Hexagon bootstrapping with Steinmann
Computer-readable files associated with the paper
"Bootstrapping a Five-Loop Amplitude from Steinmann Relations''
arXiv:1609.00669
by Simon Caron-Huot, Lance Dixon, Andrew McLeod and Matt von Hippel

Basis Defined via Coproducts
  • We provide a "trimmed'' basis of Steinmann-satisfying hexagon functions through weight 10, which is sufficient to describe the MHV and NMHV 6-point amplitude in planar N=4 super-Yang-Mills theory through five loops: hexagon_coproducts_5loops.m

    • The lines (1,v,v) and (u,1,1)
  • The MHV and NMHV amplitudes (and permutations of the latter) on the lines (u,v,w) = (1,v,v) and (u,v,w) = (u,1,1), evaluated from 1 loop through 5 loops in terms of one-dimensional harmonic polylogarithms (HPLs): eEEtHPL.m

    • Multiple Polylog Representation
  • The MHV and NMHV amplitudes through five loops, expressed in terms of multiple polylogarithms (G functions) in the so-called "Region I" inside the unit cube:
  • hedge5L.tar.gz
  • This MPL representation uses the "hedgehog variables" of arXiv:1507.01950, with a minus sign transformation to make all the G-function arguments positive in Region I, in order to aid in numerical evaluation via GiNaC, see arXiv:hep-ph/0410259
  • This set of 32 files (plus the README) is about 200MB compressed, but 2.6GB after uncompression. The 5 loop functions are each about 400MB uncompressed, and each can take a significant fraction of an hour to load into Mathematica (at least on some laptops).
  • So you are advised to play with the lower loop results first!

    • Other Limits
  • The multi-Regge limit. We give all coefficient functions p, q, g, h appearing, through weight 10 (for MHV: g, h) and weight 9 (for NMHV: p, q): PQGH.m
  • The multi-particle factorization limit for the NMHV function U = log(E): Ufact.m
  • The self-crossing limit: eESelfCrossing.m
  • The near-collinear limit through order T^3: eEEtT3.m

    • Links to Older Results
  • Files using the old (non-Steinmann satisfying) hexagon functions, for the
  • four-loop remainder function
    • and for the
  • four-loop ratio function

  • An older page for the three-loop ratio function