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

Yiannis Makris,Felix Ringer,Wouter J Waalewijn

doi:10.1007/jhep02(2021)070

Abstract

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.

Highlights

Various determinations of transverse momentum dependent (TMD) PDFs and FFs from experimental data have been performed: global extractions of unpolarized TMD PDFs and FFs [13,14,15], extractions of TMD PDFs [16, 17], and polarized TMD PDFs and FFs [18,19,20,21,22]
Non-global logarithms occur if the thrust measurement is dominated by the hemisphere that does not contain the observed hadron, since the transverse momentum measurement only probes the radiation in the hemisphere containing the hadron, and we describe how to include the leading non-global logarithms (NGLs), reducing the accuracy in this limited region of phase space to next-to-leading logarithmic (NLL)
We have presented a factorization framework for the transverse momentum of hadrons measured in e+e− collisions relative to the thrust axis

Summary

Introduction

Various determinations of TMD PDFs and FFs from experimental data have been performed: global extractions of unpolarized TMD PDFs and FFs [13,14,15], extractions of TMD PDFs [16, 17], and polarized TMD PDFs and FFs [18,19,20,21,22]. One process that is used for these extractions is hadron-pair production in e+e− annihilation, for which the factorization theorem of the cross section differential in the relative transverse momentum of the two hadrons has the following schematic form, σ ∼ HDDS This involves a TMD FF for each of the identified hadrons, denoted by D, while the hard function H describes the hard scattering and the TMD soft function S encodes the effect of soft radiation.. [42] proposed integrating out the thrust variable τ , and carried out the resummation of transverse momentum phT and threshold logarithms 1 − zh This cross section contains non-global logarithms (NGLs) [43] because the transverse momentum measurement only constrains radiation in one hemisphere. We will encounter NGLs, but in our analysis that is differential in thrust, they only appear in a restricted and clearly identified region of phase space

Objectives

Methods

Conclusion