Saved in:
Bibliographic Details
Main Authors: Yang, Li Lin, Zhang, Yiyang
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2512.19370
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1866908727958831104
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