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Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2

Published inThe journal of high energy physics, vol. 2022, no. 12, 92
Publication date2022
First online date2022-12-16
Abstract

We study two-to-two scattering amplitudes of a scalar particle of mass m. For simplicity, we assume the presence of ℤ$_{2}$ symmetry and that the particle is ℤ$_{2}$ odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale M. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in 2 ≤ d ≤ 4 space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in ϕ$^{4}$ theory computed perturbatively at weak coupling, and find that they saturate the bounds.

Keywords
  • Field Theories in Higher Dimensions
  • Field Theories in Lower Dimensions
  • Nonperturbative Effects
  • Scattering Amplitudes
  • Scalar particle: massive
  • Scalar particle: scattering amplitude
  • Scalar particle: mass
  • Space-time: dimension
  • Effective field theory
  • Unitarity
  • Nonperturbative
  • Nonlinear
  • Scattering
  • Weak coupling
  • Simplex
  • Numerical methods
Citation (ISO format)
CHEN, Hongbin, FITZPATRICK, A. Liam, KARATEEV, Denis. Nonperturbative bounds on scattering of massive scalar particles in d ≥ 2. In: The journal of high energy physics, 2022, vol. 2022, n° 12, p. 92. doi: 10.1007/jhep12(2022)092
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Article (Published version)
Identifiers
Additional URL for this publicationhttps://link.springer.com/10.1007/JHEP12(2022)092
Journal ISSN1029-8479
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18downloads

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