Empirical Fit to Precision Inclusive Electron-Proton Cross Sections in the Resonance Region

TL;DR

This work presents an empirical, wide-kinematic-range fit to inclusive electron-proton cross sections in the resonance region (0 ≤ Q^2 < 8 GeV^2, 1.1 < W < 3.1 GeV) constrained by precise L/T-separated Hall C data, un-separated Hall C data up to Q^2 ≈ 7.5 GeV^2, and photoproduction data at Q^2 = 0. The model decomposes σ_T and σ_L into resonant contributions described by threshold-dependent Breit-Wigner forms with Q^2-dependent transition amplitudes and a smoothly varying non-resonant background, ensuring correct behavior in both the photoproduction and DIS limits. Seven dominant resonances (plus a broad ~1.9 GeV state) are included, with 75 fit parameters that enable an accurate description (≈3% level) of the available cross-section data; the fit provides a practical tool for radiative corrections, spin-structure extraction, and neutrino-nucleon modeling, and the authors supply Fortran code for implementation.

Abstract

An empirical fit is described to measurements of inclusive inelastic electron-proton cross sections in the kinematic range of four-momentum transfer $0 \le Q^2<8$ GeV$^2$ and final state invariant mass $1.1<W<3.1$ GeV. The fit is constrained by the recent high precision longitudinal and transverse (L/T) separated cross section measurements from Jefferson Lab Hall C, un-separated Hall C measurements up to $Q^2$ $\approx 7.5$ ${\rm GeV}^2$, and photoproduction data at $Q^2 = 0$. Compared to previous fits, the present fit covers a wider kinematic range, fits both transverse and longitudinal cross sections, and features smooth transitions to the photoproduction data at $Q^2=0$ and DIS data at high $Q^2$ and $W$.

Figures (5)

• Figure 1: (Color online) Comparison of the fit results (solid lines) to the JLab E94-110 resonance region data e94110liang (solid triangles) versus $W^2$, for several representative kinematic settings. Beam energies $E$ are in GeV, and electron scattering angles $\theta$ are in degrees.
• Figure 2: (Color online) Comparison of fit (solid line) to the photoproduction data used in the fit (see Table \ref{['datasets']}).
• Figure 3: (Color online) Ratio of all fitted cross section data to the fit results at the eight $Q^2$ ranges indicated. The units of $Q^2$are GeV$^2$.
• Figure 4: (Color online) Ratio of selected cross section data to the fit at the seven $Q^2$ ranges indicated ($Q^2$ in units of GeV$^2$). The data for $\epsilon$$<$ 0.5 are shown as the solid triangles, while the data with $\epsilon$$>$ 0.75 are shown as the open circles.
• Figure 5: Frequency distribution for the percent differences of the data to the fit for $Q^2 > 0$.