Probing Lorentz Invariance Violation in Z Boson Mass Measurements at High-Energy Colliders

Abstract: We propose a minimal extension to the Standard Model by introducing a Lorentz Invariance Violation (LIV) term into the Z boson's dispersion relation, expressed as $p_\mu p^\mu = M_Z^2 + \delta_{LIV} (p_\mu n^\mu)^2$, where $\delta_{LIV}$ defines the violation scale and $n^\mu$ is a unit Lorentz vector specifying the direction. This modification alters the Z boson propagator and decay rate, impacting the Drell-Yan process cross-section at high-energy colliders. Observable effects are most pronounced near the resonance region at high rapidities ($|Y| > 4$), potentially shifting the perceived Z boson mass and inducing sidereal-time modulations for spacelike and lightlike LIV due to Earth's rotation. We outline a targeted search strategy for ATLAS and CMS, achieving sensitivity to LIV signatures down to $|\delta_{LIV}| \approx 10^{-8}$ (or $10^{-9}$ optimistically), offering new insights into historical and future collider data. Our model predicts systematic shifts in weak boson masses at higher collision energies, relevant to past Tevatron and LHC discrepancies, though current data are now consistent.