Extracting the Mass Radius of 4^4He from ϕ\phi-Meson Photoproduction Data

We extract the mass radius of $^4$He, a light nucleus, from near-threshold $\phi$-meson photoproduction data of the LEPS Collaboration. We evaluate the gravitational form factor using several function forms, including the monopole, dipole, Gauss, and hard-sphere forms. Our analysis reveals that the Gauss and hard-sphere form factors more accurately describe the differential cross sections in the small-$|t|$ range near the production threshold. The extracted mass radii based on the Gauss and hard-sphere form factors are $1.70\pm0.14$ fm and $1.37\pm0.08$ fm, respectively, with the combined average being smaller than the charge radius of $^4$He. More precise and wider $|t|$-coverage measurements of the coherent photoproductions of vector mesons off the nuclear target are necessary to distinguish between different models for describing the gravitational form factor and provide further insights into the mass radius of the nucleus.Comment: 6 pages, 3 figure

The Origin of Proton Mass from J/Ψ{\rm \Psi} Photo-production Data

The trace of the stress tensor characterizes the transformation of a theory under rescaling. In quantum chromodynamics (QCD), this trace contains contributions from the bare masses of the quarks and also from a purely quantum effect, called the QCD trace anomaly. It affects all masses in the theory. We present an estimation of the QCD trace anomaly from the near-threshold J/${\rm \Psi}$ photo-production data of the GlueX experiment, at JLab. We apply a vector meson dominance model to describe the photo-production of J/${\rm \Psi}$ and a running strong coupling which includes the nonperturbative effects in the low $\mu^2$ region. Despite the large uncertainty, we find that the experimental data favors a small value of the trace anomaly parameter $b=0.07\pm 0.17$. We report the resulting proton mass decompositions at $\mu^2=0.41$ GeV$^2$ and $\mu^2=4$ GeV$^2$.Comment: 6 pages, 4 figure

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 $\phi$ and J/$\psi$ 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 $M_a=0.25\exp(-A/\mu^2)M_N$ with $A=0.101\pm0.029$ GeV$^2$. The empirical result is consistent with the LQCD calculation at $\mu^2=4$ GeV$^2$. Finally, the corresponding evolution equation for trace anomaly part is given by our calculation.Comment: 6 pages, 4 figures, Corrected spelling mistake