A Measurement and QCD Analysis of the Proton Structure Function $F_2(x,Q^2)$ at HERA

TL;DR

This study delivers a high-precision measurement of the proton structure function $F_2(x,Q^2)$ over a wide kinematic range at HERA using 1994 H1 data, supported by enhanced statistics and novel low-$Q^2$ access via shifted vertices and radiative events. By combining electron and hadronic kinematic reconstructions and applying rigorous radiative corrections, the authors demonstrate a strong rise of $F_2$ at low $x$ that is well described by a Next-to-Leading-Order QCD fit and extract a rising gluon density $xg(x,Q^2)$. The work also tests perturbative QCD predictions through double asymptotic scaling and compares low-$Q^2$ data with Regge and PDF-based models, finding that GRV/MRSA' PDFs capture the behavior while Regge models tend to undershoot. Overall, the analysis provides a precise mapping of parton densities at low $x$, reinforcing the role of gluons in driving DIS at high energy and informing global PDF determinations.

Abstract

A new measurement of the proton structure function $F_2(x,Q^2)$ is reported for momentum transfers squared $Q^2$ between 1.5 GeV$^2$ and 5000 GeV$^2$ and for Bjorken $x$ between $3\cdot 10^{-5}$ and 0.32 using data collected by the HERA experiment H1 in 1994. The data represent an increase in statistics by a factor of ten with respect to the analysis of the 1993 data. Substantial extension of the kinematic range towards low $Q^2$ and $x$ has been achieved using dedicated data samples and events with initial state photon radiation. The structure function is found to increase significantly with decreasing $x$, even in the lowest accessible $Q^2$ region. The data are well described by a Next to Leading Order QCD fit and the gluon density is extracted.

Figures (12)

• Figure 1: Distribution of the event sample in the $(x,Q^2)$ plane. The 4 visible regions (A,B,C,D) correspond to A) events recorded during a period in which the interaction region was shifted with respect to the nominal position allowing access to larger $\theta_e$; B) events from the nominal vertex position taken in a period in which the innermost BEMC stacks of triangular shape were included in the trigger ("opened triangles", see text) or C) not included; D) high $Q^2$ events with the scattered electron detected in the LAr calorimeter.
• Figure 2: Shifted vertex data: experimental and Monte Carlo distributions of a) the polar angle of the scattered electron and b) the energy of the scattered electron in photoproduction background events detected in the electron tagger.
• Figure 3: Nominal vertex data with the scattered electron in the BEMC ($Q^2 \leq$ 120 GeV$^2$): experimental and Monte Carlo distributions a) of the scattered electron energy and b) of the fraction of $y_h$ contributed by the tracks, the LAr calorimeter and the BEMC.
• Figure 4: High $Q^2$ data: experimental and Monte Carlo distributions a) of the energy of the scattered electron detected in the LAr calorimeter and b) of the ratio ${y_{\Sigma}}/{y_e}$, for $y_e \ge$ 0.05.
• Figure 5: Radiative events: experimental and Monte Carlo distributions of $\Delta$ (eq. 6) with a) the energy detected in the electron tagger ($E_{etag}$) bigger than 2 GeV; b) with $E_{etag} <$ 2 GeV and c) distribution of the photon energy detected in the photon tagger. The analysis cut in b) indicates the region of $\Delta >$ 0.5 excluded from the analysis. The full solid line in b) and c) represents the sum of all three contributions in the Monte Carlo: DIS initial state radiation events (ISR MC), DIS events with a BH overlap (DIS + BH) and photoproduction events with a BH overlap ($\gamma p$ + BH).