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.
Highlights
JHEP03(2015)070 is the angular momentum operator of the i-th particle
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
Writing the action of the angular momentum operators on the four scalars amplitude using derivatives with respect to the Mandelstam s and t invariants, we find that the amplitude has a simple form in terms of a set of gauge invariant coefficients
Summary
It has been shown in [18] that in scalar QED the first subleading correction to Low’s theorem is completely fixed by gauge invariance. Compared to the scalar QED case analyzed in [18], we have a larger number of unknown functions associated with the different color structures in the internal emission diagrams. This very fact implies that there is an larger number of independent constraints to determine these functions. We have not identified any relevant role for the Jacobi identities when investigating the double copy structure in the gravitational case This is likely to be a feature of the soft limit alone
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