Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in ${\cal N}=4$ SYM
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| Format: | Preprint |
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2024
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| _version_ | 1866917949296607232 |
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| author | Guo, Yuanhong Wang, Lei Yang, Gang Yin, YiXiong |
| author_facet | Guo, Yuanhong Wang, Lei Yang, Gang Yin, YiXiong |
| contents | We compute the two-loop four-point MHV form factor of the stress-tensor supermultiplet in planar ${\cal N}=4$ super Yang-Mills (SYM). This form factor is analogous to the Higgs plus four-gluon amplitudes in the heavy-top limit of QCD when translated to the ${\cal N}=4$ SYM context. We obtain the full $D$-dimensional integrands up to two loops via unitarity-cut methods. Subsequently, we utilize IBP reduction to express the result in terms of a set of uniformly transcendental basis integrals, incorporating the two-loop non-planar five-point one-mass integrals recently given by Abreu et al. [PRL 132 (2024) 14]. We obtain the two-loop finite remainder in the functional form in terms of the pentagon functions. The symbol of our remainder confirms the bootstrap results reported by Dixon et al. [PRL 130 (2023) 11]. We perform various non-trivial checks of our results, including the triple-collinear limit, which recovers the two-loop six-gluon remainder. We also show that the form factor has a directional dual conformal symmetry at the integrand level. Our results are expected to shed further light on the study of antipodal dualities and the computation of Higgs plus four-parton amplitudes in QCD. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12445 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in ${\cal N}=4$ SYM Guo, Yuanhong Wang, Lei Yang, Gang Yin, YiXiong High Energy Physics - Theory High Energy Physics - Phenomenology We compute the two-loop four-point MHV form factor of the stress-tensor supermultiplet in planar ${\cal N}=4$ super Yang-Mills (SYM). This form factor is analogous to the Higgs plus four-gluon amplitudes in the heavy-top limit of QCD when translated to the ${\cal N}=4$ SYM context. We obtain the full $D$-dimensional integrands up to two loops via unitarity-cut methods. Subsequently, we utilize IBP reduction to express the result in terms of a set of uniformly transcendental basis integrals, incorporating the two-loop non-planar five-point one-mass integrals recently given by Abreu et al. [PRL 132 (2024) 14]. We obtain the two-loop finite remainder in the functional form in terms of the pentagon functions. The symbol of our remainder confirms the bootstrap results reported by Dixon et al. [PRL 130 (2023) 11]. We perform various non-trivial checks of our results, including the triple-collinear limit, which recovers the two-loop six-gluon remainder. We also show that the form factor has a directional dual conformal symmetry at the integrand level. Our results are expected to shed further light on the study of antipodal dualities and the computation of Higgs plus four-parton amplitudes in QCD. |
| title | Analytic two-Loop four-point form factor of the stress-tensor supermultiplet in ${\cal N}=4$ SYM |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2409.12445 |