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 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-$π$ 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 $μ^{-}μ^{+}$ production at $ ω/ρ$ 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.

Figures (3)

• Figure 1: Fits from the data Left: Spectral function of the QCD pion form factor $F$ as exctracted form data with CMD3 data. Right: Examples of selected cross sections as described in the text. The full cross section fit (solid) governed by CMD3 data is shown. The bare data-set with CMD3 data excluded and the associated fit of bare cross section (dashed) are shown as another example. Deviations are not shown for purpose of lines visibility.
• Figure 2: Pion electromagnetic form factors continued from the timelike to the spacelike region. Left panel: Pure QCD pion form factor $F(W)$ (dashed line) as obtained from world combined data without CMD3 data and the full form factors $F_F$ as extracted from the data that includes CMD3 ($F(W/CMD3)$) are shown. The border lines of the error band are shown for the later case. As it coincides with the later function $F(W)$, the upper bound is shown only from the $Q^2=0.5 GeV^2$ for the continued function $F_F$. Right panel: The form factors are compared to PT QCD asymptotics (dashed line) W (CMD3) label the function $F$ continued from the world data without and within the CMD3 data included.
• Figure 3: Square of the fine structure constant as affected by the presence or absence of CMD3 data for the $\sigma_{\pi\pi}$ cross section. The line labeled by F.J stands for HVP extractions made by polar2.