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We study the decay of the SM Higgs boson to a massive charm quark pair at thenext-to-next-to-leading order QCD and next-to-leading order electroweak. At thesecond order of QCD coupling, we consider the exact calculation offlavour-singlet contributions where the Higgs boson couples to the internal topand bottom quark. Helpful information on the running mass effects related toYukawa coupling may be obtained by analyzing this process. High precisionproduction for $h\to c\bar{c}$ within the SM makes it possible to search fornew physics that may induce relatively large interactions related to the charmquark. As an example, we evaluate the axion-like particle associate productionwith a charm quark pair in the Higgs decay and obtain some constraints for thecorresponding parameters under some assumptions.

Precise evaluation of $h\to c\bar{c}$ and axion-like particle production