Timelike meson form-factors beyond the elastic region from lattice QCD

TL;DR

This study uses lattice QCD to compute timelike meson form-factors, revealing the dominance of the rho resonance and providing insights into the resonance decay constant through analytic continuation.

Contribution

It introduces a lattice QCD approach to calculate timelike form-factors beyond the elastic region, including finite-volume corrections and resonance analysis.

Findings

Timelike form-factors are dominated by the rho resonance.

Decay constant of the rho resonance is extracted.

Spacelike form-factor is determined and modeled with dispersive analysis.

Abstract

We present a calculation of the vector-isovector timelike form-factors of the pion and the kaon using lattice quantum chromodynamics. We calculate two-point correlation functions with $m_\pi \sim 280$ MeV, extracting both the finite-volume spectrum and matrix elements for these states created from the vacuum by a vector current. After determining the coupled-channel $\pi\pi, K\overline{K}$ scattering amplitudes, we perform the necessary correction for the significant finite-volume effects present in the current matrix elements, leading to the timelike form-factors. We find these to be dominated by the presence of the $\rho$ resonance, and we extract its decay constant by an analytic continuation of the amplitudes to the resonance pole. In addition, the spacelike pion form-factor is determined on the same lattice configurations, and a dispersive parameterization is used to simultaneously describe the spacelike and elastic timelike regions.