Abstract
We propose and study a BCJ double-copy of massive particles, showing that it is equivalent to a KLT formula with a kernel given by the inverse of a matrix of massive bi-adjoint scalar amplitudes. For models with a uniform non-zero mass spectrum we demonstrate that the resulting double-copy factors on physical poles and that up to at least 5-particle scattering, color-kinematics duality satisfying numerators always exist. For the scattering of 5 or more particles, the procedure generically introduces spurious singularities that must be cancelled by imposing additional constraints. When massive particles are present, color-kinematics duality is not enough to guarantee a physical double-copy. As an example, we apply the formalism to massive Yang-Mills and show that up to 4-particle scattering the double-copy construction generates physical amplitudes of a model of dRGT massive gravity coupled to a dilaton and a two-form with dilaton parity violating couplings. We show that the spurious singularities in the 5-particle double-copy do not cancel in this example, and the construction fails to generate physically sensible amplitudes. We conjecture sufficient constraints on the mass spectrum, which in addition to massive BCJ relations, guarantee the absence of spurious singularities.
Highlights
The associated field theory limit (α → 0) relating Yang-Mills and Einstein gravity
We propose and study a BCJ double-copy of massive particles, showing that it is equivalent to a KLT formula with a kernel given by the inverse of a matrix of massive bi-adjoint scalar amplitudes
In this paper we will be concerned with the problem of generalizing the field theory double-copy relation for treelevel scattering amplitudes to models with massive particles in the spectrum
Summary
Under the assumptions outlined in the Introduction (U (N ) symmetry, external states in the adjoint representation, color-kinematics duality and the usual S-matrix axioms) it is possible to rewrite the BCJ double-copy as a KLT formula. This provides us with a different representation of the would-be double-copy in which the analysis of the singularity structure is more transparent.
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