Measurement of the Proton Structure Function F_2 at Very Low Q^2 at HERA

TL;DR

This work extends a measurement of the proton structure function F2 to very low Q^2 and low x using e^+p data from the ZEUS detector at HERA, enabled by the addition of a Beam Pipe Tracker and improved hadronic-state modeling. The analysis employs two kinematic reconstruction methods to maximize acceptance at low y, and uses iterative bin-by-bin unfolding with MC reweighting to extract F2 with ~3–4% precision in seventy bins. The results show a slower rise of F2 with decreasing x at low Q^2, consistent with Regge theory and a relatively constant ln( F2 )/ln(1/x) slope, and reveal a stronger Q^2 dependence as Q^2 decreases, approaching a regime where F2 is nearly proportional to Q^2. Together with comparisons to Regge and QCD fits, these findings illuminate the transition between deep inelastic scattering and photoproduction and constrain non-perturbative QCD dynamics at the proton’s edge.

Abstract

A measurement of the proton structure function F_2(x,Q^2) is presented in the kinematic range 0.045 GeV^2 < Q^2 < 0.65 GeV^2 and 6*10^{-7} < x < 1*10^{-3}. The results were obtained using a data sample corresponding to an integrated luminosity of 3.9pb^-1 in e^+p reactions recorded with the ZEUS detector at HERA. Information from a silicon-strip tracking detector, installed in front of the small electromagnetic calorimeter used to measure the energy of the final-state positron at small scattering angles, together with an enhanced simulation of the hadronic final state, has permitted the extension of the kinematic range beyond that of previous measurements. The uncertainties in F_2 are typically less than 4%. At the low Q^2 values of the present measurement, the rise of F_2 at low x is slower than observed in HERA data at higher Q^2 and can be described by Regge theory with a constant logarithmic slope. The dependence of F_2 on Q^2 is stronger than at higher Q^2 values, approaching, at the lowest Q^2 values of this measurement, a region where F_2 becomes nearly proportional to Q^2.

Figures (4)

• Figure 1: Distributions of reconstructed quantities in data and MC simulation in the region defined by $0.06<y_\mathrm{JB}$ and $y_e<0.74$: a) energy, $E_e'$, of the positron measured in the BPC; b) scattering angle, $\theta_e$, of the positron measured in the BPT; c) $p_T^\mathrm{had}$; d) $\delta^\mathrm{had}$; e) $\eta_\mathrm{max}$; f) $\delta$. The points denote measured data, the light shaded histogram is the sum of non-diffractive (DJANGO) and diffractive (RAPGAP) MC, the dark shaded histogram and the dashed line represent the individual contributions from RAPGAP and DJANGO, respectively.
• Figure 2: a)--c) Distributions of reconstructed kinematic quantities in data and MC simulation in the region defined by $0.06<y_\mathrm{JB}$ and $y_e<0.74$: a) $Q^2_e$; b) $x_e$; c) $y_\mathrm{JB}$. The points denote measured data, the light shaded histogram is the sum of non-diffractive (DJANGO) and diffractive (RAPGAP) MC, the dark shaded histogram and the dashed line represent the individual contributions from RAPGAP and DJANGO, respectively. d) The bins in the kinematic plane ($Q^2$ vs. $x$). The bin boundaries in $y$ are 0.005, 0.01, 0.02, 0.04, 0.08, 0.16, 0.23, 0.30, 0.37, 0.45, 0.54, 0.64, 0.74, 0.84; those in $Q^2$ are 0.040, 0.055, 0.075, 0.10, 0.13, 0.17, 0.21, 0.27, 0.35, 0.45, 0.58, $0.74\,\mathrm{Ge V}^2$. The border at $y=0.08$, above which the electron method and below which the $e\Sigma$ method was used to reconstruct the event kinematics, is also indicated.
• Figure 3: Measured $F_2$ vs. $x$ in bins of $Q^2$. The data from the present measurement are indicated by filled circles. The solid line shows the ZEUS Regge fit. Open circles denote the results from a previous analysis, filled and open triangles denote other measurements from ZEUS and H1, respectively, and squares denote results from E665. These other measurements have been shifted to the $Q^2$ values of the present measurement using the ALLM97 parameterization. The inner error bars represent statistical errors, the outer ones the sum in quadrature of statistical and systematic errors; normalization uncertainties are not included.
• Figure 4: Measured $F_2$ vs. $Q^2$ in bins of $y$. The data from the present measurement are indicated by filled circles. Triangles, filled squares and open circles denote other measurements from ZEUS and H1. The data have been scaled by the numbers in parentheses for clarity of presentation. The solid line at low $Q^2$ shows the ZEUS Regge fit, the dashed line at higher $Q^2$ the ZEUS QCD fit. The other measurements have been shifted to the $y$ values of the present measurement using the ALLM97 parameterization.