Abstract
We compute the three-loop four-gluon scattering amplitude in maximally supersymmetric Yang-Mills theory, including its full color dependence. Our result is the first complete computation of a nonplanar four-particle scattering amplitude to three loops in four-dimensional gauge theory and consequently provides highly nontrivial data for the study of nonplanar scattering amplitudes. We present the amplitude as a Laurent expansion in the dimensional regulator to finite order, with coefficients composed of harmonic polylogarithms of uniform transcendental weight, and simple rational prefactors. Our computation provides an independent check of a recent result for three-loop corrections to the soft anomalous dimension matrix that predicts the general infrared singularity structure of massless gauge theory scattering amplitudes. Taking the Regge limit of our result, we determine the three-loop gluon Regge trajectory. We also find agreement with very recent predictions for subleading logarithms.
Highlights
Introduction.—In the era of the Large Hadron Collider our understanding of the fundamental interactions of nature is probed at an unprecedented level
The maximally supersymmetric Yang-Mills theory serves as a useful testing laboratory for the development of novel methods for precise predictions and is used to explore hidden structures of quantum field theory
Links this property to integrands that can be written in terms of d-log forms [16], and, have constant leading singularities. We remark that these concepts have already proven to be very useful beyond maximally supersymmetric Yang-Mills theory [7] in computing large classes of planar and nonplanar loop integrals relevant for collider physics
Summary
Introduction.—In the era of the Large Hadron Collider our understanding of the fundamental interactions of nature is probed at an unprecedented level. The exact functional form of the four-particle amplitude in the planar limit is known to all loop orders [9,10,11]. More general scattering amplitudes can be computed using integrability methods; see, e.g., Refs. The integrand of these amplitudes can be written in terms of certain d-log forms [16].
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