Elastic and resonance structures of the nucleon from hadronic tensor in lattice QCD: implications for neutrino-nucleon scattering and hadron physics
We compute the Euclidean hadronic tensor from charge density operators and extract elastic and resonance structures by employing exponential fits to the four-point correlator, as well as a Bayesian reconstruction inverse algorithm to obtain the corresponding spectral density for qualitative comparison. 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. Beyond the elastic peak, we observe a structure located approximately $0.5-0.7$ GeV above the nucleon mass in the Bayesian reconstruction. The structure is interpreted as a mixture of the Roper resonance $(N(1440))$, and states with both positive and negative parities in this mass region, as well as multi-hadron states. Assuming the observed structure is dominated by $J^P=1/2^{\pm}$ states, we extract the transition electric form factor $G_E^{*}(Q^2)$ and the corresponding longitudinal helicity amplitude $S_{1/2}(Q^2)$, and compare them with those determined from the CLAS experimental data of nucleon-to-Roper transition. Although fitting to the four-point correlation function or using the inverse algorithm does not resolve individual resonances, it nevertheless enables the determination of total inclusive lepton-nucleon scattering cross sections in appropriate energy bins. This lattice QCD calculation presents the first major step toward studying the inclusive $N \to X$ contributions with the hadronic tensor formalism.