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

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 $N_{\mathrm{f}}=2+1$ 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.

Comments: 32 pages, 12 figures. Typos fixed, small changes to the text, Refs. updated/added, agrees with published version