Calculating the I=2 Pion Scattering Length Using Tadpole Improved Clover Wilson Action on Coarse Anisotropic Lattices

TL;DR

This study computes the I=2 pion scattering length using improved lattice QCD techniques on coarse, anisotropic lattices, successfully extrapolating to physical limits and comparing favorably with experimental and theoretical results.

Contribution

A novel method for chiral extrapolation without decay constant calculations is introduced, applied to quenched lattice QCD with improved actions on coarse lattices.

Findings

Results agree well with experimental data.

Finite volume and lattice spacing effects are effectively controlled.

The new extrapolation method proves reliable for lattice QCD calculations.

Abstract

In an exploratory study, using the tadpole improved clover Wilson quark action on small, coarse and anisotropic lattices, the $\pi\pi$ 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.