The Double Copy Structure of Soft Gravitons

TL;DR

The paper investigates subleading corrections to soft bremsstrahlung in nonabelian gauge theories and gravity for a five-point amplitude with four scalars, revealing a double-copy structure in the soft graviton contribution by expressing angular momentum actions as derivatives with respect to Mandelstam invariants $s$ and $t$. It demonstrates that, to leading and first subleading order, the gravity soft factor can be obtained as a double copy of the gauge soft factor after removing color factors, with the derivative-structure encoding the correspondence. In the high-energy Gribov limit, derivatives with respect to $s$ are suppressed, yielding Lipatov-type expressions for both gauge and gravitational emissions and extending the factorization to harder radiation. The work highlights the role of derivative representations in exposing the double-copy relation and discusses potential extensions to other amplitudes and connections to asymptotic symmetries.

Abstract

The subleading corrections to factorization theorems for soft bremsstrahlung in nonabelian gauge theories and gravity are investigated in the case of a five point amplitude with four scalars. Building on recent results, we write the action of the angular momentum operators on scattering amplitudes as derivatives with respect to the Mandelstam invariants to uncover a double copy structure in the contribution of the soft graviton to the amplitude, both in the leading term and the first correction. Using our approach, we study Gribov's theorem as extended to nonabelian gauge theories and gravity by Lipatov, and find that subleading corrections can be obtained from those to Low's theorem by dropping the terms with derivatives with respect to the center-of-mass energy, which are suppressed at high energies. In this case, the emitted gravitons are not necessarily soft.

Figures (1)

• Figure 1: Generic topologies contributing to the scattering of two distinct scalars with gluon emission. The momenta $p$ and $q$ are taken incoming, while $k$, $p'$, and $q'$ are outgoing.