Insights into the γ(*)+N(940)12+→Δ(1700)32− transition

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Abstract
We report novel theoretical results for the γ ( * ) + N ( 940 ) 1 2 + → Δ ( 1700 ) 3 2 − transition, utilizing a symmetry-preserving treatment of a vector ⊗ vector contact interaction (SCI) within the Dyson-Schwinger equation formalism. In this approach, both nucleon N ( 940 ) 1 2 + and Δ ( 1232 ) ’s parity partner Δ ( 1700 ) 3 2 − are treated as quark-diquark composites, with their internal structures governed accordingly by a tractable truncation of the Poincaré-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 Δ ( 1700 ) 3 2 − state includes contributions only from isovector-axial-vector diquarks, because the SCI 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 γ ( * ) + N ( 940 ) 1 2 + → Δ ( 1700 ) 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 Dyson-Schwinger equation frameworks.
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Funding Information
  • Universidad Michoacana de San Nicolás de Hidalgo (4.10)
  • Secretaría de Ciencia, Humanidades, Tecnología e Innovación (CBF2023-2024-3544)
  • Ministerio de Ciencia e Innovación (PID2022-140440NB-C22)
  • Junta de Andalucía (PAIDI FQM-370, PCI+D+I)
  • Universidad Pablo de Olavide

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