Double copy for tree-level form factors. Part I. Foundations

Abstract

The double-copy construction for form factors was reported in our previous work, in which a novel mechanism of turning spurious poles in Yang-Mills theory into physical poles in gravity is observed. This paper is the first of a series of two papers providing the details as well as various generalizations on the double-copy construction of tree-level form factors. In this paper, we establish the generic formalism by focusing on the form factor of $\mathrm{tr}({\varphi }^2)$ in the Yang-Mills-scalar theory. A thorough discussion is given on the emergence of the "spurious"-type poles and various related properties. We also discuss two generalizations: the Higgs amplitudes in QCD, and the $\mathrm{tr}({\varphi }^2)$ form factors with multiple external scalar states.

63 pages, 11 figures; v2: minor changes, references added, published version

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