Extraction of Proton Trace Anomaly Energy from Near-Threshold $\phi$ and $J/\psi$ photo-productions

Abstract

The trace anomalous energy contribution to the proton mass is a very important topic in non-perturbative QCD and hadron physics. In experiments, it is under the hot discussions on how to measure the trace anomalous energy.The QCD interpretation of proton trace anomaly is still not clear.To connect the theory with the experiment,we extract the trace anomaly by analyzing the near-threshold photo-production data of $\phi$ and J/$\psi$ vector mesons. Based on the vector-meson-dominance model and QCD Van der Waals representation, we find that the percentage of trace anomaly in the proton mass ranges from $16\%$ to $24\%$, which is of similar order of magnitude as the 23$\%$ given by Lattice QCD. We also provide the approximate magnitudes of the systematic uncertainties of the extracted results from the model assumptions as well as the data fitting procedures. We give relative statistical uncertainties of 17.2$\%$, 17.7$\%$, 3.6$\%$, and 8.2$\%$, total relative systematic uncertainties of 21.4$\%$, 54.2$\%$, 37.2$\%$, and 25.7$\%$, for the analyses of the GlueX, LEPS, CLAS, and SAPHIR data, respectively. We argue that the near-threshold $\Upsilon$ photo-production experiments are more beneficial for the measurement of trace anomaly in proton mass in the future.