Abstract

We report measurements of the production cross sections of charged pions, kaons, and protons as a function of fractional energy, the event-shape variable called thrust, and the transverse momentum with respect to the thrust axis. These measurements access the transverse momenta created in the fragmentation process, which are of critical importance to the understanding of any transverse-momentum-dependent distribution and fragmentation functions. The low transverse-momentum part of the cross sections can be well described by Gaussians in transverse momentum as is generally assumed but the fractional-energy dependence is nontrivial and different hadron types have varying Gaussian widths. The width of these Gaussians decreases with thrust and shows an initially rising, then decreasing fractional-energy dependence. The widths for pions and kaons are comparable within uncertainties, while those for protons are significantly narrower. These single-hadron cross sections and Gaussian widths are obtained from a 558 fb−1 data sample collected at the ϒ(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e− collider.8 MoreReceived 5 February 2019DOI:https://doi.org/10.1103/PhysRevD.99.112006Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasFragmentation into hadronsParticle productionQuantum chromodynamicsPhysical SystemsLepton collidersParticles & FieldsNuclear Physics

Highlights

  • Transverse-momentum-dependent parton distribution (PDF) and fragmentation functions (FF) have gained substantial interest due to the emergence of transverse spin dependent phenomena

  • These measurements access the transverse momenta created in the fragmentation process, which are of critical importance to the understanding of any transverse-momentum-dependent distribution and fragmentation functions

  • Another important aspect of transversemomentum-dependent distribution (TMD) that is yet to be addressed in more detail is the scale dependence, which is expected [27] to be different from the collinear Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) [28–30] evolution but again lacks data

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Summary

INTRODUCTION

Transverse-momentum-dependent parton distribution (PDF) and fragmentation functions (FF) have gained substantial interest due to the emergence of transverse spin dependent phenomena. In order to relate the TMD effects in SIDIS and eþe− to the large inclusive asymmetries measured in proton-proton collisions [21–23], transverse-momentum integrals over the TMDs are needed to arrive at the higher-twist functions relevant there [24–26] Another important aspect of TMDs that is yet to be addressed in more detail is the scale dependence, which is expected [27] to be different from the collinear Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) [28–30] evolution but again lacks data. In this paper we present the unpolarized cross sections for single charged pion, kaon as well as proton production as a function of fractional energy, transverse momentum, and thrust where the reference axis is given by the thrust axis These measurements are related to the unpolarized single-hadron fragmentation functions Dh1ðz; kT; QÞ. V. (Note: Additional figures and data files are available online in the Supplemental Material [32].)

BELLE DETECTOR AND DATA SELECTION
PID selection
HADRON ANALYSIS AND CORRECTIONS
Binning and cross-section extraction
PID correction
Non-qqbackground correction
Momentum-smearing correction
Preselection and acceptance correction
Weak decays
ISR correction
Consistency checks and total systematic uncertainties
RESULTS
Widths of PhT dependence
MC generator comparison
SUMMARY
Full Text
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