Single Higgs boson production in association with a top quark through FCNSI

We study the production and possible detection of a single Higgs boson in association with a top quark in proton-proton collisions ($pp\to th+X$) at the High-Luminosity Large Hadron Collider. This process absent in the Standard Model is predicted by other models such as the Two-Higgs Doublet Model of type III, which is the theoretical framework adopted in this work. Promising results are found for specific scenarios of the model parameter space, which consist mainly of the parameters $\tan \beta$, $\cos (\alpha -\beta )$ and the parameter ${\chi }_{tc}$, responsible for the Flavor-Changing Neutral Scalar Interactions (FCNSI). Using the machine learning $\mathit{\text{Boosted}}\mathit{\text{Decision}}\mathit{\text{Trees}}$ algorithm and considering a systematic uncertainty of $5\mathrm{\%}$, we predict $\mathit{\text{signal}}\mathit{\text{significances}}$ at level of $5\sigma$ for $\tan \beta =1$, $\cos (\alpha -\beta )=0.1$, ${\chi }_{tc}=5$, and integrated luminosities {${\mathcal{L}}_{\mathrm{i}\mathrm{n}\mathrm{t}}\gtrsim 2700f{b}^{-1}$}. Likewise, we also predict a $\mathit{\text{signal}}\mathit{\text{significance}}$ $\sigma \approx 4.4$ for $\tan \beta =1$, $\cos (\alpha -\beta )=0.1$, ${\chi }_{tc}=3$, and integrated luminosities ${\mathcal{L}}_{\mathrm{i}\mathrm{n}\mathrm{t}}=3000f{b}^{-1}$, which consider the upper limit given by HL-LHC projection on $\mathcal{B}\mathcal{R}(t\to ch)$.