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arXiv · 2212.05670

Unitarity and unstable-particle scattering amplitudes

Katsuki Aoki
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Abstract

Unitarity is the fundamental property of the S-matrix while its usage for a scattering of unstable particles has been subtle as unstable particles do not appear in the asymptotic states. Defining unstable-particle amplitudes as residues of a higher-point amplitude at an appropriate complex pole, we find unitarity equations for the 2-to-2 unstable-particle amplitudes from unitarity and analyticity of stable-particle scattering amplitudes. The unstable-particle unitarity equations take a form analogous to those of the stable-particle amplitudes when the in and out states are chosen to be complex-conjugate positions. In particular, as in the optical theorem, we find a positivity constraint on a discontinuity of the amplitudes in a positive region of the momentum transfer variable.

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Katsuki Aoki. 2022-12-12. Unitarity and unstable-particle scattering amplitudes. https://doi.org/10.1103/physrevd.107.065017

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