Double copy for tree-level form factors. Part II. Generalizations and special topics
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| Format: | Preprint |
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2023
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| _version_ | 1866911777190576128 |
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| author | Lin, Guanda Yang, Gang |
| author_facet | Lin, Guanda Yang, Gang |
| contents | 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 ${\rm tr}(ϕ^m)$ with $m\geq3$. 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 $\vec{v}$ 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 $\vec{v}$ vectors and discuss their universal properties. Finally, we consider the double copy for the form factor of the ${\rm tr}(F^2)$ operator in pure Yang-Mills theory. In this case, we propose a new prescription that involves a gauge invariant decomposition for the form factor and a combination of different CK-dual numerators appearing in the expansion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2306_04672 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Double copy for tree-level form factors. Part II. Generalizations and special topics Lin, Guanda Yang, Gang High Energy Physics - Theory 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 ${\rm tr}(ϕ^m)$ with $m\geq3$. 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 $\vec{v}$ 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 $\vec{v}$ vectors and discuss their universal properties. Finally, we consider the double copy for the form factor of the ${\rm tr}(F^2)$ operator in pure Yang-Mills theory. In this case, we propose a new prescription that involves a gauge invariant decomposition for the form factor and a combination of different CK-dual numerators appearing in the expansion. |
| title | Double copy for tree-level form factors. Part II. Generalizations and special topics |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2306.04672 |