Measurement of the longitudinal spin structure of the proton at COMPASS

Inclusive ($A_{1,p}$) and semi-inclusive ($A^{\pi +}_{1,p}$, $A^{\pi -}_{1,p}$, $A^{K+}_{1,p}$ and $A^{K-}_{1,p}$) double-spin asymmetries in deepinelastic muon-proton scattering have been measured at COMPASS (SPS CERN). The results have been obtained with data collected in 2007 for the longitudinal polarised NH$^{3}$ solid target and beam of positive muons with energy $E =$ 160 GeV. We improve the statistical precision of $g^{p}_{1} (x.Q^{2})$ by a factor of two in the low $x$ region. Proton asymmetries have been combined with published deuteron ones to extract the non-singlet spin-dependent structure function $g^{NS}_{1} (x,Q^{2})$. The first moment $\Gamma^{NS}_{1}$ confirms the validity of the Bjorken sum-rule. Our new semi-inclusive data were used to evaluate the $\Delta u$, $\Delta d$, $\Delta\bar{u}$, $\Delta\bar{d}$ and $\Delta s\equiv \Delta\bar{s}$ distributions.