We develop a “hybrid” model of the proton inelastic structure functions applicable in a wide region of invariant mass of produced states $W$ and invariant momentum transfer $Q$ including deep inelastic scattering (DIS), nucleon resonance production, as well as the region close to inelastic threshold. DIS is described in terms of the parton distributions together with higher-twist corrections from an available global QCD fit. The resonant part is addressed in terms of the Breit-Wiegner contributions from five states including the $\mathrm{\Delta }\left(1232\right)$ resonance, the $N\left(1440\right)$ Roper resonance, and three effective resonances describing the second and third resonance regions. The couplings of the nucleon resonances to photon are described in terms of helicity amplitudes. The nonresonant background is addressed in terms of DIS structure functions smoothly extrapolated to low-$W$ and low-$Q$ values with the proper behavior at the real photon limit $Q^2=0$ as well as near the inelastic threshold. We independently treat the transverse $F_T$ and the longitudinal $F_L$ structure function and fix the model parameters from a global analysis of the world hydrogen electroproduction and photoproduction cross-section data. We demonstrate a very good performance of the model by comparing our predictions with data on differential cross sections and the structure functions $F_2$ and $R=F_L/F_T$.

• Received 1 March 2021
• Revised 31 January 2022
• Accepted 4 April 2022

DOI:https://doi.org/10.1103/PhysRevC.105.045204

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Published by the American Physical Society