We consider the Higgs boson anomalous FCNC interactions with u, c, d, s and b quarks using the effective field theory framework. Constraints on anomalous couplings are derived from experimental results on Higgs boson production with subsequent decay into pair at LHC with TeV. Upper limits on the branching fractions of and are set by performing a realistic detector simulation and accurately reproducing analysis selections of the CMS Higgs boson measurement in the four-lepton final state at TeV. The searches are projected into operation conditions of HL-LHC. Sensitivity at FCC-hh to anomalous FCNC interactions is studied based on Higgs boson production with decay channel. It is shown that at FCC-hh machine one can expect to set the upper limits of the order of at 95% CL for and .
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