We study the prospects of a displaced-vertex search of sterile neutrinos at
the Large Hadron Collider (LHC) in the framework of the neutrino-extended
Standard Model Effective Field Theory (νSMEFT). The production and decay of
sterile neutrinos can proceed via the standard active-sterile neutrino mixing
in the weak current, as well as through higher-dimensional operators arising
from decoupled new physics. If sterile neutrinos are long-lived, their decay
can lead to displaced vertices which can be reconstructed. We investigate the
search sensitivities for the ATLAS/CMS detector, the future far-detector
experiments: AL3X, ANUBIS, CODEX-b, FASER, MATHUSLA, and MoEDAL-MAPP, and at
the proposed fixed-target experiment SHiP. We study scenarios where sterile
neutrinos are predominantly produced via rare charm and bottom mesons decays
through minimal mixing and/or dimension-six operators in the νSMEFT
Lagrangian. We perform simulations to determine the potential reach of
high-luminosity LHC experiments in probing the EFT operators, finding that
these experiments are very competitive with other searches.Comment: v1: 35 pages + Appendix, 12 figures, 17 tables; v2: accepted for
publication in JHEP, typos corrected, reasoning for neglecting direct
production of sterile neutrinos via parton collisions added upon referee's
suggestion, results unchange