Joint thrust and TMD resummation in electron-positron and electron-proton collisions

We present the framework for obtaining precise predictions for the transverse momentum of hadrons with respect to the thrust axis in e(+)e(-) collisions. This will enable a precise extraction of transverse momentum dependent (TMD) fragmentation functions from a recent measurement by the Belle Collaboration. Our analysis takes into account, for the first time, the nontrivial interplay between the hadron transverse momentum and the cut on the thrust event shape. To this end, we identify three different kinematic regions, derive the corresponding factorization theorems within Soft Collinear Effective Theory, and present all ingredients needed for the joint resummation of the transverse momentum and thrust spectrum at NNLL accuracy. One kinematic region can give rise to non-global logarithms (NGLs), and we describe how to include the leading NGLs. We also discuss alternative measurements in e(+)e(-) collisions that can be used to access the TMD fragmentation function. Finally, by using crossing symmetry, we obtain a new way to constrain TMD parton distributions, by measuring the displacement of the thrust axis in ep collisions.

Automated summary

The paper presents a framework for precise predictions of hadron transverse momentum relative to the thrust axis in e(+)e(-) collisions, enabling extraction of TMD fragmentation functions from recent experiments. By considering the interplay between hadron transverse momentum and thrust event shape cut, the analysis identifies three kinematic regions and provides ingredients for joint resummation of transverse momentum and thrust spectrum at NNLL accuracy. The inclusion of non-global logarithms and discussion of alternative measurements in e(+)e(-) collisions are also discussed.