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  • Letter
  • Open Access

Survival probability of unstable states in coupled-channels: Nonexponential decay of threshold cusp

Wren A. Yamada1,2,*, Osamu Morimatsu1,2,†, Toru Sato3,‡, and Koichi Yazaki4,§

  • 1Department of Physics, Faculty of Science, University of Tokyo, 7-3-1 Hongo Bunkyo-ku, Tokyo 113-0033, Japan
  • 2Theory Center, Institute of Particle and Nuclear Studies (IPNS), High Energy Accelerator Research Organization (KEK), 1-1 Oho, Tsukuba, Ibaraki, 205-0801, Japan
  • 3Research Center for Nuclear Physics (RCNP), Osaka University, Ibaraki, Osaka 567-0047, Japan
  • 4RIKEN iTHEMS, Wako, Saitama 351-0198, Japan

  • *wren-phys@g.ecc.u-tokyo.ac.jp
  • †osamu.morimatsu@kek.jp
  • ‡tsato@rcnp.osaka-u.ac.jp
  • §koichiyzk@yahoo.co.jp
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Phys. Rev. D 108, L071502 – Published 9 October, 2023

DOI: https://doi.org/10.1103/PhysRevD.108.L071502

Abstract

We investigate the survival probability of unstable states, the time-dependence of an initial state, in coupled channels. First, we extend the formulation of the survival probability from single channel to coupled channels (two channels). We derive an exact general expression of the two-channel survival probability using uniformization, a method which makes the coupled-channel S matrix single valued, and the Mittag-Leffler expansion, i.e., a pole expansion. Second, we calculate the time dependence of the two-channel survival probability by employing the derived expression. It is the minimal distance between the pole and the physical region in the complex energy plane, not the imaginary part of the pole energy, which determines not only the energy spectrum of the Green’s function but also the survival probability. The survival probability of the “threshold cusp” caused by a pole on the unusual complex-energy Riemann sheet is shown to decay, not grow in time though the imaginary part of the pole energy is positive. We also show that the decay of the “threshold cusp” is nonexponential. Thus, the “threshold cusp” is shown to be a new type of unstable mode, which is found only in coupled channels.

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Phys. Rev. D 108, L071502– Published 9 October, 2023
  • Received 26 May 2023
  • Accepted 10 August 2023
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