Abstract
Both the Bern, Carrasco, and Johansson (BCJ) and the Kawai, Lewellen, and Tye (KLT) double-copy formalisms have been recently generalized to a class of scattering matrix elements (so-called form factors) that involve local gauge-invariant operators. In this paper, we continue the study of double copy for form factors. First, we generalize the double-copy prescription to form factors of higher-length operators tr(ϕm) with m ≥ 3. These higher-length operators introduce new non-trivial color identities, but the double-copy prescription works perfectly well. The closed formulae for the CK-dual numerators are also provided. Next, we discuss the \( \overrightarrow{\upsilon} \) vectors which are central ingredients appearing in the factorization relations of both the KLT kernels and the gauge form factors. We present a general construction rule for the \( \overrightarrow{\upsilon} \) vectors and discuss their universal properties. Finally, we consider the double copy for the form factor of the tr(F 2) operator in pure Yang-Mills theory. In this case, we propose a new prescription which involves a gauge invariant decomposition for the form factor and a mixture of different CK-dual numerators appearing in the expansion. The new prescription for the more complicated double copy has been verified up to five external gluons.
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Acknowledgments
We thank Gang Chen, Jin Dong, Song He, and Congkao Wen for discussions. This work is supported in part by the National Natural Science Foundation of China (Grants No. 11935013, 12175291, 12047503) and by the CAS under Grants No. YSBR-101. We also thank the support of the HPC Cluster of ITP-CAS.
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Lin, G., Yang, G. Double copy for tree-level form factors. Part II. Generalizations and special topics. J. High Energ. Phys. 2024, 13 (2024). https://doi.org/10.1007/JHEP02(2024)013
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DOI: https://doi.org/10.1007/JHEP02(2024)013