Excited neutrino search potential of the FCC-based electron-hadron colliders

The production potential of the excited neutrinos at the FCC-based electron-hadron colliders, namely the ERL60$\otimes$FCC with $\sqrt{s}=3.46$ TeV, the ILC$\otimes$FCC with $\sqrt{s}=10$ TeV, and the PWFA-LC$\otimes$FCC with $\sqrt{s}=31.6$ TeV, has been analyzed. The branching ratios of the excited neutrinos have been calculated for the different decay channels and shown that the dominant channel is $\nu^{\star}\rightarrow eW^{+}$. We have calculated the production cross sections with the process of $ep\rightarrow\nu^{\star}q\rightarrow eW^{+}q$ and the decay widths of the excited neutrinos with the process of $\nu^{\star}\rightarrow eW^{+}$. The signals and corresponding backgrounds are studied in detail to obtain accessible mass limits. It is shown that the discovery limits obtained on the mass of the excited neutrino are $2452$ GeV for $L_{int}=100$ $fb^{-1}$, $5635$ GeV for $L_{int}=10$ $fb^{-1}$ ($6460$ GeV for $L_{int}=100$ $fb^{-1}$), and $10200$ GeV for $L_{int}=1$ $fb^{-1}$ ($13960$ GeV for $L_{int}=10$ $fb^{-1}$), for the center-of-mass energies of $3.46$, $10$, and $31.6$ TeV, respectively.