Lattice QCD calculation of $\pi\pi$ scattering length

TL;DR

This study uses lattice QCD with improved staggered fermions to calculate the pion-pion scattering lengths for different isospin channels, extrapolating to physical pion mass and including disconnected diagrams, providing results close to experimental data.

Contribution

First lattice QCD calculation of $$ pion-pion scattering length including disconnected diagrams, using chiral perturbation theory for extrapolation.

Findings

Calculated scattering lengths for I=0 and I=2 channels.

Extrapolated results are close to experimental values.

Included disconnected contributions in the I=0 channel analysis.

Abstract

We study s-wave pion-pion ($\pi\pi$) scattering length in lattice QCD for pion masses ranging from 330 MeV to 466 MeV. In the "Asqtad" improved staggered fermion formulation, we calculate the $\pi\pi$ four-point functions for isospin I=0 and 2 channels, and use chiral perturbation theory at next-to-leading order to extrapolate our simulation results. Extrapolating to the physical pion mass gives the scattering lengths as $m_\pi a_0^{I=2} = -0.0416(2)$ and $m_\pi a_0^{I=0} = 0.186(2)$ for isospin I=2 and 0 channels, respectively. Our lattice simulation for $\pi\pi$ scattering length in the I=0 channel is an exploratory study, where we include the disconnected contribution, and our preliminary result is near to its experimental value. These simulations are performed with MILC 2+1 flavor gauge configurations at lattice spacing $a \approx 0.15$ fm.