I=2 Two-Pion Wave Function and Scattering Phase Shift

Abstract

We calculate a two-pion wave function for the I=2 $S$-wave two-pion system with a finite scattering momentum and estimate the interaction range between two pions, which allows us to examine the validity of a necessary condition for the finite size formula presented by Rummukainen and Gottlieb. We work in the quenched approximation employing the plaquette gauge action for gluons and the improved Wilson action for quarks at $1/a=1.63\mathrm{GeV}$ on $32^3\times 120$ lattice. The quark masses are chosen to give $m_{\pi }=0.420$, 0.488 and $0.587\mathrm{GeV}$. We find that the energy dependence of the interaction range is small and the necessary condition is satisfied for our range of the quark mass and the scattering momentum, $k\le 0.16\mathrm{GeV}$. We also find that the scattering phase shift can be obtained with a smaller statistical error from the two-pion wave function than from the two-pion time correlator.

23 pages, 7 figures, added a reference (Phys.Rev.D73:054503,2006) in v2

References in corpus (10)

• ππscattering
• Resonance Scattering Phase Shifts on a Non-Rest Frame Lattice
• Finite-Volume Effects for Two-Hadron States in Moving Frames
• Elastic $\pi \pi$ scattering to two loops
• Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum
• I=2 pi-pi Scattering from Fully-Dynamical Mixed-Action Lattice QCD
• I=2 $\pi \pi$ Scattering Phase Shift with two Flavors of $O(a)$ Improved Dynamical Quarks
• I=2 Pion Scattering Length from Two-Pion Wave Functions
• I=2 Pion Scattering Phase Shift with Wilson Fermions
• I=2 $\pi \pi$ scattering using G-parity boundary condition

Cited by in corpus (17)

• S and D-wave phase shifts in isospin-2 pi pi scattering from lattice QCD
• The coupled-channel scattering on a torus
• Scattering phase shifts for two particles of different mass and non-zero total momentum in lattice QCD
• The pi+ pi+ scattering length from maximally twisted mass lattice QCD
• The phase-shift of isospin-2 pi-pi scattering from lattice QCD
• Two-Nucleon Bound States in Quenched Lattice QCD
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• One spatial dimensional finite volume three-body interaction for a short-range potential
• An numerical approach for finite volume three-body interaction
• Multiple-particle interaction in $1+1$ dimensional lattice model
• Chiral extrapolation of pion-pion scattering phase shifts within standard and unitarized Chiral Perturbation Theory
• Coupled-channel scattering in 1+1 dimensional lattice model
• Efficient solution of the multi-channel Lüscher determinant condition through eigenvalue decomposition
• Quark-diquark potential and diquark mass from Lattice QCD
• Hadron-hadron interaction from SU(2) lattice QCD
• On-shell Delta I = 3/2 kaon weak matrix elements with non-zero total momentum
• Hadronic interactions and nuclear physics