On the extraction of the valence transversity distributions from SIDIS data

The transversity distribution for $u$ and $d$ quarks is usually extracted from data on spin asymmetries in Semi Inclusive Deep Inelastic Scattering (SIDIS): however, due to its chiral odd nature, it has to be coupled to another chiral odd function, typically the Collins or the di-hadron fragmentation function. A recent suggestion of considering SIDIS data involving ratios of spin asymmetries and avoiding a knowledge of the Collins function, is briefly discussed. New measurements, involving ratios of cross sections, are suggested. They would allow a direct extraction of the transversity ratio, $h_1^{d_V}/h_1^{u_V}$. Numerical estimates are given.