$I=2$ $\pi\pi$ $s$-wave scattering length from lattice QCD

TL;DR

This study uses lattice QCD to accurately measure the $I=2$ $bb$ scattering length and related parameters, providing results consistent with experimental data and theoretical predictions, and exploring systematic uncertainties with multiple lattice ensembles.

Contribution

First lattice QCD calculation of $I=2$ $bb$ scattering parameters including systematic uncertainties from higher-order chiral perturbation theory.

Findings

Consistent with Roy equation and experimental data.

Provides scattering length, effective range, and shape parameter at physical point.

Analyzed systematic uncertainties using NNLO predictions.

Abstract

The $I=2$ $\pi\pi$ elastic $s$-wave scattering phase shift is measured by lattice QCD with $N_f=3$ flavors of the Asqtad-improved staggered fermions. The lattice-calculated energy-eigenvalues of $\pi\pi$ systems at one center of mass frame and some moving frames using the moving wall source technique are utilized to secure phase shifts by L\"uscher's formula. Our computations are fine enough to obtain threshold parameters: scattering length $a$, effective range $r$, and shape parameter $P$, which can be extrapolated at the physical point by NLO in chiral perturbation theory, and our relevant NNLO predictions from expanding NPLQCD's works are novelly considered as the systematic uncertainties. Our outcomes are consistent with Roy equation determinations, newer experimental data, and lattice estimations. Numerical computations are performed with a coarse ($a\approx0.12$~fm, $L^3 T = 32^3 64$), two fine ($a\approx0.09$~fm, $L^3 T = 40^3 96$) and a superfine ($a\approx0.06$~fm, $L^3 T = 48^3 144$) lattice ensembles at four pion masses of $m_\pi\sim247~{\rm MeV}$, $249~{\rm MeV}$, $275~{\rm MeV}$, and $384~{\rm MeV}$, respectively.