Trace Anomaly of Proton Mass with Vector Meson Near-Thresholds Photoproduction Data


Trace anomalous contribution to proton mass is particularly important in understanding the QCD mass structure. The value and the scale-dependent of the trace anomalous energy of the strong interaction are still not clear in combination of theories and experiments. In this paper, we explore the near-threshold photoproduction data of ϕ\phi and J/ψ\psi to study the quantum anomalous energy in QCD and its scale-dependence. The vector-meson-dominance model and the van der Waals interaction between the vector meson and the proton are used. We find that the quantum anomalous energy to the proton mass is scale-dependent and it can be described as Ma=0.25exp(A/μ2)MNM_a=0.25\exp(-A/\mu^2)M_N with A=0.101±0.029A=0.101\pm0.029 GeV2^2. The empirical result is consistent with the LQCD calculation at μ2=4\mu^2=4 GeV2^2. Finally, the corresponding evolution equation for trace anomaly part is given by our calculation.Comment: 6 pages, 4 figures, Corrected spelling mistake

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