Phenomenological extraction of a universal TMD fragmentation function from single hadron production in $e^+ e^-$ annihilations

TL;DR

This paper develops a factorization scheme to extract a universal TMD fragmentation function from $e^+ e^-$ annihilation data, enabling a better understanding of hadronization with perturbative and non-perturbative components.

Contribution

It introduces a novel factorization approach that separates perturbative calculations from a universal TMD fragmentation function for single hadron production.

Findings

Successful extraction of a process-independent TMD FF from BELLE data.

Validation of the factorization scheme with NLO-NLL accuracy.

A simple non-perturbative model complements the perturbative calculations.

Abstract

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.