We report new measurements of the production cross sections of pairs of charged pions and kaons as a function of their fractional energies using various fractional-energy definitions. Two different fractional-energy definitions were used and compared to the conventional fractional-energy definition reported previously. The new variables aim at either identifying dihadron cross sections in terms of single-hadron fragmentation functions, or to provide a means of characterizing the transverse momentum created in the fragmentation process. The results were obtained applying the updated initial-state radiation correction used in other recent Belle publications on light-hadron production cross sections. In addition, production cross sections of single charged pions, kaons, and protons were also updated using this initial-state radiation correction. The cross sections 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.
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