PolyLogTools - Polylogs for the masses

We review recent developments in the study of multiple polylogarithms, including the Hopf algebra of the multiple polylogarithms and the symbol map, as well as the construction of single valued multiple polylogarithms and discuss an algorithm for finding fibration bases. We document how these algorithms are implemented in the Mathematica package PolyLogTools and show how it can be used to study the coproduct structure of polylogarithmic expressions and how to compute iterated parametric integrals over polylogarithmic expressions that show up in Feynman integal computations at low loop orders.Comment: Package URL: https://gitlab.com/pltteam/pl

Crystallographic Orbifolds: Towards a Classification of Unitary Conformal Field Theories with Central Charge c = 2

We study the moduli space C^2 of unitary two-dimensional conformal field theories with central charge c=2. We construct all the 28 nonexceptional nonisolated irreducible components of C^2 that may be obtained by an orbifold procedure from toroidal theories. The parameter spaces and partition functions are calculated explicitly, and all multicritical points and lines are determined. We show that all but four of the 28 irreducible components of C^2 corresponding to nonexceptional orbifolds are directly or indirectly connected to the moduli space of toroidal theories in C^2. We relate our results to those by Dixon, Ginsparg, Harvey on the classification of c=3/2 superconformal field theories and thereby give geometric interpretations to all nonisolated orbifolds discussed there.Comment: 47 pages, spelling mistakes corrected; final version for JHE

Differential Higgs production at N3LO beyond threshold

We present several key steps towards the computation of differential Higgs boson cross sections at N$^3$LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise predictions for realistic LHC observables. We demonstrate how to perform an expansion of the analytic N$^3$LO coefficient functions around the production threshold of the Higgs boson. Our framework allows us to compute to arbitrarily high order in the threshold expansion and we explicitly obtain the first two expansion coefficients in analytic form. Furthermore, we assess the phenomenological viability of threshold expansions for differential distributions. In addition, we report on an interesting obstacle for the computation of N$^3$LO corrections with LHAPDF parton distribution functions and our solution. We provide files containing the analytic expressions for the partonic cross sections together with the arXiv submission.Comment: 12 plots and 1 Feynman Diagra