Abstract
We present a novel double-copy prescription for gauge fields at the Lagrangian level and apply it to the original double copy, couplings to matter and the soft theorem. The Yang-Mills Lagrangian in light-cone gauge is mapped directly to the \( \mathcal{N} \) = 0 supergravity Lagrangian in light-cone gauge to trilinear order, and we show that the obtained result is manifestly equivalent to Einstein gravity at tree level up to this order. The application of the double-copy prescription to couplings to matter is exemplified by scalar and fermionic QCD and finally the soft-collinear effective QCD Lagrangian. The mapping of the latter yields an effective description of an energetic Dirac fermion coupled to the graviton, Kalb-Ramond, and dilaton fields, from which the fermionic gravitational soft and next-to-soft theorems follow.
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Beneke, M., Hager, P. & Sanfilippo, A. Double copy for Lagrangians at trilinear order. J. High Energ. Phys. 2022, 83 (2022). https://doi.org/10.1007/JHEP02(2022)083
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DOI: https://doi.org/10.1007/JHEP02(2022)083