Abstract

We introduce on-shell variables for Heavy Particle Effective Theories (HPETs) with the goal of extending Heavy Black Hole Effective Theory to higher spins and of facilitating its application to higher post-Minkowskian orders. These variables inherit the separation of spinless and spin-inclusive effects from the HPET fields, resulting in an explicit spin-multipole expansion of the three-point amplitude for any spin. By matching amplitudes expressed using the on-shell HPET variables to those derived from the one-particle effective action, we find that the spin-multipole expansion of a heavy spin-s particle corresponds exactly to the multipole expansion (up to order 2s) of a Kerr black hole, that is, without needing to take the infinite spin limit. Finally, we show that tree-level radiative processes with same-helicity bosons emitted from a heavy spin-s particle exhibit a spin-multipole universality.

Highlights

  • The relationship between quantum scattering amplitudes and classical physics has enjoyed a surge of attention in recent years, in large part due to the observation of gravitational waves by the LIGO and Virgo collaborations as of 2015 [1]

  • By matching amplitudes expressed using the on-shell Heavy Particle Effective Theories (HPETs) variables to those derived from the oneparticle effective action, we find that the spin-multipole expansion of a heavy spin-s particle corresponds exactly to the multipole expansion of a Kerr black hole, that is, without needing to take the infinite spin limit

  • We have presented an on-shell formulation of HPETs by expressing their asymptotic states as a linear combination of the chiral and anti-chiral massive on-shell helicity variables of ref

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Summary

Introduction

The relationship between quantum scattering amplitudes and classical physics has enjoyed a surge of attention in recent years, in large part due to the observation of gravitational waves by the LIGO and Virgo collaborations as of 2015 [1]. Various methods exist for identifying the classical component of a scattering amplitude [9, 10, 30, 31] Towards this same end, Heavy Black Hole Effective Theory (HBET) was recently formulated by Damgaard and two of the present authors in ref. We express the asymptotic states of Heavy Particle Effective Theories (HPETs) — the collection of effective field theories treating large mass particles — using the massive on-shell spinor-helicity variables of ref. An explicit expansion will arise from these variables, which makes simple the task of taking classical limits of amplitudes Such an expression of the asymptotic states of HPET will lead to an explicit separation of spinning and spinless effects in the three-point minimal coupling amplitude.

Effective theories with heavy particles
On-shell HPET variables
Reparameterization
Spin operator
Three-point amplitude
General residual momentum
Zero initial residual momentum
Most general three-point amplitude
Infinite spin limit
Kerr black holes as heavy particles
On-shell amplitudes
Counting
Boson exchange
Compton scattering
Emission of n bosons
Summary and outlook
A Conventions
B Uniqueness of on-shell HPET variables
C Reparameterization and the little group
D Propagators
Spin-s projection operator
E Matching to HPET Lagrangians
Matching spin-1 Zeeman coupling
Full Text
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