Dispersive analysis of the $π^+ π^-$ production at the CMD3 experiment and the compatibility with muon pair production measurement by KLOE2 and the pion form factor by JLAB

Abstract

The spectral function of the charged pion form factor was extracted from two data sets. The difference between the two sets is based on the presence or absence of the recent measurement of the $π^+ π^-$ production by CMD-3 . Although the CMD-3 data are largely incompatible with other recent measurements, no excess was found when the data were used for analytical continuation to the spacelike region and compared to JLaB-$π$ experiment. Instead, both data sets provide a spacelike form factor that differs from the expected behavior known from perturbative analyses of quantum chromodynamics (QCD). A precise fit of the spectral functions is provided, either based on he bare form factor and the full $e^+e^-\rightarrow π^+π^-$ as well . Furthermore, the extracted pionic spectral functions were used to obtain the QED running charge. This was then compared with the KLOE-2 measurements.