The Higgs production in the two-photon fusion process is investigated where one of the photons is off-shell while the other one is on-shell. This process is realized in either electron-positron collision or electron-photon collision where the scatter
ed electron or positron is detected (single tagging) and described by the transition form factor. We calculate the contributions to the transition form factor of the Higgs boson coming from top-quark loops and W-boson loops. We then study the $Q^2$ dependence of each contribution to the total transition form factor and also of the differential cross section for the Higgs production.
We investigate the one-gluon-exchange ($alpha alpha_s$) corrections to the real photon structure functions $W_{TT} $, $W_{LT}$, $W_{TT}^{a} $ and $W_{TT}^tau$ in the massive parton model. We employ a technique based on the Cutkosky rules and the re
duction of Feynman integrals to master integrals. We show that a positivity constraint, which is derived from the Cauchy-Schwarz inequality, is satisfied among the unpolarized and polarized structure functions $W_{TT}$, $W_{TT}^a$ and $W_{TT}^tau$ calculated up to the next-to-leading order in QCD.
We investigate the one-gluon-exchange ($alpha alpha_s$) corrections to the polarized real photon structure function $g_1^gamma(x,Q^2)$ in the massive parton model. We employ a technique based on the Cutkosky rules and the reduction of Feynman integra
ls to master integrals. The NLO contribution is noticeable at large $x$ and does not vanish at the threshold of the massive quark pair production due to the Coulomb singularity. It is found that the first moment sum rule of $g_1^gamma$ is satisfied up to the NLO.
