  Factorizing the cross section for single hadron production in $e^+e^-$
annihilations, differential in $z_h$, $P_T$ and thrust, is a highly non trivial
task. We have devised a factorization scheme that allows us to recast the
$e^+e^- \to hX$ cross section in the convolution of a perturbatively calculable
coefficient and a universal Transverse Momentum Dependent (TMD) Fragmentation
Function (FF). The predictions obtained from our NLO-NLL perturbative
computation, together with a simple ansatz to model the non-perturbative part
of the TMD, are applied to the experimental measurements of the BELLE
Collaboration for the phenomenological extraction of this process independent
TMD FF.
