The Three-Point Energy Correlator in the Coplanar Limit
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915020032442368 |
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| author | Gao, Anjie Yang, Tong-Zhi Zhang, Xiaoyuan |
| author_facet | Gao, Anjie Yang, Tong-Zhi Zhang, Xiaoyuan |
| contents | Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N$^3$LL) resummation. To our knowledge, this is the first N$^3$LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09428 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Three-Point Energy Correlator in the Coplanar Limit Gao, Anjie Yang, Tong-Zhi Zhang, Xiaoyuan High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Theory Energy correlators are a type of observables that measure how energy is distributed across multiple detectors as a function of the angles between pairs of detectors. In this paper, we study the three-point energy correlator (EEEC) at lepton colliders in the three-particle near-to-plane (coplanar) limit. The leading-power contribution in this limit is governed by the three-jet (trijet) configuration. We introduce a new approach by projecting the EEEC onto the volume of the parallelepiped formed by the unit vectors aligned with three detected final-state particles. Analogous to the back-to-back limit of the two-point energy correlator probing the dijet configuration, the small-volume limit of the EEEC probes the trijet configuration. We derive a transverse momentum dependent (TMD) based factorization theorem that captures the soft and collinear logarithms in the coplanar limit, which enables us to achieve the next-to-next-to-next-to-leading logarithm (N$^3$LL) resummation. To our knowledge, this is the first N$^3$LL result for a trijet event shape. Additionally, we demonstrate that a similar factorization theorem can be applied to the fully differential EEEC in the three-particle coplanar limit, which provides a clean environment for studying different coplanar trijet shapes. |
| title | The Three-Point Energy Correlator in the Coplanar Limit |
| topic | High Energy Physics - Phenomenology High Energy Physics - Experiment Nuclear Theory |
| url | https://arxiv.org/abs/2411.09428 |