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We calculate differential cross sections for Higgs boson and/or two-photonproduction from intermediate (virtual) Higgs boson within the formalism of$k_t$-factorization. The off-shell $g^* g^* \to H$ matrix elements are used. Wecompare results obtained with infinite top fermion (quark) mass and with finitemass taken into account. The latter effect is rather small. We compare resultswith different unintegrated gluon distributions from the literature. Twomethods are used. In the first method first Higgs boson is produced in the $2\to 1$ $g g \to H$ $k_t$-factorization approach and then isotropic decay withthe Standard Model branching fraction is performed. In the second method wecalculate directly two photons coupled to the virtual Higgs boson. The resultsof the two methods are compared and differences are discussed. The results fortwo photons from the Higgs boson are compared with recent ATLAS collaborationdata. In contrast to a recent calculation the leading order $g g \to H$contribution is rather small compared to the ATLAS experimental data ($\gamma\gamma$ transverse momentum and rapidity distributions) for all unintegratedgluon distributions from the literature. We include also higher-ordercontribution $g g \to H (\to \gamma \gamma) g$, $g g \to g H g$ and thecontribution of the $W^+ W^-$ and $Z^0 Z^0$. The $gg\to Hg$ mechanism givessimilar cross section as the $gg\to H$ mechanism. We argue that there is almostno double counting when adding $gg\to H$ and $gg\to Hg$ contributions due todifferent topology of Feynman diagrams. The final sum is comparable with theATLAS two-photon data. We discuss uncertainties related to both the theoreticalapproach and existing UGDFs.

Inclusive production of Higgs boson in the two-photon channel at the LHC within $k_{t}$-factorization approach and with the Standard Model couplings