Generalized Lüscher's Formula in Multichannel Baryon-Baryon Scattering

Abstract

In this paper, Lüscher's formula is generalized to the case of two spin-$\frac{1}{2}$ particles in two-channel scattering based on Ref. \cite{Li:2012bi}. This is first done in a non-relativistic quantum mechanics model and then generalized to quantum field theory. We show that Lüscher's formula obtained from these two different methods are equivalent up to terms that are exponentially suppressed in the box size. This formalism can be readily applied to future lattice QCD calculations.

Introduction expanded and references added. 10 pages, no figures

References in corpus (10)

• Two-particle multichannel systems in a finite volume with arbitrary spin
• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• $D_{s0}^{\ast }(2317)$ Meson and $D$-Meson-Kaon Scattering from Lattice QCD
• Scalar mesons in a finite volume
• Evidence for X(3872) from DD* scattering on the lattice
• Strangeness nuclear physics: a critical review on selected topics
• Two-Nucleon Systems in a Finite Volume: (II) 3S1-3D1 Coupled Channels and the Deuteron
• The K+K+ Scattering Length from Lattice QCD
• Two-Baryon Systems with Twisted Boundary Conditions
• Fitting two nucleons inside a box: exponentially suppressed corrections to the Luscher's formula

Cited by in corpus (9)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Microscopic Clustering in Light Nuclei
• Three-body Unitarity in the Finite Volume
• Multichannel one-to-two transition amplitudes in a finite volume
• Multichannel 0-to-2 and 1-to-2 transition amplitudes for arbitrary spin particles in a finite volume
• Nuclear Reactions from Lattice QCD
• Renormalization of a Contact Interaction on a Lattice
• Review on Hadron Spectroscopy
• Formal Developments for Lattice QCD with Applications to Hadronic Systems