Abstract
We obtain full-color three-loop, three-point form factors of the stress-tensor supermultiplet and also of a length-3 half–Bogomol’nyi-Prasad-Sommerfield operator in supersymmetric Yang-Mills (SYM) theory based on the color-kinematics duality and on-shell unitarity. The integrand results are verified by all planar and nonplanar unitarity cuts, and they satisfy the minimal power counting of loop momenta and diagrammatic symmetries. Interestingly, these three-loop solutions, while manifesting all dual Jacobi relations, contain a large number of free parameters; in particular, there are 24 free parameters for the form factor of the stress-tensor supermultiplet. Such degrees of freedom are due to a new type of generalized gauge transformation associated with the operator insertion for form factors. We also perform numerical integration and obtain consistent full-color infrared divergences and the known planar remainder. The form factors we obtain can be understood as the SYM counterparts of three-loop Higgs plus three-gluon amplitudes in QCD and are expected to provide the maximally transcendental parts of the latter.
1 More- Received 26 July 2021
- Accepted 30 September 2021
DOI:https://doi.org/10.1103/PhysRevLett.127.171602
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Published by the American Physical Society