Ratios of the $u$ and $d$ quark transversity distributions have been extracted from the COMPASS Collaboration measurements of the Collins asymmetries of positively and negatively charged hadrons produced on transversely polarized proton and deuteron targets. The method we have applied does not require the $e^+e^−$ data. It was proposed long time ago, but this is the first time it is used to extract transverse spin asymmetries.
The results for the ratio $h^{d_v}_1/h^{u_v}_1$ compare well to those obtained in a previous point–by–point extraction based both on SIDIS and $e^+e^−$ data.