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

TL;DR

This study measures the proton structure function $F_2(x,Q^2)$ and the virtual photon–proton cross section in deep inelastic scattering at low $x$ and low $Q^2$ using 1995 H1 data, extending the kinematic reach by upgrading the backward detector. By employing both the electron and Sigma kinematic reconstruction methods and extensive Monte Carlo modeling, the analysis reveals a pronounced rise of $F_2$ with decreasing $x$ at higher $Q^2$, which softens at the lowest $Q^2$ values, signaling a transition toward photoproduction behavior. A suite of Regge-inspired and pQCD-based parameterizations is compared to the data; while several capture qualitative trends, none fully describes the full $(x,Q^2)$ plane, highlighting the need for refined low-$Q^2$ dynamics and unified low-$Q^2$ phenomenology. Overall, the results provide crucial constraints on the transition between DIS and photoproduction and inform modeling of parton densities in the low-$Q^2$ regime.

Abstract

The results of a measurement of the proton structure function F_2(x,Q^2)and the virtual photon-proton cross section are reported for momentum transfers squared Q^2 between 0.35 GeV^2 and 3.5 GeV^2 and for Bjorken-x values down to 6 10^{-6} using data collected by the HERA experiment H1 in 1995. The data represent an increase in kinematic reach to lower x and Q^2 values of about a factor of 5 compared to previous H1 measurements. Including measurements from fixed target experiments the rise of F_2 with decreasing x is found to be less steep for the lowest Q^2 values measured. Phenomenological models at low Q^2 are compared with the data.

Figures (10)

• Figure 1: Experimental (points) and Monte Carlo (solid lines) distributions of a) the energy in the electron tagger, and b) the energy of the (fake) electron candidate in the SPACAL, for tagged photoproduction events.
• Figure 2: Experimental (points) and Monte Carlo (solid histograms) distributions of a) the energy of the scattered electron and b) the polar angle of the scattered electron for DIS events. The Monte Carlo curves are the sum of DIS and photoproduction events and the photoproduction events alone.
• Figure 3: Experimental (points) and Monte Carlo (solid histograms) distributions of $\Sigma (E_i-P_{z,i})$ measured in the calorimeter for a) all DIS event candidates and b) DIS event candidates with $y_e> 0.55$. The Monte Carlo curves are the sum of DIS and photoproduction events and the photoproduction events alone.
• Figure 4: Experimental (points) and Monte Carlo (solid histograms) distributions for $y_{\Sigma} > 0.05$ of the ratios of a) the $y$ values measured with the $\Sigma$ and E method $y_{\Sigma}/y_{e}$, and b) the transverse momentum of the hadronic system and the electron $p_{t,h}/p_{t,e}$. The Monte Carlo curves are the sum of DIS and photoproduction events and the photoproduction events alone.
• Figure 5: Comparison of the proton structure function $F_2(x,Q^2)$ as a function of $x$ at various values of $Q^2$ (in GeV$^2$) measured with the E method (full points) and with the $\Sigma$ method (open points). The errors represent the statistical and systematic errors added in quadrature. A global normalization uncertainty of 3% is not included.