Collins functions for pions from SIDIS and new e+e- data: A first glance at their transverse momentum dependence

New data from the BABAR Collaboration, on azimuthal asymmetries measured in e+e- annihilations into pion pairs at Q2=112 GeV2, allow us to take the first, direct glance at the p⊥ dependence of the Collins functions, in addition to their z dependence. These data, together with previous e+e-→h1h2 Belle measurements and the available semi-inclusive deep inelastic scattering (SIDIS) data on the Collins asymmetry, are simultaneously analyzed in the framework of the generalized parton model, assuming two alternative Q2 evolution schemes and exploiting two different parametrizations for the Collins functions. The corresponding results for the transversity distributions are presented. Analogous data, newly released by the BESIII Collaboration, on e+e- annihilations into pion pairs at the lower Q2 of 13 GeV2, offer the possibility to explore the sensitivity of these azimuthal correlations on transverse-momentum-dependent evolution effects.