Searching for heavy neutrino in terms of tau lepton at future hadron collider

The tau lepton plays important role in the correlation between the low-energy neutrino oscillation data and the lepton flavor structure in heavy neutrino decay. We investigate the lepton flavor signatures with tau lepton at hadron collider through lepton number violating (LNV) processes. In the Type I Seesaw with U$(1)_{rm B-L}$ extension, we study the pair production of heavy neutrinos via a $Z$ resonance. We present a detailed assessment of the search sensitivity to the channels with tau lepton in the subsequent decay of heavy neutrinos. For the benchmark model with $Z$ only coupled to the third generation fermions, we find that the future circular collider (FCC-hh) can discover the LNV signal with tau lepton for $M_{Z}$ up to 2.2 (3) TeV with the gauge coupling $g=0.6$ and the integrated luminosity of 3 (30) ab$^{-1}$. The test on the flavor combinations of SM charged leptons would reveal the specific nature of different heavy neutrinos.