The double copy structure of soft gravitons

Abstract

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.

Planar zeros in gauge theories and gravity

“…This double copy structure has a historic antecedent in the Kawai, Lewellen, and Tye (KLT) relations [4], showing how, at tree level, closed string amplitudes admit a decomposition in terms of products of open string amplitudes. Similar structures have been found in various other setups [5][6][7]. It seems clear that, at the level of scattering amplitudes, there is a sense in which gravity can be considered the "square" of a gauge theory.…”

“…, 8) or (21,22,23) we recover previous examples. For instance, (a 1 , a 2 , a 3 , a 4 , a 5 ) = (7,7,6,1,5) gives the curve shown in the l.h.s. panel of figure 4, whereas (a 1 , a 2 , a 3 , a 4 , a 5 ) = (22,23,21,21,21) reproduces eq.…”

Sudakov representation of the Cachazo-He-Yuan scattering equations formalism

“…This exhibits the double-copy structure of graviton amplitudes, already found in many other physical setups [30][31][32][33][34][35]. Similarly, biadjoint scalar amplitudes can be obtained from eq.…”

“…The connection among gravitational and Yang-Mills amplitudes in this approach from the point of view of Regge kinematics [40][41][42][43] is also of interest, together with the corresponding soft theorems [35,[44][45][46][47][48]. Besides, it would be interesting to interpret the role of the gluing operator recently investigated in [37] in terms of Sudakov variables.…”

Projectivity of planar zeros in field and string theory amplitudes

“…In the limit in which the emitted positive (resp. negative) helicity gluon is soft, p 5 → 0, the leading behavior of the amplitude takes the form [40] A 5,soft = 2g…”