Using wavelet analysis to compare the QCD prediction and experimental data on $R_{e^+e^-}$ and to determine parameters of the charmonium states above the $D\bar D$ threshold

The first part of our analysis uses the wavelet method to compare the Quantum Chromodynamic (QCD) prediction for the ratio of hadronic to muon cross sections in electron-positron collisions, $R$, with experimental data for $R$ over a center of mass energy range up to about 7 GeV. A direct comparison of the raw experimental data and the QCD prediction is difficult because the data have a wide range of structures and large statistical errors and the QCD description contains sharp quark-antiquark thresholds. However, a meaningful comparison can be made if a type of "smearing" procedure is used to smooth out rapid variations in both the theoretical and experimental values of $R$. A wavelet analysis (WA) can be used to achieve this smearing effect. The second part of the analysis we concentrate on the 3.0 - 6.0 GeV energy region containing the relatively wide charmonium resonances $\psi(1^-)$. We use the wavelet methodology. Both analyses are examples of the usefulness of WA in extracting information in a model independent way from high energy physics data.