We have studied open charm production in $\gamma \gamma$ collisions with the TOPAZ detector at the TRISTAN $e~{+}e~{-}$ collider. In this study, charm quarks were identified by electrons (and positrons) from semi-leptonic decays of charmed hadrons. The data corresponded to an integrated luminosity of 95.3 pb$~{-1}$ at a center-of-mass energy of 58 GeV. The results are presented as the cross sections of inclusive electron production in $\gamma \gamma$ collisions with an anti-tag condition, as well as the subprocess cross sections, which correspond to resolved-photon processes. The latter were measured by using a sub-sample with remnant jets. A comparison with various theoretical predictions based on direct and resolved-photon processes showed that our data prefer that with relatively large gluon contents in a photon at small $x (x \le 0.1)$, with the next-to-leading order correction, and with a charm-quark mass of 1.3 GeV.
The shape of jets produced in (quasi-) real photon-photon collisions as well as in e^+e^- annihilation process has been studied with a cone jet finding algorithm, using the data taken with the TOPAZ detector at the TRISTAN e^+e^- collider at an average center-of-mass energy of 58 GeV. The results are presented in terms of the jet width as a function of the jet transverse energy(E^{jet}_T) as well as a scaled transverse jet energy, x_T(=2E^{jet}_T/root(s)). The jet width narrows as E^{jet}_T increases; however, at the same value of E^{jet}_T the jet width in gamma-gamma collisions at TRISTAN is significantly narrower than that in gamma p collisions at HERA. By comparing our results with the data in other reactions, it has been shown that the jet width in gamma-gamma, gamma p, p\bar{p} collisions as well as the e^+e^- annihilation process has an approximate scaling behavior as a function of x_T.
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