Timelike meson form factors beyond the elastic region from lattice QCD

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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>m</a:mi><a:mi>π</a:mi></a:msub><a:mo>∼</a:mo><a:mn>280</a:mn><a:mtext> </a:mtext><a:mtext> </a:mtext><a:mi>MeV</a:mi></a:math>, 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 <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>π</c:mi><c:mi>π</c:mi><c:mo>,</c:mo><c:mi>K</c:mi><c:mover accent="true"><c:mi>K</c:mi><c:mo stretchy="false">¯</c:mo></c:mover></c:math> 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 <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>ρ</g:mi></g:math> 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 parametrization is used to simultaneously describe the spacelike and elastic timelike regions. Published by the American Physical Society 2024