This article is cited in 4 papers

METHODOLOGICAL NOTES

Unitarity relation and unitarity bounds for scalars with different sound speeds

Yu. A. Ageeva^abc, P. K. Petrov<sup>a

a</sup> Institute for Nuclear Research, Russian Academy of Sciences, Moscow
^b Faculty of Physics, Lomonosov Moscow State University
^c Institute for Theoretical and Mathematical Physics, Lomonosov Moscow State University

Abstract: We consider a theory which contains massless scalar fields with different sound speeds. For these theories we derive unitarity relations for partial wave amplitudes of $ 2 \to 2$ scattering, with explicit formulas for contributions of two-particle intermediate states. We also obtain unitarity bounds both in the most general case and in the case considered in the literature for the speed of sound, equal to unity. We illustrate our unitarity relations by explicit one-loop calculation to the first nontrivial order in couplings in a simple model of two scalar fields with different sound speeds. Obtained unitarity bounds can be used to estimating the strong coupling scale of a pertinent effective field theory (EFT).

Keywords: unitarity, quantum field theory, scalar field, cosmology.

PACS: 11.10.-z, 98.80.-k

Received: June 29, 2022
Revised: November 5, 2022
Accepted: November 8, 2022

DOI: 10.3367/UFNr.2022.11.039259

 English version: Physics–Uspekhi, 2023, 66:11, 1134–1141

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