Transverse momentum dependent fragmentation functions from recent BELLE data

A new formalism for the factorization of cross section single-hadron production in ${e}^{+}{e}^{\ensuremath{-}}$ annihilations, differential ${z}_{h}$, ${P}_{T}$, and thrust, is applied to phenomenological analysis data recently measured by BELLE Collaboration. Within this scheme ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}hX$ can be recast convolution a perturbatively calculable coefficient universal transverse-momentum-dependent fragmentation function. While performing next-to-leading-order calculation perturbative part process next-to-leading logarithmic accuracy, we examine thoroughly discuss suitability number possible Ans\"atze model nonperturbative function, showing extent which present experimental actually constrain its shape functional form terms thrust.