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In this paper we present a fully-differential calculation for thecontributions to the partial widths $H\rightarrow b\bar{b}$ and $H\rightarrowc\bar{c}$ that are sensitive to the top quark Yukawa coupling $y_t$ to order$\alpha_s^3$. These contributions first enter at order $\alpha_s^2$ throughterms proportional to $y_t y_q$ ($q=b,c$). At order $\alpha_s^3$ corrections tothe mixed terms are present as well as a new contribution proportional to$y_t^2$. Our results retain the mass of the final-state quarks throughout,while the top quark is integrated out resulting in an effective field theory(EFT). Our results are implemented into a Monte Carlo code allowing for theapplication of arbitrary final-state selection cuts. As an example we presentdifferential distributions for observables in the Higgs boson rest frame usingthe Durham jet clustering algorithm. We find that the total impact of thetop-induced (i.e. EFT) pieces is sensitive to the nature of the final-statecuts, particularly b-tagging and c-tagging requirements. For bottom quarks, theEFT pieces contribute to the total width (and differential distributions) ataround the percent level. The impact is much bigger for the $H\rightarrowc\bar{c}$ channel, with effects as large as 15%. We show however that theirimpact can be significantly reduced by the application of jet-tagging selectioncuts.

Top-induced contributions to $H\rightarrow b\bar{b}$ and $H\rightarrow c\bar{c}$ at $\mathcal{O}(\alpha_s^3)$