Joint Theory Seminar: Paolo Di Vecchia

Title: Classical observables of General Relativity from scattering amplitudes in the PM expansion

Abstract:
I will start considering the elastic scattering of two massive spinless particles and from their scattering amplitude I will construct the eikonal and the classical deflection angle up to 3PM. It turns out that at 3PM the eikonal develops an imaginary part that can be computed from the contribution of the 3-particle cut, including two massive particles and a graviton, to the unitarity relation. This is a sign that we have neglected radiation. Then, I will include inelastic processes with the emission of gravitons, first in the limit in which gravitons are soft and then with gravitons of arbitrary frequency. In the inelastic case the eikonal becomes an operator containing the creation and annihilation operators of the gravitons. For each of the two cases I will construct two eikonal operators: one without and one with static modes. The case of soft gravitons can be treated following the Bloch-Nordsieck approach and in this case I will be computing the zero frequency limit (ZFL) of the spectrum dE/d\omega of emitted radiation and the angular momentum loss at 2PM and 3PM. In the case of gravitons with arbitrary frequency, it turns out that the $5$-point amplitude including an extra graviton in the classical limit enters in the eikonal operator. Then, in this framework, I will be computing both the linear and angular momentum of both particles and field and I will show that they satisfy a balance equation. If I have time left I will be computing the waveform of the radiation emitted. I will conclude using the eikonal operator to compute a part of the linear momentum at 4PM and discussing universality and the problem of divergences at high energy.