[Paper Review] Double Copy of Form Factors and Higgs Amplitudes: A mechanism of turning spurious poles in Yang-Mills into physical poles in gravity

Guanda Lin, Gang Yang|arXiv (Cornell University)|Nov 24, 2021

Particle Accelerators and Free-Electron Lasers4 citations

TL;DR

This paper extends the double copy formalism to form factors—matrix elements involving local gauge-invariant operators—demonstrating that spurious poles in Yang-Mills form factors become physical propagators in the corresponding gravity form factors. The mechanism relies on color-kinematics duality and generalized BCJ relations, revealing a novel mapping where unphysical singularities in gauge theory acquire physical meaning in gravity through the double copy construction.

ABSTRACT

We extend the double copy picture of scattering amplitudes to a class of matrix elements (so-called form factors) that involve local gauge invariant operators. Both the Bern, Carrasco and Johansson (BCJ) and the Kawai, Lewellen and Tye (KLT) formalisms are considered and novel properties are observed. One remarkable feature is that through the double-copy construction, certain spurious poles hidden in the gauge form factors become physical propagators in gravity. This mechanism also reveals new hidden relations for form factors which can be understood as a generalization of the BCJ relations.

Motivation & Objective

• To extend the double copy formalism from scattering amplitudes to form factors involving local gauge-invariant operators.
• To investigate whether spurious poles in Yang-Mills form factors can be transformed into physical propagators in gravity via the double copy.
• To establish generalized BCJ relations for form factors using operator-induced duality and kinematic numerator constraints.
• To confirm the physical consistency of the resulting gravity form factors through diffeomorphism invariance and factorization properties.
• To provide the first double copy construction for amplitudes involving a color-singlet particle, such as Higgs amplitudes.

Proposed method

• Utilizes both BCJ and KLT formalisms to construct gravity form factors from Yang-Mills form factors via squaring kinematic numerators.
• Imposes operator-induced color-kinematics duality relations to ensure diffeomorphism invariance in the gravity theory.
• Derives generalized BCJ vectors as rational functions of Mandelstam invariants to encode hidden relations in form factors.
• Employs KLT kernel decomposition to relate gravity form factor residues to products of gauge-theory form factors and amplitudes.
• Analyzes factorization properties on new poles arising from the double copy, confirming consistency with gravity dynamics.
• Validates the construction by showing that factorization on new poles matches expected gravity behavior, using orthogonal complements of BCJ vectors.

Experimental results

Research questions

• RQ1 Can the double copy construction be consistently applied to form factors involving local gauge-invariant operators, despite gravity's diffeomorphism invariance constraints?
• RQ2 How do spurious poles in Yang-Mills form factors transform under the double copy, and can they become physical propagators in gravity?
• RQ3 What generalized BCJ relations emerge for form factors, and how do they relate to the structure of the KLT kernel?
• RQ4 Does the double-copy of form factors preserve diffeomorphism invariance and correct factorization on physical poles?
• RQ5 Can this mechanism be extended to describe Higgs amplitudes and other processes involving color-singlet particles?

Key findings

• Spurious poles in Yang-Mills form factors—unphysical singularities in the gauge theory—become physical propagators in the gravity form factor after double copy.
• The double copy construction reveals new hidden relations among form factors, generalizing the BCJ relations to matrix elements with local operators.
• The KLT kernel decomposes into products of form factors and amplitudes when evaluated at new poles, confirming consistency with gravity dynamics.
• Factorization on the new poles in gravity is reproduced by the product of a form factor and an amplitude, as required by unitarity.
• The method ensures diffeomorphism invariance in gravity by enforcing operator-induced color-kinematics duality on the numerators.
• Explicit examples at five points confirm the validity of the generalized BCJ relations and the factorization structure of the gravity form factors.