Deep-inelastic inclusive ep scattering at low cursive Greek chi and a determination of α_s

A precise measurement of the inclusive deep-inelastic e⁺p scattering cross section is reported in the kinematic range 1.5 ≤ Q² ≤ 150 GeV² and 3 · 10^-5 ≤ cursive Greek chi ≤ 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 F₂(cursive Greek chi, Q²) and the longitudinal structure function F_L(cursive Greek chi, Q²) are extracted, is measured with typically 1% statistical and 3% systematic uncertainties. The measured derivative (∂F₂ (cursive Greek chi, Q²)/∂ln Q²)_{cursive Greek chi}, is observed to rise continuously towards small cursive Greek chi for fixed Q². The cross section data are combined with published H1 measurements at high Q² for a next-to-leading order DGLAP QGD analysis. The H1 data determine the gluon momentum distribution in the range 3 · 10^-4 ≤ cursive Greek chi ≤ 0.1 to within an experimental accuracy of about 3% for Q² = 20 GeV². A fit of the H1 measurements and the μp data of the BCDMS collaboration allows the strong coupling constant α_s and the gluon distribution to be simultaneously determined. A value of α_s(M²_Z) = 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.