A Three-Point Form Factor Through Five Loops

Abstract

We bootstrap the three-point form factor of the chiral part of the stress-tensor supermultiplet in planar N = 4 super-Yang-Mills theory, obtaining new results at three, four, and five loops. Our construction employs known conditions on the first, second, and final entries of the symbol, combined with new multiple-final-entry conditions, "extended-Steinmann-like" conditions, and near-collinear data from the recently-developed form factor operator product expansion. Our results are expected to give the maximally transcendental parts of the gg → Hg and H → ggg amplitudes in the heavy-top limit of QCD. Moreover, we conjecture that the extended-Steinmann-like space of functions we describe contains all transcendental functions required for four-point amplitudes with one massive and three massless external legs, and all massless internal lines, including processes such as gg → Hg and γ * → q qg. We present evidence that the planar N = 4 three-point form factor can be placed in an even smaller space of functions, with no independent ζ values at weights two and three.

Cluster algebras for Feynman integrals

“…Eqs. ( 11) also hold for the non-planar integrals of [43], as was first noticed in [48]. In terms of the equivalent alphabet (9), this implies that the letters 1−z i and 1−z j for i = j never appear next to each other in a symbol.…”

Notes on cluster algebras and some all-loop Feynman integrals

“…was given by A 3 cluster algebra [42], and the so-called cluster adjacency condition was observed for certain seven-point integrals in E 6 [43]. One can bootstrap Feynman integrals [44,45] based on such knowledge (see also [46]). Very recently, the authors of [47] have argued that cluster algebra structures appear for rather general Feynman integrals which go way beyond planar N = 4 SYM.…”

The elliptic double box and symbology beyond polylogarithms

“…to make an ansatz based on an assumed symbol alphabet [8] and to fix the coefficients via various constraints such as the Steinmann conditions [9][10][11] and cluster adjacency [12,13]; see e.g. [14][15][16][17][18][19]. For slightly more legs, however, also symbol alphabets with φ α occur that are not simultaneously rationalizable [20][21][22][23].…”