# Transverse momentum dependent production cross sections of charged pions, kaons and protons produced in inclusive $e^+e^-$ annihilation at $\sqrt{s}=$ 10.58 GeV

## TL;DR

This paper measures how charged pions, kaons, and protons are produced in electron-positron collisions at 10.58 GeV, revealing detailed transverse momentum distributions and their dependence on energy and event shape, crucial for understanding fragmentation processes.

## Contribution

It provides the first detailed measurements of transverse momentum dependent production cross sections for identified hadrons at this energy, including Gaussian widths and their dependence on fractional energy and thrust.

## Key findings

- Transverse momentum distributions are well described by Gaussians at low pT.
- Gaussian widths vary with fractional energy and thrust, differing among hadron types.
- Protons have narrower Gaussian widths compared to pions and kaons.

## 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 non-trivial 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 $558\,{\rm fb}^{-1}$ data sample collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider.