Double copies of fermions as only gravitational interacting matter

TL;DR

This paper extends the gauge–gravity double copy to QCD-like theories containing fermions in the fundamental representation, formulating double copies of gluons, quarks, and antiquarks that interact only gravitationally. It presents two equivalent, non-supersymmetric methods to compute gravitational amplitudes: colour–kinematics duality and a generalized KLT framework, the latter introducing a momentum-kernel $S$ that relates gauge and gravity amplitudes in the presence of flavour. The authors derive explicit four-point gravitational amplitudes involving double copies of fermions, establish their pole structure, and compute cross sections, including a non-relativistic limit that connects to Rutherford scattering with a distinctive factor. They discuss the potential relevance of such massive, non-relativistic double-copy states as dark matter candidates, noting the required non-thermal production and the generality of the approach beyond supersymmetry or string theory. The work provides a concrete, calculable bridge between gauge theory amplitudes and gravity in a non-standard matter content, with explicit phenomenological implications for dark matter phenomenology and early-universe production mechanisms.

Abstract

Inspired by the recent progress in the field of scattering amplitudes, we discuss hypothetical particles which can be characterised as the double copies of fermions -- in the same way gravitons can be viewed as double copies of gauge bosons. As the gravitons, these hypothetical particles interact only through gravitational interactions. We present two equivalent methods for the computation of the relevant scattering amplitudes. The hypothetical particles can be massive and non-relativistic.