https://doi.org/10.1140/epjc/s10052-024-12517-y
Regular Article - Theoretical Physics
Recursive construction for expansions of tree Yang–Mills amplitudes from soft theorem
1
School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, 310024, Hangzhou, China
2
University of Chinese Academy of Sciences, 100049, Beijing, China
3
Center for Gravitation and Cosmology, College of Physical Science and Technology, Yangzhou University, 225009, Yangzhou, China
Received:
9
November
2023
Accepted:
4
February
2024
Published online:
2
March
2024
In this paper, we introduce a fundamentally different approach, based on a bottom-up methodology, for expanding tree-level Yang–Mills (YM) amplitudes into Yang–Mills-scalar (YMS) amplitudes and bi-adjoint-scalar (BAS) amplitudes. Our method relies solely on the intrinsic soft behavior of external gluons, eliminating the need for external aids such as Feynman rules or CHY rules. The recursive procedure consistently preserves explicit gauge invariance at every step, ultimately resulting in a manifest gauge-invariant outcome when the initial expression is already framed in a gauge-invariant manner. The resulting expansion can be directly analogized to the expansions of gravitational (GR) amplitudes using the double copy structure. When combined with the expansions of Einstein–Yang–Mills amplitudes obtained using the covariant color-kinematic duality method from existing literature, the expansions presented in this note yield gauge-invariant Bern–Carrasco–Johansson (BCJ) numerators.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.