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

TL;DR

This paper calculates the I=2 pion scattering length using two-pion wave functions on lattice QCD, demonstrating improved accuracy and validating the method's applicability for larger lattice volumes.

Contribution

It introduces a wave function-based method for extracting scattering lengths, showing reduced statistical errors and validating the approach with lattice volume analysis.

Findings

Scattering length extracted with smaller statistical error than previous methods.

Validation of Lüscher's formula applicability for lattice volumes ≥ 3.92 fm.

Successful calculation at multiple lattice sizes with improved actions.

Abstract

We present a report on a calculation of scattering length for I=2 $S$-wave two-pion system from two-pion wave function. Calculations are made with an RG-improved action for gluons and improved Wilson action for quarks at $a^{-1}=1.207(12) {\rm GeV}$ on $16^3 \times 80$, $20^3 \times 80$ and $24^3 \times 80$ lattices. We investigate the validity of necessary condition for application of L\"uscher's formula through the wave function. We find that the condition is satisfied for lattice volumes $L\ge 3.92 {\rm fm}$ for the quark mass range $m_\pi^2 = 0.273-0.736 {\rm GeV}^2$. We also find that the scattering length can be extracted with a smaller statistical error from the wave function than with a time correlation function used in previous studies.