Elastic differential cross section of ep scattering fitted via the differential cross section of eq scatterings with cloud-covering effects Jingle B. Magallanes * and Jinky B. Bornales Department of Physics, Mindanao State University—Iligan Institute of Technology, Iligan City 9200, Philippines Ren´ e Luna-García Centro de Investigación en Computación, Instituto Polit´ ecnico Nacional, Mexico City 07738, Mexico (Received 26 February 2020; accepted 5 January 2021; published 24 March 2021) The angular-averaged differential cross section (dcs) of the elastic electron-proton (ep) scattering, covering Q 2 < 1.0 GeV 2 , was fitted via a combined modified eq-scatterings where q is a point particle. The modifications represent the cloud-covering effects to q. An energy-decaying ratio (edr) was derived by inspecting the generated dcs ep from the form factor data gathered at Mainz Microtron (A1-Collaboration) and Continuous Electron Beam Accelerator Facility (Jefferson Laboratory) when compared to the dcs eq with modified relativistic recoil factor. The diminishing cloud layer, edr, has a decay rate of -2.8 for the datasets under investigation. The formulated spin bare mass (SBM) and spin effective mass (SEM) fitting models use the bare and effective u and d-quark masses, respectively, while spin with other criteria bare mass (SCBM) and spin with other criteria effective mass (SCEM) integrate other considerations. Three comparison methods were used and all of them favor the models with other additional considerations. SCEM was the most favored model in general. DOI: 10.1103/PhysRevD.103.054032 I. INTRODUCTION Electron-nucleon scattering has been used to extensively measure the nucleon’ s electromagnetic form factors to study the charge and magnetization distributions [1]. For this, it is important to measure the scattering’ s differential cross section (dcs) since it is proportional to the probability for any given reaction or process to occur. The objective of this study is to demonstrate a fitting model to the angular- averaged dcs of the elastic electron-proton (ep) scattering, dcs ep , generated from different form factor datasets cover- ing the transfer momentum, Q< 1 GeV. Initially, it was thought that fitting the dcs ep through electron-point particle (eq) scatterings would be impossible since the proton is definitely not a point particle as characterized by the form factors. However, it could and would be possible by putting some cloud-covering effects on the point particle q. Inasmuch as, at low-energy quantum chromodynamics (QCD) where both perturbation theory and asymptotic freedom are not possible, there are signifi- cant collective interactions between the valence and sea quarks; and the effects are in the form of cloud coverings. The valence quarks get surrounded by some dense concentration of virtual quarks and gluons. When probed at low energy, this cloud is the high energy barrier to the core of the proton. For the range of transfer momenta in consideration, eq- scattering would have to be masked by modifications man- tling the particle. This includes the modifications in dcs eq ’ s recoil factor (fixed cloud layer) and the energy dependent ratio (diminishing cloud layer) between dcs ep and dcs eq . II. THE ELECTRON-PROTON (EP) SCATTERING The elastic ep-scattering is one of the fundamental interactions used in the understanding of the structure and the build-up of hadronic physics [2]. It is called Mott or no-structure (ns) scattering when it is the electron that is scattered by the point-particle nucleus. Electrons are very light; with high energies, they can penetrate further into the nucleus. However, they couple to the nuclear magnetic field because they have nonzero spin, an effect carried by the final term in the dcs given in Equation (1). This equation also contains the ratio between the final (E 0 ) and initial (E) energies of the electron called the relativistic recoil factor of the nucleon. The cross-section is denoted by σ ns for the Mott scattering: dσ dΩMott ¼ σ ns ¼ ðZ 1 Z 2 αÞ 2 4k 2 sin 4 ð θ 2 Þ  E 0 E  1 - v 2 sin 2  θ 2  ð1Þ * Also a researcher at Premier Research Institute of Science and Mathematics (PRISM). jingle.magallanes@g.msuiit.edu.ph; jbmagallanes@gmail.com PHYSICAL REVIEW D 103, 054032 (2021) 2470-0010=2021=103(5)=054032(9) 054032-1 © 2021 American Physical Society