New data from the BABAR Collaboration, on azimuthal asymmetries measured in $e^{+}{e}^{-}$ annihilations into pion pairs at $Q^2=112{\mathrm{GeV}}^2$, allow us to take the first, direct glance at the $p_{\perp }$ dependence of the Collins functions, in addition to their $z$ dependence. These data, together with previous $e^{+}{e}^{-}\to h_1{h}_2$ 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 $Q^2$ 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 $Q^2$ of $13{\mathrm{GeV}}^2$, offer the possibility to explore the sensitivity of these azimuthal correlations on transverse-momentum-dependent evolution effects.

• Received 23 October 2015

DOI:https://doi.org/10.1103/PhysRevD.92.114023