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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.02061 |
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| _version_ | 1866918044185395200 |
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| author | Ma, Rourou Gong, Jianyu Lin, Jingwen Yan, Kai Yang, Gang Zhang, Yang |
| author_facet | Ma, Rourou Gong, Jianyu Lin, Jingwen Yan, Kai Yang, Gang Zhang, Yang |
| contents | Energy Correlators (EC) are the simplest IR finite observables, which connect theories and experiments. In this paper, we provide a systematic algorithm to calculate the canonical differential equations for energy correlators at generic angle in $\mathcal{N}=4$ super Yang-Mills theory. The integrand is obtained from the 5-point form factor square for scalar half-BPS operators. Applying the algorithm, we obtain the canonical basis for three-point EC and the full set of master integrals for four-point EC. We analyze the function space for four-point case. For multiple polylogrithmic (MPLs) integrals, we calculate their symbols, and for integrals beyond MPLs, we make further investigation by Picard-Fuchs operators. We find two elliptic curves and one genus 2 hyperelliptic curve. The results are achieved by means of integration by part (IBP) reduction and differential equations powered by computational algebraic geometry methods. We provide a package that implements the algorithm. The data is a valuable reference for exploring the structure of physical observables in perturbation theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02061 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Differential Equations for Energy Correlators in Any Angle Ma, Rourou Gong, Jianyu Lin, Jingwen Yan, Kai Yang, Gang Zhang, Yang High Energy Physics - Phenomenology High Energy Physics - Theory Energy Correlators (EC) are the simplest IR finite observables, which connect theories and experiments. In this paper, we provide a systematic algorithm to calculate the canonical differential equations for energy correlators at generic angle in $\mathcal{N}=4$ super Yang-Mills theory. The integrand is obtained from the 5-point form factor square for scalar half-BPS operators. Applying the algorithm, we obtain the canonical basis for three-point EC and the full set of master integrals for four-point EC. We analyze the function space for four-point case. For multiple polylogrithmic (MPLs) integrals, we calculate their symbols, and for integrals beyond MPLs, we make further investigation by Picard-Fuchs operators. We find two elliptic curves and one genus 2 hyperelliptic curve. The results are achieved by means of integration by part (IBP) reduction and differential equations powered by computational algebraic geometry methods. We provide a package that implements the algorithm. The data is a valuable reference for exploring the structure of physical observables in perturbation theories. |
| title | Differential Equations for Energy Correlators in Any Angle |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2506.02061 |