论文标题
通过五个循环的三分形尺寸
A Three-Point Form Factor Through Five Loops
论文作者
论文摘要
我们在平面$ \ Mathcal {n} = 4 $ super-yang-mills理论中引导压力调节超级速度的手性部分的三点形式，以三个，四个和五个回路获得新的结果。我们的施工在该符号的第一个，第二和最后一个条目中采用已知条件，结合了新的多项预订条件，``延长steinmann''状况以及来自最近开发的外形操作员产品扩展的近似数据。我们的结果预计将在QCD的重型上限以$ gg \ \ $ gg \ to Hg $的最大先验部分和$ h \ ggg $振幅。在两个回路上，我们描述的扩展的steinmann函数空间包含四点振幅所需的所有先验功能，其中一个巨大的和三个无质量的外腿以及所有无质量的内部线，包括$ gg \ to等过程，例如$ gg \ to hg $ to hg $和$γ^*\ to q \ bar {q \ bar {q} g $。我们预计，延长的steinmann样空间也将在更高的循环中包含这些振幅，尽管不是任意高循环顺序。我们提供了证据表明，平面$ \ MATHCAL {N} = 4 $三分尺寸可以放置在较小的功能空间中，而权重二和三的独立$ζ$值都没有独立的$ζ$值。
We bootstrap the three-point form factor of the chiral part of the stress-tensor supermultiplet in planar $\mathcal{N}=4$ 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 $gg\to Hg$ and $H\to ggg$ 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 $gg\to Hg$ and $γ^*\to q\bar{q}g$. 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 $\mathcal{N}=4$ three-point form factor can be placed in an even smaller space of functions, with no independent $ζ$ values at weights two and three.
