Measurement of the Proton Structure Function F_2 and σ_{tot}^{γ^* p} at Low Q^2 and Very Low x at HERA

TL;DR

This work expands the measurement of the proton structure function F2 and the total virtual photon–proton cross section to very low Q2 and x using the ZEUS BPC, covering 0.11 ≤ Q2 ≤ 0.65 GeV^2 and 2×10^-6 ≤ x ≤ 6×10^-5. Through a dedicated detector setup, detailed calibrations, and an iterative analysis that integrates detailed simulations and radiative corrections, the study quantifies F2 and σ_tot^{γ*p} and compares them to multiple theoretical models. The results reveal a gradual rise of F2 with decreasing x in this regime, with GRV over- or under-estimations depending on Q2, and indicate that pQCD-inspired dynamics contribute meaningfully starting around Q2 ≈ 1 GeV^2. These findings help delineate the transition between Regge-dominated hadronic physics and perturbative QCD in the proton structure at the extreme low-Q2, low-x frontier.

Abstract

A small electromagnetic sampling calorimeter, installed in the ZEUS experiment in 1995, significantly enhanced the acceptance for very low x and low Q^2 inelastic neutral current scattering, e^{+}p \to e^{+}X, at HERA. A measurement of the proton structure function F_2 and the total virtual photon-proton (γ^*p) cross-section is presented for 0.11 \le Q^{2} \le 0.65 GeV^2 and 2 \times 10^{-6} \le x \le 6 \times 10^{-5}, corresponding to a range in the γ^{*}p c.m. energy of 100 \le W \le 230 GeV. Comparisons with various models are also presented.

Figures (4)

• Figure 1: (a) Schematic layout of the BPC and the beampipe. The BPC is located at Z=-2937 mm, and the inner edge is at X=44 mm. (b) The fractional deviation from the mean energy for KP events as a function of the scattered positron X impact position at the BPC. (c) A comparison between MC and data of the ratio of the measured positron energy in the BPC, E$_{BPC}$, to the calculated positron energy, E$_{calc}$ for elastic $\rho^0$ events. (d) The FLT trigger efficiency as a function of BPC energy.
• Figure 2: Comparisons between simulated and data distributions for the variables: (a) scattered positron energy; (b) $Q^2$; (c) $x$; and (d) $\delta$ . Data are shown as solid circles, photoproduction simulation as shaded regions, and the sum of the signal and photoproduction simulations as solid lines. In figure (d) the signal simulation is shown as a dashed line and the measured background as triangular points. The structure function in the simulation has been reweighted to that measured in the present analysis.
• Figure 3: $F_2 (x, Q^2)$ as a function of $x$ for different Q$^2$ bins. The data from this analysis, ZEUS BPC 95, are shown as solid dots, with E665, H1 and previous ZEUS points shown as open squares, open circles and solid triangles, respectively. New points from H1h1-svtx at low $Q^2$ are also shown as solid inverted triangles (the point at $Q^2=0.35$ GeV$^2$ is displayed in the 0.4 GeV$^2$ panel; additional points at 2.5 and 3.5 GeV$^2$ not shown.) Curves from the models of DL, CKMT, BK, ABY and GRV are overlaid.
• Figure 4: The total virtual photon-proton cross-section $\sigma_{tot}^{\gamma^*p}$ as a function of $W^2$. The data from this analysis (ZEUS BPC 95), previous 1994 ZEUS analyses, H1, and E665 are shown. The total cross-section for real photon-proton scattering from ZEUS, H1 and photoproduction experiments at low $W$ are also shown. The predictions of DL and GRV (at the ZEUS $Q^2$ values) are indicated by the dotted and dashed curves respectively.