On differential operators and unifying relations for $1$-loop Feynman integrands
High Energy Physics - Theory
2026-05-05 v1
Abstract
We generalize the unifying relations for tree amplitudes to the -loop Feynman integrands. By employing the -loop CHY formula, we construct differential operators which transmute the -loop gravitational Feynman integrand to Feynman integrands for a wide range of theories, include Einstein-Yang-Mills theory, Einstein-Maxwell theory, pure Yang-Mills theory, Yang-Mills-scalar theory, Born-Infeld theory, Dirac-Born-Infeld theory, bi-adjoint scalar theory, non-linear sigma model, as well as special Galileon theory. The unified web at -loop level is established. Under the well known unitarity cut, the -loop level operators will factorize into two tree level operators. Such factorization is also discussed.
Cite
@article{arxiv.2108.04025,
title = {On differential operators and unifying relations for $1$-loop Feynman integrands},
author = {Kang Zhou},
journal= {arXiv preprint arXiv:2108.04025},
year = {2026}
}
Comments
42 pages, 3 figures, 4 tables