ZEUS Results on the Measurement and Phenomenology of $F_2$ at Low x and Low Q^2

TL;DR

This work reports ZEUS measurements of the proton structure function F2 at low x and low Q^2, using shifted-vertex data to extend coverage and derive both dF2/dlnQ^2 and d ln F2/d ln(1/x). It combines non-perturbative GVMD/Regge phenomenology for the very low-Q^2 region with an NLO DGLAP QCD fit to extract the gluon distribution xg(x,Q^2) and the sea quark density, highlighting a rising quark sea at small x even as the gluon density becomes suppressed at the lowest Q^2. The analysis shows that, above Q^2 ≈ 0.9–1 GeV^2, perturbative QCD provides a coherent description of the data and that the transition from non-perturbative to perturbative dynamics is visible in both the F2 slopes and their x-dependence. The results yield a significantly improved determination of the gluon momentum density at small x and quantify the limitations of purely non-perturbative models in describing the transition region. Overall, the study reinforces the applicability of NLO QCD in the studied kinematic range and provides essential constraints on parton densities in the proton at low x.

Abstract

Measurements of the proton structure function $F_2$ for $0.6 < Q^2 < 17 {GeV}^2$ and $1.2 \times 10^{-5} < x <1.9 \times 10^{-3}$ from ZEUS 1995 shifted vertex data are presented. From ZEUS $F_2$ data the slopes $dF_2/d\ln Q^2$ at fixed $x$ and $d\ln F_2/d\ln(1/x)$ for $x < 0.01$ at fixed $Q^2$ are derived. For the latter E665 data are also used. The transition region in $Q^2$ is explored using the simplest non-perturbative models and NLO QCD. The data at very low $Q^2$ $\leq 0.65 {GeV}^2$ are described successfully by a combination of generalised vector meson dominance and Regge theory. From a NLO QCD fit to ZEUS data the gluon density in the proton is extracted in the range $3\times 10^{-5} < x < 0.7$. Data from NMC and BCDMS constrain the fit at large $x$. Assuming the NLO QCD description to be valid down to $Q^2\sim 1 {GeV}^2$, it is found that the $q\bar{q}$ sea distribution is still rising at small $x$ and the lowest $Q^2$ values whereas the gluon distribution is strongly suppressed.

Figures (12)

• Figure 1: The $(x,Q^2)$ plane showing the regions covered by the ZEUS data sets BPC95, ZEUS94 and SVX95 together with regions covered by the fixed target experiments E665, BCDMS and NMC.
• Figure 2: Distributions from the SVX95 analysis showing the comparison between data and simulation: (a) $\delta$ or $E-P_Z$ as defined in Sec. \ref{['sec:svxcuts']}; (b) the $Z$-position of the primary vertex; (c) the positron scattering angle $\theta_e$; (d) the energy, $E^\prime_e$, of the scattered positron; (e) $\log_{10}Q^2$; (f) $\log_{10}y$. In all cases the data are represented by filled circles, the simulation by the open histograms and the photoproduction background (calculated from the MC described in Sec. \ref{['sec:svxmc']}) by the filled triangles. Both MC calculations are normalised to the luminosity of the data.
• Figure 3: The ZEUS SVX95 $F_2$ data as a function of $x$ for different $Q^2$ bins together with previous ZEUS data (ZEUS 1994 ZF2, ZEUS BPC 1995 ZBPC), data from H1 SVX95 H1_svx95 and fixed target data (E665 E665F2). Error bars correspond to the statistical and systematic errors added in quadrature. The overall normalisation errors are not shown. The curves shown are (dotted) the Donnachie-Landshoff Regge model dltwo and (full) the ZEUS NLO QCD fit.
• Figure 4: The total $\gamma^*p$ cross-section, $\sigma_{\rm tot}^{\gamma^*p}$, as a function of $W^2$ at different $Q^2$ [GeV$^2$]. The data of this analysis (ZEUS SVX95) are shown together with previous ZEUS and H1 data (ZEUS94, ZEUS BPC95, H1 SVX95). Also the total photoproduction cross-sections from ZEUS and H1 and from fixed target experiments at lower $W$ are shown. Predictions from the DL dltwo and GRV94 grv94 models are indicated by the dotted and dashed curves, respectively.
• Figure 5: Upper plot. ZEUS BPC measurements of the total cross-section $\sigma_T + \epsilon \sigma_L$ in bins of $W$ as a function of $Q^2$ and the GVMD fit to the data. Lower plot.$\sigma_{\rm tot}^{\gamma p}$ as a function of $W^2$. The ZEUS BPC95 points are those from the GVMD extrapolation ($\sigma_{0}^{\gamma p}$). Also shown are direct measurements of the total photoproduction cross-section from H1, ZEUS and earlier experiments at low energies. The curves show Regge fits: the original DL fit dltwo to the low $W$ data (dotted); the Pomeron only fit to the BPC $\sigma_{0}^{\gamma p}$ data (dashed) and the Pomeron+Reggeon fit to the low $W$ and BPC $\sigma_{0}^{\gamma p}$ data (full).