I=2 Pion scattering length with improved actions on anisotropic lattices

TL;DR

This paper calculates the I=2 pion scattering length using improved lattice actions on anisotropic lattices, extrapolating to physical limits, and finds results consistent with theory, experiment, and prior lattice studies.

Contribution

It introduces an improved lattice calculation of the I=2 pion scattering length on anisotropic lattices, refining previous results and aligning with theoretical and experimental values.

Findings

The scattering length is $a^{(2)}_0m_= -0.0467(45)$ in the continuum limit.

Results are consistent with Chiral Perturbation Theory and experimental data.

The method improves the precision of lattice calculations for scattering lengths.

Abstract

$\pi\pi$ scattering length in the I=2 channel is calculated within quenched approximation using improved gauge and improved Wilson fermion actions on anisotropic lattices. The results are extrapolated towards the chiral, infinite volume and continuum limit. This result improves our previous result on the scattering length. In the chiral, infinite volume and continuum limit, we obtain $a^{(2)}_0m_\pi=-0.0467(45)$, which is consistent with the result from Chiral Perturbation Theory, the experiment and results from other lattice calculations.