Year: 2026
Type: preprint
Abstract: The maximally transcendental, or most complicated, terms of gauge-theory scattering amplitudes have long been singled out, following Lipatov and collaborators, as those parts of a QCD amplitude that most closely mirror maximally supersymmetric Yang--Mills theory. We report on a programme that turns this observation into a practical computational tool. We show that the rational prefactors multiplying the highest-weight special functions of planar QCD amplitudes are governed by four-dimensional leading singularities, which can be classified and evaluated using on-shell diagrams. The resulting prefactors are manifestly conformally invariant and admit compact spinor-helicity expressions that hold for arbitrary multiplicity. Combining this input with the recently established two-loop six-particle function space, we set up a symbol bootstrap and determine, for the first time, the maximal-weight symbol of the planar two-loop six-gluon amplitude in massless QCD, first for the ${-}{-}{+}{+}{+}{+}$ helicity configuration and subsequently for all MHV configurations. The answer is fixed uniquely by physical consistency conditions, requires a reduced alphabet of only $137$ symbol letters, and yields as a byproduct previously unknown two-loop triple-collinear and double-soft splitting functions. We summarise the method and the results, and outline the directions they open up.
Source: arXiv (Cornell University)
Institution: Max Planck Institute for Physics
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7166548856
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