Exploring nonstandard $Hb\overline{b}$ interactions at future electron-proton colliders

In this paper, we use the charged-current Higgs boson production process at future electron-proton colliders, $e^{-}p\to Hj{\nu }_e$, with the subsequent decay of the Higgs boson into a $b\overline{b}$ pair, to probe the Standard Model effective field theory with dimension-six operators involving the Higgs boson and the bottom quark. The study is performed for two proposed future high-energy electron-proton colliders, the Large Hadron Electron Collider (LHeC) and the Future Circular Collider (FCC-he) at the center-of-mass energies of 1.3 TeV and 3.46 TeV, respectively. Constraints on the $CP$-even and $CP$-odd $Hb\overline{b}$ couplings are derived by analyzing the simulated signal and background samples. A realistic detector simulation is performed and a multivariate technique using the gradient boosted decision trees algorithm is employed to discriminate the signal from background. Expected limits are obtained at 95% confidence level for the LHeC and FCC-he assuming the integrated luminosities of 1, 2 and $10{\mathrm{ab}}^{-1}$. We find that using $1{\mathrm{ab}}^{-1}$ of data, the $CP$-even and $CP$-odd $Hb\overline{b}$ couplings can be constrained with accuracies of the order of ${10}^{-3}$ and ${10}^{-2}$, respectively, and a significant region of the unprobed parameter space becomes accessible.