Calculating the I=2 pion scattering length using tadpole improved clover Wilson action on coarse anisotropic lattices

Abstract

In an exploratory study, using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, the ππ scattering length in the I = 2 channel is calculated within quenched approximation. A new method is proposed which enables us to make chiral extrapolation of our lattice results without calculating the decay constant on the lattice. Finite volume and finite lattice spacing errors are analyzed and the results are extrapolated towards the infinite volume and continuum limit. Comparisons of our lattice results with the new experiment and the results from Chiral Perturbation Theory are made. Good agreements are found.

I=2 Pion Scattering Length With Improved Actions on Anisotropic Lattices

“…In this letter, we report our recent quenched lattice result on the ππ scattering length in the I = 2 channel. The result in this letter is an improvement over our previous result on the scattering length [5].…”

“…Lattice QCD is a genuine non-perturbative method which can handle hadron-hadron scattering at low-energies. In recent years, owing to the progress in computing facilities and the use of improved actions, there have been several studies on pion pion [4,5,6,7,8,9], pion nucleon [10], pion kaon [11] and kaon nucleon [12] scattering in quenched lattice QCD. Very recently, CP-PACS collaboration even calculated pion pion scattering phase shift in the I = 2 channel using their unquenched configurations [13,14].…”

“…Using this gauge action together with improved Wilson fermion actions, glueball and hadron spectra have been studied within quenched approximation [15,16,17,18,19,20,21]. Configurations generated from the gauge action have also been utilized to calculate the the scattering length for ππ scattering in the I = 2 channel [5], KN scattering in the I = 1 channel [12] and the Kπ scattering in the I = 3/2 channel [11]. In this letter, we update our result on the ππ scattering length in the I = 2 channel.…”

Hadronic Interactions From Lattice QCD

“…[86]. The first lattice calculations of ππ scattering were performed in quenched QCD [93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113], and the first partially-quenched QCD calculation of ππ scattering (the scattering length and phase-shift) was carried through by the CP-PACS collaboration, who exploited the finitevolume strategy to study I = 2, s-wave scattering with two flavors (n f = 2) of improved Wilson fermions [114], with pion masses in the range m π 0.5 − 1.1 GeV. The first fullydynamical calculation of the I = 2 ππ scattering length with three flavors (n f = 2 + 1) of light quarks was performed by NPLQCD using domain-wall valence quarks on asqtadimproved staggered sea quarks at four pion masses in the range m π 0.3 − 0.5 GeV at a single lattice spacing, b ∼ 0.125 fm [78].…”

Exotic meson decay widths using lattice quantum chromodynamics

“…Scattering lengths have also been studied, for example see [58,59,60], by looking at the lattice volume depen dence of low lying two-particle energy levels [6 1 , 62], and hybrid decays in the heavy quark lim it were investigated in [44].…”