Measurement of the Proton Structure Function ${F_2}$ at low ${x}$ and low ${Q^2}$ at HERA

TL;DR

This work extends measurements of the proton structure function $F_2(x,Q^2)$ to very low $x$ and low $Q^2$ at HERA using two complementary ZEUS analyses: SVX with a shifted vertex and ISR with initial-state radiation. A detailed Monte Carlo framework and a QCD NLO fit are employed to correct for detector effects and extract $F_2$, yielding results that confirm the rise of $F_2$ with decreasing $x$ and show perturbative QCD describes the $Q^2$ evolution down to $Q^2=1.5\ \mathrm{GeV^2}$. The data favor GRV(94) parton densities and disfavor Regge-based soft-pomeron models at higher $Q^2$, while revealing a steeply rising virtual photon-proton cross section $\sigma_{tot}^{\gamma^* p}$ with energy $W$, bridging photoproduction and DIS. Overall, the study demonstrates the applicability of pQCD dynamics in the transition region between real and virtual photon-proton scattering and provides robust, high-precision constraints on the low-$x$ proton structure.

Abstract

We report on a measurement of the proton structure function $F_2$ in the range $3.5\times10^{-5}\leq x \leq 4\times10^{-3}$ and 1.5 ${\rm GeV^2} \leq Q^2 \leq15$ ${\rm GeV^2}$ at the $ep$ collider HERA operating at a centre-of-mass energy of $\sqrt{s} = 300$ ${\rm GeV}$. The rise of $F_2$ with decreasing $x$ observed in the previous HERA measurements persists in this lower $x$ and $Q^2$ range. The $Q^2$ evolution of $F_2$, even at the lowest $Q^2$ and $x$ measured, is consistent with perturbative QCD.

Figures (6)

• Figure 1: a) The correlation between the energy measured in the calorimeter and the energy in the SRTD in units of mips (mean energy deposited by one minimum ionising particle) for the kinematic peak (KP) events. b) The distribution of the corrected positron energy for the data, shown as the points, and the MC simulation, shown as the histogram, for KP events. The arrows in a) and b) indicate the positron beam energy. c) Measured fractional deviation between the mean corrected calorimeter energy and the predicted energy as a function of the corrected energy. d) The measured energy resolution of the calorimeter as a function of energy. The curve corresponds to 26% $\cdot\sqrt{E({\rm GeV})}$, the resolution used in the MC simulation. For c) and d), the data are results using QED Compton (squares), DIS elastic $\rho^{o}$ (triangles) and KP (dots) events. See text for details.
• Figure 2: The $x$-$Q^2$ distribution for events passing the selection criteria from the 1994 SVX analysis. The extension in the accepted region compared to the 1993 analyses is shown between the dashed line labeled "Z=0, 1993 cuts" and the solid line labeled "Z=67 cm, 1994 cuts (shifted vertex)". See text for more details.
• Figure 3: a) The reconstructed $Q_e^2$ of the SVX event sample. b) The reconstructed $x_e$ distribution of the SVX event sample. c) The spectrum of the scattered positron energy. d) The distribution of the positron scattering angles. In the figures the data (dots) are compared with the MC simulation (histograms). All events with a reconstructed $Q^2_e > 1$${\rm GeV^2}$ which pass the selection criteria described in Sect. \ref{['s:event_selection']} are shown. The background has not been subtracted from the data. The MC distributions have been reweighted using the final $F_2$ parameterisation from the QCD NLO fit to the ZEUS data and normalised to the luminosity of the data.
• Figure 4: a) The reconstructed $Q^2_e$ distribution of the ISR sample. b) The reconstructed $x_e$ distribution of the ISR sample. c) The spectrum of the photon energy measured in the LUMI photon calorimeter without the cut on the photon energy. d) The difference between the photon energy measured in the LUMI photon calorimeter and that determined from the CAL. In the figures the data (dots), background estimate (hatched histogram) and sum of the background and DIS MC (solid histogram) are shown. All events with a reconstructed $Q^2_e > 1$${\rm GeV^2}$ which pass the selection criteria described in Sect. 6.1 are shown. The MC distributions have been reweighted using the final $F_2$ parameterisation from the QCD NLO fit to the ZEUS data and normalised to the luminosity of the data.
• Figure 5: The measured $F_2$ from the SVX analysis (solid dots), the ISR analysis (solid triangles) and the 1993 results (open squares) compared with the expectations from GRV(94) (solid line) and Donnachie and Landshoff (DL) (dashed line). Overall normalisation uncertainties of 3% for the 1994 results and 3.5% for the 1993 points are not shown. The inner error bars represent the statistical errors while the outer error bars represent the systematic errors added in quadrature to the statistical errors.