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arXiv · 2404.02997

The off-shell expansion relation of the Yang-Mills scalar theory

Yi-Xiao Tao·Konglong Wu
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Abstract

In this work, we investigated the off-shell expansion relation of the Yang-Mills scalar theory. We explicitly showed that the single-trace Berends-Giele currents in the Yang-Mills scalar theory can be decomposed into a term expressed by a linear combination of bi-adjoint scalar Berends-Giele currents and one that vanishes under the on-shell limit. We proved that the bi-adjoint scalar currents, as well as the corresponding coefficients, can be characterized by a graphic approach that was originally studied in Einstein-Yang-Mills expansion. Furthermore, we generalized the decomposition to the multi-trace case through unifying relations and established the connection both in single-trace and multi-trace graphic descriptions. Finally, we established the relations between the Yang-Mills currents and the single-trace Yang-Mills scalar currents choosing special reference orders of the Yang-Mills graphs.

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Yi-Xiao Tao, Konglong Wu. 2024-04-03. The off-shell expansion relation of the Yang-Mills scalar theory. https://doi.org/10.1103/physrevd.111.105025

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