Three-particle scattering amplitudes from a finite volume formalism
By R. Briceño, Zohreh Davoudi. 2012
149 citations recorded by the source corpus.
We present a quantization condition for the spectrum of a system composed of three identical bosons in a finite volume with periodic boundary conditions. This condition gives a relation between the finite volume spectrum and infinite volume scattering amplitudes. The quantization condition presented is an integral equation that in general must be solved numerically. However, for systems with an attractive two-body force that supports a two-body bound state, a diboson, and for energies below the diboson breakup, the quantization condition reduces to the well-known L\"uscher formula with exponential corrections in volume that scale with the diboson binding momentum. To accurately determine infinite volume phase shifts, it is necessary to extrapolate the phase shifts obtained from the L\"uscher formula for the boson-diboson system to the infinite volume limit. For energies above the breakup threshold, or for systems with no two-body bound state (with only scattering states and resonances) the L\"uscher formula gets power-law volume corrections and consequently fails to describe the three-particle system. These corrections are nonperturbatively included in the quantization condition presented.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/6a6bfc881c10e2430fa9f9bfa43818ae645f12eb
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Nuclear and High Energy Physics
Citations in the corpus
- Hadronic molecules (2017, methodology): “…resonances), this method needs to be extended in various directions, such as considering higher partial waves and spins (Bernard et al., 2008; Briceño and Davoudi, 2013a; Göckeler et al., 2012; König et al., 2011, 2012; Luu and Savage, 2011), moving frames (Bour et al., 2011; Davoudi and…”
- The XYZ states: Experimental and theoretical status and perspectives (2019, unknown): “[858–877].”
- Nuclear effective field theory: Status and perspectives (2019, methodology): “The formulation of the threeparticle quantization condition in a finite volume using the dibaryon formalism, which is required for the extraction of scattering phase shifts from lattice calculations, was considered by Briceno and Davoudi (2013), Hammer et al. (2017c), and Hammer et al. (2017b).”
- Scattering processes and resonances from lattice QCD (2017, methodology): “…be they elastic, coupledchannel, featuring spinless hadrons or hadrons with spin (Bedaque, 2004; Bernard et al., 2008a, 2011; Briceno, 2014; Briceno and Davoudi, 2013a; Briceno et al., 2014; Christ et al., 2005; Feng et al., 2004; Fu, 2012; Gockeler et al., 2012; Guo et al., 2013; Hansen…”