QCD corrections to $q\bar{q}\to \gamma \gamma g$ and $qg\to \gamma \gamma q$
• Master integrals for the four-loop Sudakov form factor
• Two-loop helicity amplitudes for $gg\to ZZ$ with full top-quark mass effects
• Ansätze for Scattering Amplitudes from $p$-adic Numbers and Algebraic Geometry
• Analytic Computation of Three-point Energy Correlator in QCD
• Calculation of two-loop QCD corrections for hadronic single top-quark production in the t channel
• The $N_f{C}_F^3$ contribution to the non-singlet splitting function at four-loop order
• Three-loop soft function for heavy-to-light quark decays
• Complete $N_f^2$ contributions to four-loop pure-singlet splitting functions
• Real corrections to Higgs boson pair production at NNLO in the large top quark mass limit
• Two-loop QCD penguin contribution to the width difference in $B_s-{\bar{B}}_s$ mixing
• Mass-corrections to double-Higgs production & TopoID
• One-loop corrections to the double-real emission contribution to the zero-jettiness soft function at N3LO in QCD
• The {\tt Mathematica} package {\tt TopoID} and its application to the Higgs boson production cross section
• Three-loop soft function for energetic electroweak boson production at hadron colliders
• On the finite basis topologies for multi-loop high-multiplicity Feynman integrals
• Four-dimensional differential equations for the leading divergences of dimensionally-regulated loop integrals
• Three-loop jet function for boosted heavy quarks
• Three-loop helicity amplitudes for four-quark scattering in massless QCD
• Low-energy moments of non-diagonal quark current correlators at four loops
• A new method for finding more symmetry relations of Feynman integrals
• Four-loop relation between the $\overline{\mathrm{MS}}$ and on-shell quark mass
• FeAmGen.jl: A Julia Program for Feynman Amplitude Generation