Published December 13, 2021 | Version 1.0.0
Dataset Open

Four-point six-loop super-Yang-Mills integrand

  • 1. Northwestern University
  • 2. Uppsala University
  • 3. Uppsala University and Nordita

Description

The integrand contains data for 151653 diagrams, which are split between two types of files.
First is the complete list of graphs in Graphs_SYM_6L.  The diagram count can quickly be verified by running the terminal command

$ wc -l Graphs_SYM_6L

The notation for each graph is as follows:

g[k, v, i] -> {vertex_1, vertex_2, vertex_3, vertex_4,…}

where each vertex is composed of a list of integers that correspond to outgoing edge (or leg) labels

vertex_j = {edge_1, edge_2, edge_3,…}

where edge labels that are negative correspond to incoming legs.   

The momenta of the graph edges satisfy

p_{edge} = -p_{-edge},

\sum_{edge \in vertex} p_{edge} = 0,  

and for convenience we only make use of the independent momenta p_1 through p_9, where p_1, p_2, p_3 are the independent external momenta, and p_4, p_5, p_6, p_7, p_8, p_9 are the independent loop momenta. (The fourth external leg is here denoted by edge = 0, and we do not use its momentum.)

The graphs are labeled by the shorthand name g[k, v, i] where k is the (Next-to)^k-maximal-cut level that they contribute to, and v is an index that groups the graphs according to which vacuum topology they belong to, and i is an index that distinguishes graphs of the same {k,v} class.

For cubic vertices, {edge_1, edge_2, edge_3}, the ordering of the vertex is in one-to-one correspondence with the ordering of the color factor f^{a_{edge_1} a_{edge_2} a_{edge_3}}. Whereas for quartic and higher degree vertices, the information of the color factor is included in the numerator. As a consequence, the cubic vertices are ordered, whereas the higher degree vertices are unordered.

The numerators corresponding to the diagrams are labeled as n[k, v, i] and they are collected into separate files Numers_SYM_6L_k_v according to their {k,v} class.  Verifying the total number of numerators can be accomplished via

$ wc -l Numers_SYM_*

where the total result should be 151653.

All numerators contain Lorentz products between momentum, given by

dij = p_i . p_j

For k>= 1, the numerators also contain color factors c[vertex_i] for each higher-than-cubic vertex.  Each vertex's color factors have been reduced to an arbitrary (n-2)! half-ladder (Del Duca-Dixon-Maltoni [hep-ph/9910563]) basis for that vertex.

This description is reproduced in the "ancillary_readme" file.

Since Zenodo does not currently provide a "Download All" button, we suggest you use a Zenodo-targeted downloading tool like Zenodo_get.  We will provide a ZIPed version in a future upload.

Files

Files (611.8 MB)

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