Cosmically Normalized Six-Point Amplitudes
Computer-readable ancillary files associated with the paper
"Six-Gluon Amplitudes in Planar N=4 Super-Yang-Mills Theory
at Six and Seven Loops''
arXiv:1903.10890
by Simon Caron-Huot, Lance Dixon, Falko Dulat, Matt von Hippel,
Andrew McLeod and Georgios Papathanasiou
and with the paper
"An Eight Loop Amplitude via Antipodal Duality''
arXiv:2308.08199
by Lance Dixon and Yu-Ting (Andy) Liu
Amplitudes Defined via Coproducts
All the definitions needed to specify the MHV amplitude through 7 loops
and the NMHV amplitude through 6 loops.
We do so via the amplitudes' differentials, or {n-1,1} coproducts, plus their
values at the point (1,1,1). As part of this description, we provide a
complete basis for " H^hex " through weight 11 (80MB unzipped):
SixGluonAmpsAndCops.zip
The lines (u,u,1) and (u,1,1)
The MHV (NMHV) amplitudes (and permutations of the latter) on the lines (u,v,w) = (u,u,1) and (u,v,w) = (u,1,1), evaluated from 1 loop through 7 (6) loops in terms of one-dimensional harmonic polylogarithms (HPLs) (3.2MB unzipped):
SixGluonHPLLines.zip
The MHV amplitudes only on the lines (u,v,w) = (u,u,1) and (u,v,w) = (u,1,1), evaluated from 1 loop through 8 loops in terms of one-dimensional harmonic polylogarithms (HPLs) in the newest cosmic normalization ("EZ"):
EZMHVg_uu1_lin.zip and
EZMHVg_u11_lin.zip
MHV Amplitude in Self-Crossing Limit
The MHV amplitude through seven loops on the line (1,v,v) for both 3 -> 3 and 2 -> 4 kinematics, as well as at the special points v = 0, 1 and infinity (2MB unzipped):
SelfCross.zip
MHV Singular Terms in Self-Crossing Limit
Just the terms with singular logs, ln(-delta) for 3 -> 3 kinematics, as delta -> 0 in the self-crossing limit, evaluated to 20 loops (0.6MB unzipped):
SelfCrossSingular.zip
The Fourier-Mellin integrals entering the 2 -> 4 and 3 -> 3
multi-Regge limits
of the MHV (NMHV) amplitudes through 7 (6) loops (2.6MB unzipped):
hexMRKL1-7.zip
The Fourier-Mellin integrals entering the 2 -> 4 and 3 -> 3
multi-Regge limits
of the MHV amplitudes through 8 loops:
MRKSigma.zip
The near-collinear limit
of the bosonic Wilson loop through the first six loops and through order T^2 (4.5MB unzipped):
WL0-6.zip
The near-collinear limit
of the 1111 component of the NMHV super Wilson loop through the first six loops and through order T^2 (14MB unzipped):
W1111L0-6.zip
The near-collinear limit
of the bosonic Wilson loop at seven loops and through order T^2
(17MB unzipped):
WL7.zip
The near-collinear limit
of the MHV remainder function through eight loops and through order T^1,
in terms of HPLS (Iy(...) = G([...],y))):
RLncy.zip
Series expansion in S of the order T^1 terms in the near-collinear limit
of the MHV remainder function through eight loops:
RLncyser.txt
The building blocks for
constructing the near-collinear limits
at orders T^1 F^{+-1} and T^2 F^{+-2}
from the flux-tube OPE (18MB unzipped):
WLOPEblocks.zip
More Eight Loop Results
The {11,1,1,1,1,1} quintuple coproducts of the eight-loop MHV amplitude in terms of weight 11 hexagon functions:
MHV8quintuples.zip
Conversion between "conventional" multiple zeta values (MZVs) and f-alphabet representation through weight 16:
ftoMZV16.txt
Projection to a slightly smaller space of hexagon functions after using the newest cosmic normalization:
EZsmallercoproductspace.txt
Values of MHV amplitudes and coproducts at (1,1,1) through eight loops:
EZMHVcoproducts111.txt
Values of weight 16 "Z" functions at the origin (0,0,0):
Zorigin.txt
Links to Older Results
Files using the Steinmann satisfying hexagon functions, but not cosmically
normalized, for the
six-point amplitudes through five loops
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