Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911477786476544 |
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| author | Du, Yi-Jian Fu, Chih-Hao Wang, Yihong Xie, Chongsi |
| author_facet | Du, Yi-Jian Fu, Chih-Hao Wang, Yihong Xie, Chongsi |
| contents | We study the algebraic structure of one-loop BCJ numerators in Yang-Mills and related theories. Starting from the propagator matrix that connects colour-ordered integrands to numerators, we identify the consistency conditions that ensure the existence of Jacobi-satisfying numerator solutions and determine the unique construction. The relation between one-loop numerators and forward-limit tree numerators is clarified, together with the additional physical conditions required for a consistent double-copy interpretation.
We propose a two-step expansion strategy for obtaining explicit one-loop numerators. The Yang-Mills integrand is first decomposed into scalar-loop Yang-Mills-scalar building blocks, which are then expanded into bi-adjoint scalar integrands. We derive explicit results for up to three external gluons, showing how the kinematic consistency conditions uniquely determine the coefficients in each case. Similar results for Einstein-Yang-Mills and gravity amplitudes are also presented. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_10963 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories Du, Yi-Jian Fu, Chih-Hao Wang, Yihong Xie, Chongsi High Energy Physics - Theory High Energy Physics - Phenomenology We study the algebraic structure of one-loop BCJ numerators in Yang-Mills and related theories. Starting from the propagator matrix that connects colour-ordered integrands to numerators, we identify the consistency conditions that ensure the existence of Jacobi-satisfying numerator solutions and determine the unique construction. The relation between one-loop numerators and forward-limit tree numerators is clarified, together with the additional physical conditions required for a consistent double-copy interpretation. We propose a two-step expansion strategy for obtaining explicit one-loop numerators. The Yang-Mills integrand is first decomposed into scalar-loop Yang-Mills-scalar building blocks, which are then expanded into bi-adjoint scalar integrands. We derive explicit results for up to three external gluons, showing how the kinematic consistency conditions uniquely determine the coefficients in each case. Similar results for Einstein-Yang-Mills and gravity amplitudes are also presented. |
| title | Algebraic Consistency and Explicit Construction of One-Loop BCJ Numerators of Yang-Mills and Related Theories |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2511.10963 |