Probing Lorentz invariance violation in Z boson mass measurements at high-energy colliders

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 μ p μ = M Z 2 + δ LIV ( p μ n μ ) 2 , where δ LIV defines the violation scale and n μ 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 | δ LIV | ≈ 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.