Unitarity relation and unitarity bounds for scalars with different sound speeds

Yu.A. Ageeva^†^a, b, c, P.K. Petrov^‡^a
^aInstitute for Nuclear Research, Russian Academy of Sciences, prosp. 60-letiya Oktyabrya 7a, Moscow, 117312, Russian Federation
^bLomonosov Moscow State University, Faculty of Physics, Vorobevy gory, Moscow, 119899, Russian Federation
^cInstitute of Theoretical and Mathematical Physics, Lomonosov Moscow State University, Lomonosovskii prosp. 27, korp. 1, Moscow, 119192, Russian Federation

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 → 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 (all)
DOI: 10.3367/UFNe.2022.11.039259
URL: https://ufn.ru/en/articles/2023/11/d/
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2-s2.0-85182879492
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2023PhyU...66.1134A
Citation: Ageeva Yu A, Petrov P K "Unitarity relation and unitarity bounds for scalars with different sound speeds" Phys. Usp. 66 1134–1141 (2023)

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Received: 29th, June 2022, revised: 5th, November 2022, accepted: 8th, November 2022

Оригинал: Агеева Ю А, Петров П К «Соотношение унитарности и унитарные ограничения для теории скалярных полей с разными скоростями звука» УФН 193 1205–1213 (2023); DOI: 10.3367/UFNr.2022.11.039259