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We report measurements of the production cross sections of charged pions,kaons, and protons as a function of fractional energy, the event-shape variablecalled thrust, and the transverse momentum with respect to the thrust axis.These measurements access the transverse momenta created in the fragmentationprocess, which are of critical importance to the understanding of anytransverse momentum dependent distribution and fragmentation functions. The lowtransverse momentum part of the cross sections can be well described byGaussians in transverse momentum as is generally assumed but thefractional-energy dependence is non-trivial and different hadron types havevarying Gaussian widths. The width of these Gaussians decreases with thrust andshows an initially rising, then decreasing fractional-energy dependence. Thewidths for pions and kaons are comparable within uncertainties, while those forprotons are significantly narrower. These single-hadron cross sections andGaussian widths are obtained from a $558\,{\rm fb}^{-1}$ data sample collectedat the $\Upsilon(4S)$ resonance with the Belle detector at the KEKBasymmetric-energy $e^+ e^-$ collider.

physical review. d/physical review. d.

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