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Impacts of B-factory measurements on determination of fragmentation functions from electron-positron annihilation data

Fragmentation functions are determined for the pion and kaon by global analyses of charged-hadron production data in electron-positron annihilation. Accurate measurements were reported by the Belle and BaBar collaborations for the fragmentation functions at the center-of-mass energies of 10.52 GeV and 10.54 GeV, respectively, at the KEK and SLAC B factories, whereas other available $e^+e^-$ measurements were mostly done at higher energies, mainly at the $Z$ mass of 91.2 GeV. There is a possibility that gluon fragmentation functions, as well as quark fragmentation functions, are accurately determined by scaling violation. We report our global analysis of the fragmentation functions especially to show impacts of the B-factory measurements on the fragmentation function determination. Our results indicate that the fragmentation functions are determined more accurately not only by the scaling violation but also by high-statistical nature of the Belle and BaBar data. However, there are some tensions between the Belle and BaBar data in comparison with previous measurements. We also explain how the flavor dependence of quark fragmentation functions and the gluon function are separated by using measurements at different $Q^2$ values. In particular, the electric and weak changes are different depending on the quark type, so that a light-quark flavor separation also became possible in principle due to the precise data at both $\sqrt{s}\simeq 10.5$ GeV and 91.2 GeV.