Speaker
Description
Nucleon resonances provide an important window into nonperturbative QCD and the internal structure of hadrons. While the time evolution of unstable states has been widely studied in many quantum systems, its role in connecting pole-defined hadron resonances with physical scattering observables remains less explored. In this work, we revisit a resonance described by the Gamow vector $|\psi^{\rm Gamow}\rangle$ in the complex momentum basis $|\vec p e^{-i\theta}\rangle$ and construct its physical representation $|\psi^{\rm phys}\rangle$ in the real momentum basis $|\vec p\rangle$ through analytic continuation. With the assistance of a finite number of discrete virtual-state vectors, the physical and virtual components together satisfy the Hamiltonian eigenvalue equation at the complex pole energy. The time evolution $|\psi^{\rm phys},t\rangle=\exp(-iH t) \, |\psi^{\rm phys}\rangle$ then describes, within the ordinary Hilbert space, both the survival of the resonance and the production of outgoing scattering states. The state at $t=0$ reveals the finite spatial extent and channel content of the resonance, whereas the asymptotic state at $t\to+\infty$ gives the final-state energy distribution relevant to scattering experiments. A two-channel hadronic toy model is used to illustrate this connection between resonance wavefunctions and experimentally accessible distributions.