Observing short-range correlations in nuclei through $\rho^0$ photo-production

Short-range correlations (SRCs) are a universal feature of nuclear structure. A wide range of measurements, primarily using electron scattering, have revealed SRC properties, such as their abundance in different nuclei, as well as the strong preference for proton-neutron pairing over proton-proton or neutron-neutron pairing. Despite the inherent complexity of many-body systems, a number of the salient features of electron scattering measurements are described by a simple, factorized theory called Generalized Contact Formalism. A key element of this theory, the factorization of the interaction with a hard probe, has yet to be tested. An experiment conducted at Jefferson Lab in 2021 collected data from scattering a tagged photon beam, with an energy up to 10 GeV, from several nuclear targets, measuring final state particles in the large-acceptance GlueX spectrometer. In this paper, we propose a test of probe factorization by measuring cross section ratios sensitive to proton-proton pair prevalence and relative SRC abundances in $^4$He and $^{12}$C. We present GCF predictions of the observables and make projections of the expected precision the experiment can achieve.