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$B_c$ production rate in Higgs boson decays is evaluated in NRQCD framework.Given Higgs total decay width is about $4.20~MeV$ and the vector $B^*_c$ mesondecays completely to the ground state, we find that the branching fraction of$B_c$ meson production in Higgs decays is $8.50\times10^{-4}$, where bothleading QED and QCD contributions are included. This process is hencedetectable in the high-luminosity/energy LHC. In confronting to the quarkoniaproduction, we find that the fraction rate of $B_c$ production is more than anorder of magnitude bigger than those of charmonium and bottomoium production inHiggs decays. In the calculation, various differential distributions anduncertainties of the concerned processes are analysed.

$B_c$ Production in Higgs Boson Decays