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

TL;DR

This paper develops a formal framework for the double-copy construction of tree-level form factors, focusing on the ${ m tr}(^2)$ form factor in Yang-Mills-scalar theory, and explores generalizations including Higgs amplitudes and multiple scalars.

Contribution

It establishes a general formalism for double-copy construction of form factors and analyzes the emergence of spurious poles, extending previous work with new generalizations.

Findings

Identified how spurious poles become physical in gravity via double copy.

Developed a formalism for ${ m tr}(^2)$ form factors in Yang-Mills-scalar theory.

Explored extensions to Higgs amplitudes and multi-scalar form factors.

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 ${\rm tr}(\phi^2)$ 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 ${\rm tr}(\phi^2)$ form factors with multiple external scalar states.