Deep-inelastic inclusive ep scattering at low x and a determination of alpha(s)

A precise measurement of the inclusive deep-inelastic c(+)p scattering cros s section is reported in the kinematic range 1.5 less than or equal to Q(2) less than or equal to 150 GeV2 and 3.10(-5) less than or equal to x less t han or equal to 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). Th e double differential cross section, from which the proton structure functi on F-2 (x, Q(2)) and the longitudinal structure function FL (x, Q2) are ext racted, is measured with typically 1% statistical and 3% systematic uncerta inties. The measured derivative (partial derivativeF(2) (x, Q(2))/partial d erivative ln Q(2))(x) is observed to rise continuously towards small x for fixed Q(2). The cross section data are combined with published III measurem ents at high Q2 for a next-to-leading order DGLAP QCD analysis. The H1 data determine the gluon momentum distribution in the range 3.10(-4) less than or equal to x less than or equal to 0.1 to within an experimental accuracy of about 3% for Q(2) = 20 GeV2. A fit of the H1 measurements and the mup da ta of the BCDMS collaboration allows the strong coupling constant alpha (s) and the gluon distribution to be simultaneously determined. A value of alp ha (s)(M-Z(2)) = 0.1150 +/-0.0017(exp)(-0.0005)(+0.0009) (model) is obtaine d in NLO, with an additional theoretical uncertainty of about +/-0.005, mai nly due to the uncertainty of the renormalisation scale.