Insights into the $\mathbf{\gamma^{(*)} + N(940)\frac{1}{2}^+ \to \Delta(1700)\frac{3}{2}^{-}}$ transition

Abstract

We report novel theoretical results for the $\gamma^{(*)} + N(940)\frac{1}{2}^+ \to \Delta(1700)\frac{3}{2}^{-}$ transition, utilizing a symmetry-preserving treatment of a vector$\,\otimes\,$vector contact interaction (SCI) within the Dyson-Schwinger equations (DSEs) formalism. In this approach, both nucleon, $N(940)\frac{1}{2}^+$, and $\Delta(1232)$'s parity partner, $\Delta(1700)\frac{3}{2}^{-}$, are treated as quark-diquark composites, with their internal structures governed accordingly by a tractable truncation of the Poincar\'e-covariant Faddeev equation. Nonpointlike quark+quark (diquark) correlations within baryons, which are deeply tied to the processes driving hadron mass generation, are inherently dynamic in the sense that they continually break apart and recombine guided by the Faddeev kernel. For the nucleon, isoscalar-scalar and isovector-axial-vector diquarks dominate, while the $\Delta(1700)\frac{3}{2}^{-}$ state only includes contributions from isovector-axial-vector diquarks because the SCI-interaction excludes isovector-vector diquarks. Once the Faddeev wave function of the baryons involved in the electromagnetic transition is normalized taking into account that its elastic electric form factor must be one at the on-shell photon point, we compute the transition form factors that describe the $\gamma^{(*)} + N(940)\frac{1}{2}^+ \to \Delta(1700)\frac{3}{2}^{-}$ reaction and, using algebraic relations, derive the corresponding helicity amplitudes. When comparing with experiment, our findings highlight a strong sensitivity of these observables to the internal structure of baryons, offering valuable insights. Although the SCI-framework has obvious limitations, its algebraic simplicity provides analytical predictions that serve as useful benchmarks for guiding more refined studies within QCD-based DSEs frameworks.