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We calculated a differential cross section of the Higgs boson production inthe $h\to ZZ^*\to 4\ell$ decay channel within the framework of$k_T$-factorization. Results are obtained using an off-shell matrix element forthe $g^*g^*\to h\to ZZ^*\to 4\ell$ process together withCiafaloni-Catani-Fiorani-Marchesini (CCFM) evolution equations for anunintegrated gluon distribution function. We have presented a comparison of ourresults with the latest experimental measurements at $\sqrt{S}$ = 8 TeV and$\sqrt{S}$ = 13 TeV from the ATLAS and CMS collaborations at the LHC. Inaddition to this, we have compared our results with the results from thecollinear factorization formalism calculated up to next-to-next-to-leadingorder plus next-to-next-to-leading logarithm (NNLO + NNLL) accuracy obtainedusing the HRes code for the Higgs boson production in the gluon-gluon fusionprocess. Our estimates are consistently close to NNLO + NNLL results obtainedusing a collinear factorization formalism and are also in agreement withexperimental measurements.

$k_T$-factorization approach to the Higgs boson production in $ZZ^*\to 4\ell$ channel at the LHC