58 research outputs found
Feynman integrals via hyperlogarithms
This talk summarizes recent developments in the evaluation of Feynman
integrals using hyperlogarithms. We discuss extensions of the original method,
new results that were obtained with this approach and point out current
problems and future directions.Comment: 8 pages, 5 figures, Proceedings of "Loops & Legs 2014", Weimar
(Germany), April 27 -- May
Numerical evaluation of two-loop integrals with pySecDec
We describe the program pySecDec, which factorises endpoint singularities
from multi-dimensional parameter integrals and can serve to calculate integrals
occurring in higher order perturbative calculations numerically. We focus on
the new features and on frequently asked questions about the usage of the
program.Comment: 11 pages, to appear in the proceedings of the HiggsTools Final
Meeting, IPPP, University of Durham, UK, September 201
Numerical evaluation of multi-loop integrals
We present updates on the development of pySecDec, a toolbox to numerically
evaluate parameter integrals in the context of dimensional regularization. We
discuss difficulties with loop integrals in the special kinematic condition
where the squared momentum of a leg is equal to the squared mass of a
propagator. We further discuss some features of a Quasi Monte Carlo (QMC)
integrator that can optionally run on Graphics Processing Units (GPUs).Comment: 10 pages, 5 figures, contribution to the proceedings of Loops and
Legs 2018, St. Goar, German
Towards a four-loop form factor
The four-loop, two-point form factor contains the first non-planar correction
to the lightlike cusp anomalous dimension. This anomalous dimension is a
universal function which appears in many applications. Its planar part in N = 4
SYM is known, in principle, exactly from AdS/CFT and integrability while its
non-planar part has been conjectured to vanish. The integrand of the form
factor of the stress-tensor multiplet in N = 4 SYM including the non-planar
part was obtained in previous work. We parametrise the difficulty of
integrating this integrand. We have obtained a basis of master integrals for
all integrals in the four-loop, two-point class in two ways. First, we computed
an IBP reduction of the integrand of the N = 4 form factor using massive
computer algebra (Reduze). Second, we computed a list of master integrals based
on methods of the Mint package, suitably extended using Macaulay2 / Singular.
The master integrals obtained in both ways are consistent with some minor
exceptions. The second method indicates that the master integrals apply beyond
N = 4 SYM, in particular to QCD. The numerical integration of several of the
master integrals will be reported and remaining obstacles will be outlinedComment: 9 Pages, Radcor/Loopfest 2015 Proceeding
An Analytic Result for the Two-Loop Hexagon Wilson Loop in N = 4 SYM
In the planar N=4 supersymmetric Yang-Mills theory, the conformal symmetry
constrains multi-loop n-edged Wilson loops to be basically given in terms of
the one-loop n-edged Wilson loop, augmented, for n greater than 6, by a
function of conformally invariant cross ratios. We identify a class of
kinematics for which the Wilson loop exhibits exact Regge factorisation and
which leave invariant the analytic form of the multi-loop n-edged Wilson loop.
In those kinematics, the analytic result for the Wilson loop is the same as in
general kinematics, although the computation is remarkably simplified with
respect to general kinematics. Using the simplest of those kinematics, we have
performed the first analytic computation of the two-loop six-edged Wilson loop
in general kinematics.Comment: 17 pages. Extended discussion on how the QMRK limit is taken. Version
accepted by JHEP. A text file containing the Mathematica code with the
analytic expression for the 6-point remainder function is include
Computation of in FDH and DRED: renormalization, operator mixing, and explicit two-loop results
The amplitude relevant for Higgs production via gluon fusion is
computed in the four-dimensional helicity scheme (FDH) and in dimensional
reduction (DRED) at the two-loop level. The required renormalization is
developed and described in detail, including the treatment of evanescent
-scalar contributions. In FDH and DRED there are additional
dimension-5 operators generating the vertices, where can either be
a gluon or an -scalar. An appropriate operator basis is given and the
operator mixing through renormalization is described. The results of the
present paper provide building blocks for further computations, and they allow
to complete the study of the infrared divergence structure of two-loop
amplitudes in FDH and DRED
- …