Symmetry- Preserving Contact Interaction Approaches: An Overview of Meson and Diquark Form Factors

We present an updated overview of the symmetry-preserving contact interaction model in hadronic physics, which was developed a little over a decade ago to describe the mass spectrum and internal structure of mesons and diquarks composed of light and heavy quarks. Over the years, the contact interaction model has evolved into a framework capable of treating both ground and excited states, providing a simple yet consistent approach to nonperturbative QCD. In this review, we examine the mass spectrum and elastic form factors of forty mesons with different spins and parities, together with their corresponding diquark partners. Importantly, we update the comparison of contact interaction predictions using recent results from the literature, offering a fresh perspective on the model’s performance, strengths, and limitations. The analysis presented here refines previous conclusions and supports the contact interaction model as a practical tool for hadron structure studies, with potential applications to baryons and multiquark states. We also present comparisons with other theoretical models and approaches, including lattice quantum chromodynamics, and comment on future prospects in view of ongoing and planned experimental programs regarding hadron structure. In particular, forthcoming measurements at FAIR together with future studies at Jefferson Lab and the Electron Ion Collider are expected to provide key insights into hadron structure, with FAIR offering indirect constraints via hadron spectroscopy, hadronic interactions, and in-medium properties; high-precision data on meson structure and form factors from Jefferson Lab and the Electron Ion Collider will provide valuable benchmarks with which to confront predictions based on the contact interaction model.