For massless scalar-mediated scattering, the entire late-time and early-time expansion of the scalar waveform is determined by the particles' asymptotic momenta and charges, with an explicit all-order formula for two-body scattering.
Soft Scalars don't decouple
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abstract
It is demonstrated that it is possible to find a field theory containing massless scalar particles which has infrared structure closely resembling that of quantum electrodynamics and perturbative quantum gravity but exhibiting no gauge invariance or internal symmetries at all, and in particular, no apparent asymptotic symmetry. It is shown that, unlike soft photons and gravitons, the soft scalars do not decouple from dressed states and they are generically produced when hard dressed particles interact. However, the entanglement of the hard and resulting soft particles is vanishingly small.
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Waveform, memory and classical soft scalar theorems
For massless scalar-mediated scattering, the entire late-time and early-time expansion of the scalar waveform is determined by the particles' asymptotic momenta and charges, with an explicit all-order formula for two-body scattering.