Unitarity relation and unitarity bounds for scalars with different sound speeds

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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).

About the authors

Yulia Aleksandrovna Ageeva

Institute for Nuclear Research, Russian Academy of Sciences; Lomonosov Moscow State University, Faculty of Physics; Institute for Theoretical and Mathematical Physics of Lomonosov Moscow State University

without scientific degree, no status

Pavel Konstantinovich Petrov

Institute for Nuclear Research, Russian Academy of Sciences

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