On Friedrichs Model with Two Continuum States

Abstract

The Friedrichs model with one discrete state coupled to more than one continuum is studied. The exact eigenstates for the full Hamiltonian can be solved explicitly. The discrete state is found to generate more than one virtual state pole or more than one pair of resonance poles in different Riemann sheets in different situations. The form factors could also generate new states on different sheets. All these states can appear in the generalized completeness relation.

13 pages, 9 figures, publication version

References in corpus (6)

• Higher Charmonia and X,Y,Z states with Screened Potential
• Bound states in the continuum in a single-level Fano-Anderson model
• Decay channels and charmonium mass-shifts
• Distinguishing cusp effects and near-threshold-pole effects
• The Friedrichs-Model with fermion-boson couplings
• The Friedrichs-Model with fermion-boson couplings II

Cited by in corpus (13)

• Hadronic molecules
• On the nature of near-threshold bound and virtual states
• Generalization of Weinberg's Compositeness Relations
• Discussions on the Line-shape of $X(4660)$ Resonance
• Comprehending Isospin breaking effects of $X(3872)$ in a Friedrichs-model-like scheme
• Partial Wave Decomposition in Friedrichs Model With Self-interacting Continua
• Decays of $X(3872)$ to ${\chi }_{cJ}{\pi }^0$ and $J/\psi {\pi }^{+}{\pi }^{-}$
• Capturing non-exponential dynamics in the presence of two decay channels
• Multichannel decay law
• Does the bottomonium counterpart of $X(3872)$ exist?
• Relativistic Friedrichs-Lee model and quark-pair creation model
• Inverse scattering problem with a bare state
• Bound states and decay dynamics in $N$-level Friedrichs model with factorizable interactions