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

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.