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/
Web of Science

001131650500003
Scopus

2-s2.0-85182879492
ADS NASA

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

References (176) Similar articles (14) ↓

I.D. Novikov “Antigravitation in the Universe” 61 692–696 (2018)
A.A. Logunov “The theory of the classical gravitational field” 38 179–193 (1995)
M.I. Shirokov “Signal velocity in quantum electrodynamics” 21 345–358 (1978)
A.V. Toporensky, S.B. Popov “The Hubble flow: an observer’s perspective” 57 708–713 (2014)
V.L. Ginzburg, V.P. Frolov “Vacuum in a homogeneous gravitational field and excitation of a uniformly accelerated detector” 30 1073–1095 (1987)
Ya.B. Zel’dovich, A.V. Mamaev, S.F. Shandarin “Laboratory observation of caustics, optical simulation of the motion of particles, and cosmology” 26 77–83 (1983)
V.V. Mityugov “Thermodynamics of simple quantum systems” 43 631–637 (2000)
V.L. Pokrovsky “Landau and modern physics” 52 1169–1176 (2009)
G.B. Malykin “Para-Lorentz transformations” 52 263–266 (2009)
D.S. Agafontsev, E.A. Kuznetsov et al “Compressible vortex structures and their role in the onset of hydrodynamic turbulence” 65 189–208 (2022)
I.N. Toptygin, G.D. Fleishman “Eigenmode generation by a given current in anisotropic and gyrotropic media” 51 363–374 (2008)
L.A. Rivlin “Photons in a waveguide (some thought experiments)” 40 291–303 (1997)
A.Yu. Andreev, D.A. Kirzhnits “Tachyons and the instability of physical systems” 39 1071–1076 (1996)
D.A. Kirzhnits “Are the Kramers-Kronig relations for the dielectric permittivity of a material always valid?” 19 530–537 (1976)

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