Journal of High Energy Physics
007 (43 pg.)
In this work, we use an extension of the quantization condition, given in ref. , to numerically explore the finite-volume spectrum of three relativistic particles, in the case that two-particle subsets are either resonant or bound. The original form of the relativistic three-particle quantization condition was derived under a technical assumption on the two-particle K matrix that required the absence of two-particle bound states or narrow two-particle resonances. Here we describe how this restriction can be lifted in a simple way using the freedom in the definition of the K-matrix-like quantity that enters the quantization condition. With this in hand, we extend previous numerical studies of the quantization condition to explore the finite-volume signature for a variety of two- and three-particle interactions. We determine the spectrum for parameters such that the system contains both dimers (two-particle bound states) and one or more trimers (in which all three particles are bound), and also for cases where the two-particle subchannel is resonant. We also show how the quantization condition provides a tool for determining infinite-volume dimer-particle scattering amplitudes for energies below the dimer breakup. We illustrate this for a series of examples, including one that parallels physical deuteron-nucleon scattering. All calculations presented here are restricted to the case of three identical scalar particles.
Original Publication Citation
Romero-Lopez, F., Sharpe, S. R., Blanton, T. D., Briceno, R. A., & Hansen, M. T. (2019). Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states. Journal of High Energy Physics(10), 007. doi:10.1007/jhep10(2019)007
Romero-López, Fernando; Sharpe, Stephen R.; Blanton, Tyler D.; Briceño, Raúl A.; and Hansen, Maxwell T., "Numerical Exploration of Three Relativistic Particles in a Finite Volume Including Two-Particle Resonances and Bound States" (2019). Physics Faculty Publications. 402.