The double copy for heavy particles

TL;DR

This work extends the double-copy construction to heavy-particle effective theories by showing that HBET amplitudes can be obtained as double-copies of HQET amplitudes, provided propagator-expansion and external wavefunction contaminants are properly identified and removed. Using color-kinematics duality and careful external-state matching via wavefunction factors $\mathcal{R}$, the authors demonstrate explicit double-copy prescriptions at tree level for three cases: (i) spin-1 HBET from spin-1 gauge theory and spin-0, (ii) spin-1/2 HBET from spin-1/2 gauge theory and spin-0, and (iii) heavy-scalar five-point radiative processes with ghost subtraction to eliminate dilaton contamination. They derive and compare the corresponding HBET Lagrangians, including novel all-order-in-mass Lagrangians for spin-1 heavy particles, and discuss the finite-$m$ corrections order-by-order in $\hbar$. The results provide a practical framework for relating HQET and HBET amplitudes and offer insights into the quantum-classical connection within the double-copy paradigm, with potential applicability to other heavy EFTs.

Abstract

We show how to double-copy Heavy Quark Effective Theory (HQET) to Heavy Black Hole Effective Theory (HBET) for spin $s\leq 1$. In particular, the double copy of spin-$s$ HQET with scalar QCD produces spin-$s$ HBET, while the double copy of spin-1/2 HQET with itself gives spin-1 HBET. Finally, we present novel all-order-in-mass Lagrangians for spin-1 heavy particles.