I=2 Pion Scattering Length from Two-Pion Wave Function

TL;DR

This paper reports a preliminary lattice QCD calculation of the I=2 pion scattering length using two different methods, comparing results to validate the approach, with calculations performed on specific lattice configurations.

Contribution

It introduces a direct method to compute the I=2 pion scattering length from the two-pion wave function, providing a novel approach compared to traditional four-point function analysis.

Findings

Results are consistent between wave function and four-point function methods.

Calculations performed at a specific lattice spacing and volume.

Preliminary results show promising agreement with theoretical expectations.

Abstract

We present a preliminary report on a calculation of scattering length for I=2 $S$-wave two-pion system directly from the two-pion wave function. Results are compared with those calculated from the time dependence of two-pion four-point functions. Calculations are made with an RG-improved action for gluons and improved Wilson action for quarks at $a^{-1}=1.207(12)$ GeV on $20^3 \times 48$ and $24^3 \times 48$ lattices.