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Analytic evaluation of the three-loop three-point form factor of $\operatorname{tr}\phi^3$ in $\mathcal{N}=4$ sYM

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arxiv 2410.22465 v1 pith:3VIRUZXI submitted 2024-10-29 hep-th hep-ph

Johannes M. Henn , Jungwon Lim , William J. Torres Bobadilla This is my paper · ORCID
classification hep-thhep-ph
keywords resultintegralstextthree-loopadjacencyagreementanalyticanalytically
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abstract

We compute analytically the three-loop correlation function of the local operator $\text{tr} \, \phi^3$ inserted into three on-shell states, in maximally supersymmetric Yang-Mills theory. The result is expressed in terms of Chen iterated integrals. We also present our result using generalised polylogarithms, and evaluate them numerically, finding agreement with a previous numerical result in the literature. We observe that the result depends on fewer kinematic singularities compared to individual Feynman integrals. Furthermore, upon choosing a suitable definition of the finite part, we find that the latter satisfies powerful symbol adjacency relations similar to those previously observed for the $\text{tr} \, \phi^2$ case.

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Cited by 3 Pith papers

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  1. Two-loop MHV Form Factors from the Periodic Wilson Loop

    hep-th 2024-12 conditional novelty 7.0 of 10

    The periodic Wilson loop duality is extended beyond one loop, yielding the two-loop n-particle MHV form factor integrand and new five- and six-particle symbols.

  2. All planar three-loop Feynman integrals for the production of two vector bosons at hadron colliders

    hep-ph 2025-12 accept novelty 6.0 of 10

    All nine planar three-loop four-point integral families for two massive external legs are cast into canonical differential equations and evaluated numerically, completing the set needed for leading-colour N3LO diboson...

  3. Off-shell minimal form factors

    hep-th 2024-11 conditional novelty 6.0 of 10

    Off-shell minimal form factors in planar N=4 SYM exponentiate at two loops with the octagon anomalous dimension; their finite remainder shares the conformal symbol but differs beyond it.

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