One-loop Feynman integrals for $2\to 3$ scattering involving many scales including internal masses

Abstract

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 four for families with two and three massive external legs and massless propagators, as well as with one massive internal line and up to two massive external legs. This is the first time this computational approach is applied to cases involving internal masses.

arXiv comment22 pages, results in ancillary files; v2: fixed a typo in eq. (2.3), includes a new subsection (3.4) on the choice of integral families, version accepted for publication in JHEP

References in corpus (24)

• Multiloop integrals in dimensional regularization made simple
• Differential Equations for Two-Loop Four-Point Functions
• Numerical evaluation of multiple polylogarithms
• Integral Reduction with Kira 2.0 and Finite Field Methods
• Lectures on differential equations for Feynman integrals
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
• FIESTA 4: optimized Feynman integral calculations with GPU support
• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Analytic form of the two-loop planar five-gluon all-plus-helicity amplitude in QCD
• Expansion by regions: revealing potential and Glauber regions automatically
• Pentagon functions for massless planar scattering amplitudes
• Elliptic polylogarithms and iterated integrals on elliptic curves II: an application to the sunrise integral
• All master integrals for three-jet production at NNLO
• Elliptic Feynman integrals and pure functions
• An Elliptic Generalization of Multiple Polylogarithms
• Multiple polylogarithms with algebraic arguments and the two-loop EW-QCD Drell-Yan master integrals
• Azurite: An algebraic geometry based package for finding bases of loop integrals
• HandyG -- rapid numerical evaluation of generalised polylogarithms in Fortran
• Analytic result for the nonplanar hexa-box integrals
• Two-loop QCD corrections to $Wb\bar{b}$ production at hadron colliders
• Differential equations from unitarity cuts: nonplanar hexa-box integrals
• RationalizeRoots: Software Package for the Rationalization of Square Roots
• Two-Loop Hexa-Box Integrals for Non-Planar Five-Point One-Mass Processes
• Algorithms and tools for iterated Eisenstein integrals