Unraveling Proton Strangeness: Determination of the Strangeness Sigma Term with Statistical Significance

This study delves into the contribution of the strange quark within the proton, which influences several fundamental proton properties. By establishing a robust relationship between the proton's quantum anomalous energy and the sigma term, we successfully extract the contribution of the strangeness sigma term in the proton, obtaining it from parameterized fits of the differential cross-section using exponential and dipole forms. The extracted sigma term values are estimated to be $455.62\pm64.60$ MeV (exponential fit) and $337.74\pm106.79$ MeV (dipole fit). Additionally, we present novel results for the proton trace anomalous energy, observing values of $0.13\pm0.02$ (exponential fit) and $0.15 \pm 0.03$ (dipole fit). Our analysis integrates the novel data from the $J/\psi-007$ and GlueX collaborations, to some extent providing an experimental phenomenological window into the non-zero strange quark content inside proton, with the statistical significances: $7.1\sigma$ (exponential fit) and $3.2\sigma$ (dipole fit), respectively. Furthermore, we discussed the possibility of scheme-independence in the extraction results and examine the uniformity of sigma terms obtained from the datasets provided by the two collaborations. Our analysis may reveals compatibility between the extracted results of the respective experiments.