Deep-Inelastic Inclusive ep Scattering at Low x and a Determination of alpha_s

TL;DR

This paper presents precise inclusive deep-inelastic ep scattering measurements at low Bjorken-$x$ with the H1 detector at HERA, extracting $F_2$ and $F_L$ and mapping the gluon distribution $xg(x,Q^2)$ via NLO DGLAP fits. By combining low-$x$ H1 data with high-$x$ BCDMS muon-proton data, it achieves a simultaneous determination of the strong coupling constant $oldsymbol{α_s(M_Z^2)}$ and the gluon density, reporting $α_s(M_Z^2)=0.1150^{+0.0017}_{-0.0005}~(exp)^{+0.0009}_{-0.0005}~(model)$ with a sizeable theoretical scale uncertainty of about $oldsymbol{±0.005}$. The results support DGLAP evolution at low $x$, provide 3–5% level constraints on $xg(x,Q^2)$ in the range $3 imes10^{-4} ime 0.1$ at $Q^2=20$ GeV$^2$, and offer a detailed treatment of systematic uncertainties, enabling reliable inclusion in global parton distribution analyses. The work demonstrates the feasibility and value of integrating low- and high-$x$ DIS data to pin down the proton’s parton structure and QCD coupling in the perturbative regime.

Abstract

A precise measurement of the inclusive deep-inelastic e^+p scattering cross section is reported in the kinematic range 1.5<= Q^2 <=150 GeV^2 and 3*10^(-5)<= x <=0.2. The data were recorded with the H1 detector at HERA in 1996 and 1997, and correspond to an integrated luminosity of 20 pb^(-1). The double differential cross section, from which the proton structure function F_2(x,Q^2) and the longitudinal structure function F_L(x,Q^2) are extracted, is measured with typically 1% statistical and 3% systematic uncertainties. The measured partial derivative (dF_2(x,Q^2)/dln Q^2)_x is observed to rise continuously towards small x for fixed Q^2. The cross section data are combined with published H1 measurements at high Q^2 for a next-to-leading order DGLAP QCD analysis.The H1 data determine the gluon momentum distribution in the range 3*10^(-4)<= x <=0.1 to within an experimental accuracy of about 3% for Q^2 =20 GeV^2. A fit of the H1 measurements and the mu p data of the BCDMS collaboration allows the strong coupling constant alpha_s and the gluon distribution to be simultaneously determined. A value of alpha _s(M_Z^2)=0.1150+-0.0017 (exp) +0.0009-0.0005 (model) is obtained in NLO, with an additional theoretical uncertainty of about +-0.005, mainly due to the uncertainty of the renormalisation scale.

Figures (24)

• Figure 1: Distributions of a) the energy, b) the polar angle of the scattered positron, and c) $y_h$ for the data sample $A$ taken in 1996/97 (solid points). The histograms show the simulation of DIS and the small photoproduction background (shaded), normalised to the luminosity of the data.
• Figure 2: Distributions of a) the energy, b) the polar angle of the scattered positron, and c) $y_h$ for the low $Q^2$ data sample $B$ taken in 1997. The histograms represent the simulation of DIS and the small photoproduction background (shaded), normalised to the luminosity of the data.
• Figure 3: Distributions illustrating the cross-section measurement at high $y$ ($0.46 < y < 0.82$) and low $Q^2$ ($2 < Q^2 < 5$ GeV$^2$) for events in the BST acceptance range. DIS event distributions of a) the polar angle a) and b) the SPACAL energy of the scattered positron candidate. c) SPACAL energy distribution for tagged photoproduction events fulfilling the DIS event selection criteria, apart from the $E-p_z$ requirement. Solid points: H1 data; shaded histograms: simulation of photoproduction events; open histograms: added distributions of simulated DIS and photoproduction events.
• Figure 4: Distributions illustrating the cross-section measurement at high $y$ ($0.46 < y < 0.89$) and large $Q^2$ ($10 < Q^2 < 35$ GeV$^2$). a) Polar angle and b) SPACAL energy distributions before subtraction of the photoproduction background using the charge measurement by the CJC. Solid points: data with positive charge assignment. Shaded histogram: data with negative charge assignment. Open histogram: sum of data with negative charge assignment and DIS event simulation, normalized to the data luminosity. c) Spectrum of energy measured in the electron tagger for DIS candidate events with a linked track of either positive charge (solid points) or of negative charge (histogram).
• Figure 5: Division of the $(x, Q^2)$ plane for the measurement of the inclusive DIS cross section. At low $y$ the bin size increases as the resolution deteriorates. At large $y$ the data are binned in intervals of $Q^2$ and $y$ in order to account for the $y$ dependent effect of $F_{L}\,$ on the cross-section and the variation of the systematics with $y$. The triangular regions inside the acceptance do not represent valid analysis bins.