The $I=1$ pion-pion scattering amplitude and timelike pion form factor from $N_{\rm f} = 2+1$ lattice QCD

TL;DR

This study uses lattice QCD with 2+1 flavors to compute the I=1 pion-pion scattering amplitude and the timelike pion form factor, analyzing systematic errors across multiple lattice parameters.

Contribution

First lattice QCD calculation of the I=1 pion-pion scattering amplitude and timelike pion form factor with systematic error analysis using multiple ensembles.

Findings

Scattering amplitude fit by Breit-Wigner resonance lineshape.

Form factor better described by a thrice-subtracted dispersion relation.

Systematic errors assessed across lattice spacings and volumes.

Abstract

The elastic $I=1$ $p$-wave $\pi\pi$ scattering amplitude is calculated together with the isovector timelike pion form factor using lattice QCD with $N_{\rm f}=2+1$ dynamical quark flavors. Wilson clover ensembles generated by the Coordinated Lattice Simulations (CLS) initiative are employed at four lattice spacings down to $a = 0.05\,\mathrm{fm}$, several pion masses down to $m_{\pi} = 200\,\mathrm{MeV}$, and spatial volumes of extent $L = 3.1-5.5\,\mathrm{fm}$. The set of measurements on these ensembles, which is publicly available, enables an investigation of systematic errors due to the finite lattice spacing and spatial volume. The $\pi\pi$ scattering amplitude is fit on each ensemble by a Breit-Wigner resonance lineshape, while the form factor is described better by a thrice-subtracted dispersion relation than the Gounaris-Sakurai parametrization.