We propose a minimal extension of the Standard Model by introducing a Lorentz invariance violation (LIV) term into the $Z$ boson’s dispersion relation, expressed as $p_{\mu }{p}^{\mu }=M_Z^2+{\delta }_{\mathrm{LIV}}(p_{\mu }{n}^{\mu }{)}^2$, where ${\delta }_{\mathrm{LIV}}$ defines the violation scale and $n^{\mu }$ is a unit Lorentz vector specifying the direction of the violation. This perturbative 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 in general LIV cases and inducing additional sidereal-time modulations for spacelike and lightlike LIV due to the Earth’s rotation relative to distant stars. We outline a targeted search strategy for ATLAS and CMS, achieving sensitivity to LIV signatures down to $|{\delta }_{\mathrm{LIV}}|\approx {10}^{-8}$ (or even ${10}^{-9}$ in an optimistic scenario), offering a fresh perspective on historical and future collider data. Our model predicts that, in experiments with higher collision energies (and thus greater rapidities), the conventionally reconstructed weak boson mass exhibits a systematic shift. This could be particularly intriguing in the historical context of Tevatron and LHC weak boson mass measurements, where the discrepancy in $W$ mass measurements aligns with our LIV scenario.

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• Dynamical symmetry breaking models
• Extensions of gauge sector
• Particle interactions
• Phenomenology
• Symmetries
• W & Z bosons
• High-energy accelerators & colliders
• Lorentz symmetry
• Spacetime symmetries