TY - JOUR

T1 - Wave scattering event shapes at high energies

AU - Gonzo, Riccardo

AU - Ilderton, Anton

N1 - 37 pages, 8 figures
Funding Information:
We thank T. Adamo, N.E.J. Bjerrum-Bohr, A. Cristofoli, G. Komchersky, D. Kosmopoulos, S. Klisch, M. Lavelle, D. McMullan, R. Stegeman, M. Zeng and S. Zhiboedov for insightful discussions. We are extremely grateful to H. Hannesdottir and M. Schwartz for useful discussions on the KLN theorem [] and for comments on the draft, as well as to C. Heissenberg for interesting comments on the high-energy limit and for a critical reading of this manuscript. A.I. thanks Polux Gabriel Garcia Elizondo for useful discussions on the literature. This research was supported by the National Science Foundation under Grant No. NSF PHY-1748958 (RG) and the STFC consolidator grant ST/X000494/1 “Particle Theory at the Higgs Centre” (AI).
Publisher Copyright:
© 2023, The Author(s).

PY - 2023/10/17

Y1 - 2023/10/17

N2 - We study the space and properties of global and local observables for radiation emitted in the scattering of a massive scalar field in gauge and gravitational plane-wave backgrounds, in both the quantum and classical theory. We first compute the radiated momentum and angular momentum flow, demonstrating that they are good local observables determined by the amplitude and phase of the waveform. We then focus on the corresponding global observables, which in the gravitational case requires dealing with the collinear divergence of the gravitational Compton cross-section. We show using the KLN theorem that we can obtain an infrared-finite cross-section only by summing over forward scattering diagrams; this suggests dressing the initial state in the direction collinear to the plane wave in order to be able to compute observables integrated over the celestial sphere. Finally, we explore the high-energy behaviour of our observables. We find that classical global observables generically exhibit a power-law mass divergence in electrodynamics and a logarithmic mass divergence in gravity, even when radiation reaction is included. We then show explicitly how this is consistently resolved in the full quantum theory.

AB - We study the space and properties of global and local observables for radiation emitted in the scattering of a massive scalar field in gauge and gravitational plane-wave backgrounds, in both the quantum and classical theory. We first compute the radiated momentum and angular momentum flow, demonstrating that they are good local observables determined by the amplitude and phase of the waveform. We then focus on the corresponding global observables, which in the gravitational case requires dealing with the collinear divergence of the gravitational Compton cross-section. We show using the KLN theorem that we can obtain an infrared-finite cross-section only by summing over forward scattering diagrams; this suggests dressing the initial state in the direction collinear to the plane wave in order to be able to compute observables integrated over the celestial sphere. Finally, we explore the high-energy behaviour of our observables. We find that classical global observables generically exhibit a power-law mass divergence in electrodynamics and a logarithmic mass divergence in gravity, even when radiation reaction is included. We then show explicitly how this is consistently resolved in the full quantum theory.

KW - Classical Theories of Gravity

KW - Effective Field Theories

KW - Scattering Amplitudes

U2 - 10.1007/JHEP10(2023)108

DO - 10.1007/JHEP10(2023)108

M3 - Article

SN - 1126-6708

VL - 2023

SP - 1

EP - 41

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 108

ER -