Mass radius and mechanical properties of the proton via strange $\phi$ meson photoproduction

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In this work, the cross sections of $\phi$ photoproduction are systematically investigated with the two gluon exchange model and the pomeron model.

• The results obtained show that the theoretical values of the two models agree well with the experimental data.
• Since the mass radius and mechanical properties of the proton are encoded in the scalar gravitational form factor of the momentum energy tensor, based on the differential cross sections of $\phi$ photoproduction at near-threshold predicted by the two gluon exchange model, the average mass radius of the proton is derived as $\sqrt{\left\langle r^{2}\right\rangle_\mathrm{m} }=0.78 \pm 0.06$ fm.
• As a comparison, we directly extract the proton mass radius from the experimental data of $\phi$ photoproduction to obtain an average value of $0.80\pm0.05$ fm, which is very close to the result given by the two gluon exchange model.