FCC-he sensitivity estimates on the anomalous electromagnetic dipole moments of the top-quark

In this paper, we study the production of a top-quark in association with a bottom-quark and a electron-neutrino at the Future Circular Collider Hadron Electron (FCC-he) to probe the sensitivity on its magnetic moment $\left({\stackrel{ˆ}{a}}_{V}\right)$ and its electromagnetic dipole moment $\left({\stackrel{ˆ}{a}}_{A}\right)$ through the process ${e}^{-}p\to {e}^{-}\gamma p\to \overline{t}{\nu }_{e}bp$. Assuming a large amount of collisions, as well as of data with cleaner environments, the FCC-he is an excellent option to study new physics, such as the ${\stackrel{ˆ}{a}}_{V}$ and ${\stackrel{ˆ}{a}}_{A}$. For our sensitivity study on ${\stackrel{ˆ}{a}}_{V}$ and ${\stackrel{ˆ}{a}}_{A}$, we consider center-of-mass energies $\sqrt{s}=7.07,10\text{TeV}$ and luminosities $L=50,100,300,500,1000{\text{fb}}^{-1}$. In addition, we apply systematic uncertainties ${\delta }_{sys}=0\text{%},3\text{%},5\text{%}$ and we consider unpolarized and polarized electron beam. Our results show that the FCC-he is a very good perspective to probe the ${\stackrel{ˆ}{a}}_{V}$ and ${\stackrel{ˆ}{a}}_{A}$ at high-energy and high-luminosity frontier.