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 $1.5 \le Q^2 \le 150$ 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 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 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.