Single Top and Higgs Production in $e^- p$ collisions

In this proceedings some studies on the prospects of single top production at the Large Hadron Electron Collider (LHeC) and double Higgs production at the Future Circular Hadron Electron Collider (FCC-he) shall be presented. In particular, we investigated the $tbW$ couplings via single top quark production with the introduction of possible anomalous Lorentz structures, and measured the sensitivity of the Higgs self coupling ($λ$) through double Higgs production. The studies are performed with 60 GeV electrons colliding with 7 (50) TeV protons for the LHeC (FCC-he). For the single top studies a parton level study has been performed, and we find the sensitivity of the anomalous coupling at a 95\% C.L, considering 10-1\% systematic errors. The double Higgs production has been studied with speculated detector parameters and the sensitivity of $λ$ estimated via the cross section study around the Standard Model Higgs self coupling strength ($λ_{SM}$) considering 5\% systematic error in signal and backgrounds. Effects of non-standard CP-even and CP-odd couplings for $hhh$, $hWW$ and $hhWW$ vertices have been studied and constrained at 95\% C.L.

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