Abstract
We bootstrap the three-point form factor of the chiral part of the stresstensor supermultiplet in planar $$ \mathcal{N} $$
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. At two loops, 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* → $$ q\overline{q}g $$
q
q
¯
g
. We expect the extended-Steinmann-like space to contain these amplitudes at higher loops as well, although not to arbitrarily high loop order. We present evidence that the planar $$ \mathcal{N} $$
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.
The three-loop form factor in N=4 super Yang-Mills
