The deuteron spin-dependent structure function g1d and its first moment

We present a measurement of the deuteron spin-dependent structure function g1d based on the data collected by the COMPASS experiment at CERN during the years 2002-2004. The data provide an accurate evaluation for Γ1d, the first moment of g1d(x), and for the matrix element of the singlet axial current, a0. The results of QCD fits in the next to leading order (NLO) on all g1 deep inelastic scattering data are also presented. They provide two solutions with the gluon spin distribution function ΔG positive or negative, which describe the data equally well. In both cases, at Q2=3(GeV/c)2 the first moment of ΔG(x) is found to be of the order of 0.2-0.3 in absolute value.