Abstract
Recent BELLE measurements provide the cross section for single hadron production in e^+e^- annihilations, differential in thrust and in the hadron transverse momentum 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.
Highlights
QCD describes hadronic matter through the dynamics of its elementary consituents, quarks and gluons
In this paper we have extended the transverse momentum dependent (TMD) factorization mechanism to processes belonging to different hadron classes
This is potentially a very powerful tool, as it allows us to exploit the same definition of TMD parton densities in different processes, which up to now could not be used in a simultaneous data analysis
Summary
QCD describes hadronic matter through the dynamics of its elementary consituents, quarks and gluons. Confinement prevents the direct observation of partonic degrees of freedom, which are shaded by the hadronization mechanism These data have triggered a great interest of the high energy physics community, especially among the experts in the phenomenological study of TMD phenomena and factorization. In this new definition, the soft factor of the process, which is responsible for potential universality breaking effects, is not absorbed in the TMD, to prevent it from influencing its genuinely universal nature. The soft factor of the process, which is responsible for potential universality breaking effects, is not absorbed in the TMD, to prevent it from influencing its genuinely universal nature Instead, it appears explicitly in the cross section which acquires a new term, that we will call soft model, MS. Later on in the paper we will define what we mean exactly by “class”; for the moment being we anticipate that, for instance, Drell-Yan, Semi Inclusive Deep Inelastic Scattering (SIDIS) and e+e− → HA HB X processes belong to the same hadron class, while DIS and e+e− → H X belong to a different class
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