Prepared for submission to JHEP Universality-breaking effects in e+e− hadronic production processes M. Boglione, and A. Simonelli Dipartimento di Fisica Teorica, Universit`adi Torino, Via P. Giuria 1, I-10125 Torino, Italy INFN, Sezione di Torino, Via P. Giuria 1, I-10125 Torino, Italy E-mail:
[email protected],
[email protected] Abstract: Recent BELLE measurements provide the cross section for single hadron pro- duction in e+e− annihilations, differential in thrust and in the hadron transverse momen- tum with respect to the thrust axis. Universality breaking effects due to process-dependent soft factors make it very difficult to relate this cross sections to those corresponding to hadron-pair production in e+e− annihilations, where transverse momentum dependent (TMD) factorization can be applied. The correspondence between these two cross sections is examined in the framework of the Collins-Soper-Sterman factorization, in the collinear as well as in the TMD approach. We propose a scheme that allows to relate the TMD parton densities defined in 1-hadron and in 2-hadron processes, neatly separating, within the soft and collinear parts, the non-perturbative terms from the contributions that can be calculated perturbatively. The regularization of rapidity divergences introduces cut-offs, the arbitrariness of which will be properly reabsorbed by means of a mechanism closely reminiscent of a gauge transformation. In this way, we restore the possibility to perform global phenomenological studies of TMD physics, simultaneously analyzing data belonging to different hadron classes. arXiv:2007.13674v2 [hep-ph] 1 Nov 2020 Contents 1 Introduction2 1.1 Collinear and TMD Factorization3 2 Soft Factor6 2.1 2-h Soft Factor9 3 Collinear Parts and TMDs 11 3.1 Evolution Equations for TMDs 14 3.2 Rapidity dilations 16 3.2.1 Rapidity dilation and z-axis reflection 21 4 Universality and Process Classification 22 5 The 2-hadron class 25 5.1 2-h Class Cross Section 25 5.2 Factorization Definition vs.