Probing Lorentz Invariance Violation at High-Energy Colliders via Intermediate Massive Boson Mass Measurements: Z Boson Example

Lorentz invariance (LI) is a foundational principle of modern physics, yet its possible violation (LIV) remains an intriguing window to physics beyond the Standard Model. While stringent constraints exist in the electromagnetic and hadronic sectors, the weak sector-particularly unstable bosons-remains largely unexplored. In this work, based on our recent studies and conference presentation, we analyze how LIV manifests in high-energy collider experiments, focusing on modifications of Z boson dispersion relations and their impact on resonance measurements in Drell--Yan processes. We argue that precision measurements of resonance masses at colliders provide sensitivity to LIV at the level of $10^{-9}$, comparable to bounds derived from cosmic rays. We also discuss the interplay between LIV and gauge invariance, highlighting why only specific operators provide physical effects. The phenomenological implications for both Z and W bosons are outlined, with emphasis on experimental strategies for current and future colliders.