# Infrared features of gravitational scattering and radiation in the eikonal approach

Ciafaloni, Marcello (Dipartimento di Fisica, Università di Firenze Via Sansone 1, 50019 Sesto Fiorentino, Italy) ; Colferai, Dimitri (Dipartimento di Fisica, Università di Firenze and INFN, Sezione di Firenze Via Sansone 1, 50019 Sesto Fiorentino, Italy) ; Veneziano, Gabriele (Theory Department, CERN, CH-1211 Geneva 23, Switzerland and Collège de France, 11 place M. Berthelot, 75005 Paris, France)

22 March 2019

Abstract: Following a semiclassical eikonal approach—justified at transplanckian energies order by order in the deflection angle ${\Theta }_{s}\sim \frac{4G\sqrt{s}}{b}\equiv \frac{2R}{b}$—we investigate the infrared features of gravitational scattering and radiation in four space-time dimensions, and we illustrate the factorization and cancellation of the infinite Coulomb phase for scattering and the eikonal resummation for radiation. As a consequence, both the eikonal phase $2\delta \left(E,b\right)$ and the gravitational-wave (GW) spectrum $\frac{d{E}^{\mathrm{GW}}}{d\omega }$ are free from infrared problems in a frequency region extending from zero to (and possibly beyond) $\omega =1/R$. The infrared-singular behavior of 4-D gravity leaves a memory in the deep infrared region ($\omega R\ll \omega b<1$) of the spectrum. At $O\left(\omega b\right)$ we confirm the presence of logarithmic enhancements of the form already pointed out by Sen and collaborators on the basis of nonleading corrections to soft-graviton theorems. These, however, do not contribute to the unpolarized and/or azimuthally averaged flux. At $O\left({\omega }^{2}{b}^{2}\right)$ we find instead a positive logarithmically enhanced correction to the total flux implying an unexpected maximum of its spectrum at $\omega b\sim 0.5$. At higher orders we find subleading enhanced contributions as well, which can be resummed, and have the interpretation of a finite rescattering Coulomb phase of emitted gravitons.

Published in: Physical Review D 99 (2019)