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

TL;DR

This paper employs wavelet analysis to compare QCD predictions with experimental data on $R_{e^+e^-}$, smoothing out data structures to extract meaningful insights and determine parameters of charmonium states above the $Dar D$ threshold.

Contribution

It introduces a wavelet-based method for model-independent comparison of theoretical predictions and experimental data in high energy physics.

Findings

Wavelet analysis effectively smooths data for comparison.

The method helps identify charmonium resonance parameters.

Wavelet approach is useful for extracting information from complex data.

Abstract

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.