A search for the standard model Higgs boson decaying to a charm quark-antiquark pair, H $\to$$\mathrm{c\bar{c}}$, produced in association with a top quark-antiquark pair ($\mathrm{t\bar{t}}$H) is presented. The search is performed with data from proton-proton collisions at $\sqrt{s}$ = 13 TeV, corresponding to an integrated luminosity of 138 fb$^{-1}$. Advanced machine learning techniques are employed for jet flavor identification and event classification. The Higgs boson decay to a bottom quark-antiquark pair is measured simultaneously and the observed $\mathrm{t\bar{t}}$H bb event rate relative to the standard model expectation is 0.91$\pm^{+0.26}_{-0.22}$. The observed (expected) upper limit on the product of production cross section and branching fraction $σ$($\mathrm{t\bar{t}}$H)$\mathcal{B}$(H $\to$$\mathrm{c\bar{c}}$) is 0.11 (0.13$\pm^{+0.06}_{-0.04}$) pb at 95% confidence level, corresponding to 7.8 (8.7$\pm^{+4.0}_{-2.6}$) times the standard model prediction. When combined with the previous search for H $\to$ $\mathrm{c\bar{c}}$ via associated production with a W or Z boson, the observed (expected) 95% confidence interval on the Higgs-charm Yukawa coupling modifier, $κ_\mathrm{c}$, is $\lvert{κ_\mathrm{c}}\rvert$ $\lt$ 3.5 (2.7), the most stringent constraint to date.
Upper limits on the signal strength for $\text{H}\to\text{c}\overline{\text{c}}$ decays with respect to the standard model expectation of unity.
Upper limits on the signal strength for $\text{t}\overline{\text{t}}\text{H}(\text{H}\to\text{c}\overline{\text{c}})$ decays with respect to the standard model expectation of unity.
Signal strength and significance for $\text{t}\overline{\text{t}}\text{H}(\text{H}\to\text{b}\overline{\text{b}})$ decays with respect to the standard model expectation of unity.
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