Physical Review D
In previous work, we have developed a relativistic, model-independent three-particle quantization condition, but only under the assumption that no poles are present in the two-particle K matrices that appear as scattering subprocesses [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 90, 116003 (2014); M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015); R. A. Briceño et al., Phys. Rev. D 95, 074510 (2017).]. Here we lift this restriction, by deriving the quantization condition for identical scalar particles with a G-parity symmetry, in the case that the two-particle K matrix has a pole in the kinematic regime of interest. As in earlier work, our result involves intermediate infinite-volume quantities with no direct physical interpretation, and we show how these are related to the physical three-to-three scattering amplitude by integral equations. This work opens the door to study processes such as a2→ρπ→πππ, in which the ρ is rigorously treated as a resonance state.
Original Publication Citation
Briceño, R. A., Hansen, M. T., & Sharpe, S. R. (2019). Three-particle systems with resonant subprocesses in a finite volume. Physical Review D, 99(1), 014516. doi:10.1103/PhysRevD.99.014516
Briceño, Raúl A.; Hansen, Maxwell T.; and Sharpe, Stephen R., "Three-Particle Systems With Resonant Subprocesses in a Finite Volume" (2019). Physics Faculty Publications. 351.