Polarised quark distributions in the nucleon from semi-inclusive spin asymmetries

We present a measurement of semi-inclusive spin asymmetries for positively and negatively charged hadrons from deep inelastic scattering of polarised muons on polarised protons and deuterons in the range $0.003<x<0.7$ and $Q^2>$1~GeV$^2$. Compared to our previous publication on this subject, with the new data the statistical errors have been reduced by nearly a factor of two. From these asymmetries and our inclusive spin asymmetries we determine the polarised quark distributions of valence quarks and non-strange sea quarks at $Q^2$=10~GeV$^2$. The polarised $u$ valence quark distribution, $\Delta u_v(x)$, is positive and the polarisation increases with $x$. The polarised $d$ valence quark distribution, $\Delta d_v(x)$, is negative and the non-strange sea distribution, $\Delta \bar q(x)$, is consistent with zero over the measured range of $x$. We find for the first moments $\int_0^1 \Delta u_v(x) {\rm d}x = 0.77 \pm 0.10 \pm 0.08$, $\int_0^1 \Delta d_v(x) {\rm d}x = -0.52 \pm 0.14 \pm 0.09$ and $\int_0^1 \Delta \bar q(x) {\rm d}x= 0.01 \pm 0.04 \pm 0.03$, where we assumed $\Delta \bar u(x) = \Delta \bar d(x)$. We also determine for the first time the second moments of the valence distributions $\int_0^1 x \Delta q_v(x) {\rm d}x$.