Factorization of the e+e- ---> H X cross section, differential in z_h, P_T and thrust, in the 2-jet limit

Factorizing the cross section for single hadron production in e+e- annihilations is a highly non trivial task when the transverse momentum of the outgoing hadron with respect to the thrust axis is taken into account. We work in a scheme that allows to factorize the e+e- ---> HX cross section as a convolution of a calculable hard coefficient and a Transverse Momentum Dependent (TMD) fragmentation function. The result, differential in z_h, P_T and thrust, will be given to all orders in perturbation theory and explicitly computed to Next to Leading Order (NLO) and Next to Leading Log (NLL) accuracy. The predictions obtained from our computation, applying the simplest and most natural ansatz to model the non-perturbative part of the TMD, are in exceptional agreement with the experimental measurements of the BELLE Collaboration. The factorization scheme we propose relates the TMD parton densities defined in 1-hadron and 2-hadron processes, restoring the possibility to perform global phenomenological studies of TMD physics including experimental data from semi-inclusive deep inelastic scattering, Drell-Yan processes, e+e- ---> H_1 H_2 X and e+e- ---> HX annihilations.