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

TL;DR

This study analyzes the charged pion form factor using dispersive methods with data from CMD3, KLOE2, and JLAB, revealing inconsistencies among datasets but providing insights into the pion spectral function and the QED running charge.

Contribution

It introduces a dispersive analysis incorporating recent CMD3 data and compares it with other measurements, highlighting dataset incompatibilities and their impact on the pion form factor and QED running charge.

Findings

CMD3 data largely incompatible with other measurements

No excess found when CMD3 data are used for analytical continuation

Evidence of incompatibility between CMD3 and JLAB spacelike pion form factors

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 $\pi^+ \pi^-$ production by CMD3. Although the CMD3 data are largely incompatible with other recent measurements, it was found to provide no excess when used for analytical continuation to spacelike region. Consequently, there is evidence for incompatibility when it is compared to the spacelike pion form factor obtained by the JLaB-$\pi$ experiment. Furthermore, the extracted pionic spectral function was used to obtain the QED running charge. It was then compared with the KLOE2 experiment for radiative return $\mu^{-}\mu^{+}$ production at $ \omega/\rho $ meson energy. For this purpose the hadronic vacuum polarization has been extracted from exclusive hadronic productions in $e^+e^-$ collisions via the dispersion relation using combined data with and without the CMD3 data set included in.