The COMPASS Collaboration at CERN has measured the transverse spin azimuthal asymmetry of charged hadrons produced in semi-inclusive deep inelastic scattering using a 160 GeV positive muon beam and a transversely polarised NH_3 target. The Collins asymmetry of the proton was extracted in the Bjorken x range 0.003<x<0.7. These new measurements confirm with higher accuracy previous measurements from the COMPASS and HERMES collaborations, which exhibit a definite effect in the valence quark region. The asymmetries for negative and positive hadrons are similar in magnitude and opposite in sign. They are compatible with model calculations in which the u-quark transversity is opposite in sign and somewhat larger than the d-quark transversity distribution function. The asymmetry is extracted as a function of Bjorken $x$, the relative hadron energy $z$ and the hadron transverse momentum p_T^h. The high statistics and quality of the data also allow for more detailed investigations of the dependence on the kinematic variables. These studies confirm the leading-twist nature of the Collins asymmetry.
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