Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics

Understanding the transitions of nucleons into various resonance structures through electromagnetic interactions plays a pivotal role in advancing our comprehension of the strong interactions within the domain of quark confinement. Furthermore, gaining precise insights into the elastic and resonance structures of nucleons is indispensable for deciphering the physics from neutrino-nucleus scattering cross sections experimental data, which remain theoretically challenging, even in the context of neutrino-nucleon interactions whose profound understanding is imperative for the neutrino oscillation experiments. One promising avenue involves the direct evaluation of the lepton-nucleon scattering cross sections across quasi-elastic, resonance, shallow-inelastic, and deep inelastic regions, which can be achieved through the hadronic tensor formalism in lattice QCD. In this work, we present the determination of the nucleon's Sachs electric form factor using the hadronic tensor formalism and verify that it is consistent with that from the conventional three-point function calculation. We additionally obtain the transition form factor from the nucleon to its first radial excited state within a finite volume. Consequently, we identify the latter with the nucleon-to-Roper transition form factor $G_E^*(Q^2)$, determine the corresponding longitudinal helicity amplitude $S_{1/2}(Q^2)$ and compare our findings with experimental measurements, for the first time using the hadronic tensor formalism. The limitations and systematic improvements of the approach are also discussed.