Analytic evaluation of the three-loop three-point form factor of $\operatorname{tr}ϕ^3$ in $\mathcal{N}=4$ sYM
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913567284920320 |
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| author | Henn, Johannes M. Lim, Jungwon Bobadilla, William J. Torres |
| author_facet | Henn, Johannes M. Lim, Jungwon Bobadilla, William J. Torres |
| contents | We compute analytically the three-loop correlation function of the local operator $\text{tr} \, ϕ^3$ 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 $\text{tr} \, ϕ^2$ case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic evaluation of the three-loop three-point form factor of $\operatorname{tr}ϕ^3$ in $\mathcal{N}=4$ sYM Henn, Johannes M. Lim, Jungwon Bobadilla, William J. Torres High Energy Physics - Theory High Energy Physics - Phenomenology We compute analytically the three-loop correlation function of the local operator $\text{tr} \, ϕ^3$ 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 $\text{tr} \, ϕ^2$ case. |
| title | Analytic evaluation of the three-loop three-point form factor of $\operatorname{tr}ϕ^3$ in $\mathcal{N}=4$ sYM |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2410.22465 |