Deep-inelastic inclusive ep scattering at low x and a determination of $$\alpha_s$$

Abstract. A precise measurement of the inclusive deep-inelastic $$e^+ p$$ scattering cross section is reported in the kinematic range \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$1.5 \le Q^2 \le 150$\end{document} GeV$$^2$$ and $$ 3 \cdot 10^{-5} \le x \le 0.2$$. 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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}F_2(x,Q^2)\end{document} and the longitudinal structure function $$F_L(x,Q^2)$$ are extracted, is measured with typically 1% statistical and 3% systematic uncertainties. The measured derivative $$(\partial F_2(x,Q^2) / \partial \ln Q^2)_x $$ 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 $$3 \cdot 10^{-4} \le x \le 0.1$$ 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 $$\alpha_s (M_Z^2) =0.1150 \pm 0.0017 (exp)^{+0.0009}_{-0.0005} (model)$$ is obtained in NLO, with an additional theoretical uncertainty of about $$\pm 0.005$$, mainly due to the uncertainty of the renormalisation scale.