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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/2512.19370 |
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| _version_ | 1866908727958831104 |
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| author | Yang, Li Lin Zhang, Yiyang |
| author_facet | Yang, Li Lin Zhang, Yiyang |
| contents | We propose '$\mathrm{d} \mathcal{E}$-forms' as fundamental building blocks of canonical integrands for elliptic Feynman integrals, which lead to Kronecker-Eisenstein $ω$-form symbol letters. Built upon pure elliptic multiple polylogarithms, they provide a natural extension of the '$\mathrm{d} \! \log$-form' integrands and $\mathrm{d} \! \log$ letters for polylogarithmic cases. By introducing an extended basis treating all marked points equally, we manifest a hidden symmetry structure in the canonical connection matrix, and demonstrate its covariance under modular transformations. Our result provides a novel perspective on describing canonical bases and symbol letters in a unified language of pure functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_19370 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From $\mathrm{d} \! \log$ to $\mathrm{d} \mathcal{E}$: Canonical Elliptic Integrands and Modular Symbol Letters with Pure eMPLs Yang, Li Lin Zhang, Yiyang High Energy Physics - Theory High Energy Physics - Phenomenology We propose '$\mathrm{d} \mathcal{E}$-forms' as fundamental building blocks of canonical integrands for elliptic Feynman integrals, which lead to Kronecker-Eisenstein $ω$-form symbol letters. Built upon pure elliptic multiple polylogarithms, they provide a natural extension of the '$\mathrm{d} \! \log$-form' integrands and $\mathrm{d} \! \log$ letters for polylogarithmic cases. By introducing an extended basis treating all marked points equally, we manifest a hidden symmetry structure in the canonical connection matrix, and demonstrate its covariance under modular transformations. Our result provides a novel perspective on describing canonical bases and symbol letters in a unified language of pure functions. |
| title | From $\mathrm{d} \! \log$ to $\mathrm{d} \mathcal{E}$: Canonical Elliptic Integrands and Modular Symbol Letters with Pure eMPLs |
| topic | High Energy Physics - Theory High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2512.19370 |