Isotropic and Anisotropic Lorentz-Violating Signatures in Z Boson Resonances at the LHC

We investigate the effects of Lorentz invariance violation (LIV) on the resonance structure of the Z boson in high-energy collider experiments. Building on previous work where resonance line-shape distortions were established, we extend the analysis to include spacelike and lightlike orientations of the LIV vector. The modified dispersion relation induces rapidity-dependent distortions of the resonance profile, with effects growing strongly at large rapidities. In anisotropic scenarios, the signal exhibits characteristic sidereal-time modulation due to the rotation of the Earth relative to the preferred LIV direction. We show that, while global analyses dilute the effect, dedicated studies focusing on high-rapidity bins and sidereal-time dependence can significantly enhance sensitivity. The resulting shifts in reconstructed resonance parameters can reach or exceed current experimental precision for LIV scales as low as δLIV∼10−8. These results demonstrate that collider measurements of unstable gauge bosons provide a complementary and competitive probe of Lorentz violation.