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arxiv: 2504.11248 · v1 · submitted 2025-04-15 · ✦ hep-ph · hep-ex· hep-th

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

Juansher Jejelava , Zurab Kepuladze This is my paper

Pith reviewed 2026-05-22 20:00 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-th
keywords Lorentz invariance violationZ bosonDrell-Yan processhigh-rapiditymass measurementLHCsidereal modulation
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The pith

A Lorentz invariance violation added to the Z boson dispersion relation alters its propagator and shifts the apparent mass in high-rapidity Drell-Yan events.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a minimal Lorentz invariance violation term into the Z boson's dispersion relation of the form p_μ p^μ = M_Z² + δ_LIV (p_μ n^μ)². This change modifies the propagator and decay width, which in turn affects the Drell-Yan cross section at collider energies. The resulting distortions appear most clearly near the resonance at large rapidities and can produce both a systematic mass shift and sidereal-time variations caused by Earth's rotation. The authors map out a search strategy that would reach sensitivity to |δ_LIV| values around 10^{-8} using ATLAS and CMS data, while noting that the same modification would induce energy-dependent shifts in weak-boson masses.

Core claim

The central claim is that the added LIV term in the Z dispersion relation changes the propagator and decay rate in the Drell-Yan channel, producing measurable distortions of the Z resonance peak at high rapidities that would appear as a shifted mass or as sidereal modulations, with current and future collider data able to constrain |δ_LIV| down to 10^{-8}.

What carries the argument

The modified dispersion relation p_μ p^μ = M_Z² + δ_LIV (p_μ n^μ)² that alters the Z propagator and decay width.

If this is right

  • The model predicts systematic shifts in measured weak-boson masses that grow with collision energy.
  • Targeted high-rapidity selections in ATLAS and CMS can reach |δ_LIV| ≈ 10^{-8}.
  • Spacelike and lightlike LIV vectors produce sidereal-time modulations due to Earth's rotation.
  • The same framework offers a possible account for earlier Tevatron and LHC mass discrepancies that are now consistent with the Standard Model.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same dispersion modification could be applied to the W boson to test consistency across the electroweak sector.
  • High-luminosity LHC runs or future colliders at higher energies would tighten the bound by another order of magnitude.
  • If a signal appears, cross-checks against other precision observables (such as forward-backward asymmetries) would be needed to isolate the LIV origin.

Load-bearing premise

The LIV term affects only the Z propagator and decay in the Drell-Yan process and does not produce effects in other particles or channels that precision measurements would already have ruled out.

What would settle it

Absence of any shift or sidereal modulation in the Z mass peak extracted from Drell-Yan events at |Y| > 4 in existing or future LHC data at the stated sensitivity level.

Figures

Figures reproduced from arXiv: 2504.11248 by Juansher Jejelava, Zurab Kepuladze.

Figure 1
Figure 1. Figure 1: (σLIV − σLI )/σLI Y=6 Y=5.5 Y=5 Y=4.5 Y=4 75 80 85 90 95 100 105 GeV -1.0 -0.5 0.0 0.5 1.0 1.5 Δσ/σ, % Mz δLIV= -10-8 Y=6 Y=5.5 Y=5 Y=4.5 Y=4 75 80 85 90 95 100 105 GeV -1.0 -0.5 0.0 0.5 1.0 1.5 Δσ/σ, % Mz δLIV= 10-8 The plot illustrates the difference between σLIV (the Lorentz-violating cross-section) and σLI (the Lorentz-invariant cross-section, equivalent to the Standard Model cross-section). By dividin… view at source ↗
Figure 2
Figure 2. Figure 2: Highly exaggerated comparison of LIV and LI cross-sections. [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes a minimal LIV extension to the SM by adding the term δ_LIV (p_μ n^μ)^2 to the Z-boson dispersion relation p_μ p^μ = M_Z^2. This modifies the Z propagator and decay kinematics in the Drell-Yan channel, producing observable shifts in the apparent Z mass and sidereal modulations at high rapidities (|Y| > 4). The authors outline a targeted ATLAS/CMS search strategy claiming sensitivity down to |δ_LIV| ≈ 10^{-8} (optimistically 10^{-9}) and suggest relevance to historical Tevatron/LHC weak-boson mass discrepancies.

Significance. If the central assumptions hold, the work offers a concrete, falsifiable collider search for LIV in the electroweak sector that exploits existing high-rapidity data and could be implemented with current detectors. The emphasis on sidereal-time dependence and high-|Y| resonance region provides a distinctive experimental signature. The significance is reduced by the absence of explicit compatibility checks with precision low-energy data.

major comments (2)
  1. [Abstract and dispersion-relation definition] The LIV term alters the on-shell condition for any four-momentum, so the partial widths Γ(Z → f f̄) acquire a δ_LIV-dependent correction even for a Z at rest. The manuscript provides no explicit calculation demonstrating that |δ_LIV| ≈ 10^{-8} remains compatible with the LEP total-width measurement (0.1 % precision) for generic n^μ. This compatibility is load-bearing for the claimed sensitivity, because the effect must be invisible at low boost while appearing only at |Y| > 4.
  2. [Search strategy and sensitivity projection] The sensitivity estimate to |δ_LIV| ≈ 10^{-8} is derived from the modified Drell-Yan cross section near resonance without a full propagation of experimental systematics, PDF uncertainties, or background modeling at |Y| > 4. The optimistic 10^{-9} reach is stated without quantitative justification.
minor comments (2)
  1. [Model definition] Define the possible choices (timelike, spacelike, lightlike) for the preferred vector n^μ and show how each produces or suppresses the sidereal modulation.
  2. [Introduction] Clarify whether the same LIV term is assumed to affect only the Z or also the W boson, and state the resulting constraint from W-mass measurements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The two major comments identify genuine gaps in the current manuscript: the lack of an explicit LEP-width compatibility calculation and the preliminary nature of the sensitivity projections. We will revise the paper to address both points directly, adding the required calculations and clarifying the scope of the estimates. No standing objections remain.

read point-by-point responses

  1. Referee: [Abstract and dispersion-relation definition] The LIV term alters the on-shell condition for any four-momentum, so the partial widths Γ(Z → f f̄) acquire a δ_LIV-dependent correction even for a Z at rest. The manuscript provides no explicit calculation demonstrating that |δ_LIV| ≈ 10^{-8} remains compatible with the LEP total-width measurement (0.1 % precision) for generic n^μ. This compatibility is load-bearing for the claimed sensitivity, because the effect must be invisible at low boost while appearing only at |Y| > 4.

    Authors: We agree this is a necessary consistency check. For the spacelike n^μ cases that produce sidereal modulations, the correction to the on-shell condition vanishes at rest (p·n = 0), so the partial widths are unaffected at leading order. For lightlike n^μ a small shift appears. We will add an explicit analytic calculation of the modified Γ(Z → f f̄) in the revised manuscript, demonstrating that |δ_LIV| = 10^{-8} induces a fractional width change ≪ 0.1 % for the n^μ directions under consideration, thereby preserving compatibility with LEP. This calculation will be placed in a new subsection on low-energy constraints. revision: yes

  2. Referee: [Search strategy and sensitivity projection] The sensitivity estimate to |δ_LIV| ≈ 10^{-8} is derived from the modified Drell-Yan cross section near resonance without a full propagation of experimental systematics, PDF uncertainties, or background modeling at |Y| > 4. The optimistic 10^{-9} reach is stated without quantitative justification.

    Authors: We accept that the quoted reaches are indicative order-of-magnitude estimates based solely on the leading modification to the resonant cross section. A complete experimental projection would indeed require full simulation of high-rapidity systematics, PDF uncertainties, and backgrounds, which lies outside the scope of this theoretical proposal. In the revision we will (i) explicitly label both numbers as preliminary, (ii) state the main experimental challenges at |Y| > 4, and (iii) remove or qualify the 10^{-9} figure unless a simple scaling argument can be supplied. The core claim will be reframed as a motivation for a dedicated analysis rather than a finalized sensitivity. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper introduces a new LIV modification to the Z dispersion relation as an ansatz and then computes its consequences for the propagator, decay kinematics, and Drell-Yan cross section at high rapidity. The quoted sensitivity reach |δ_LIV| ≈ 10^{-8} is an order-of-magnitude estimate derived from that model applied to ATLAS/CMS kinematics, not a fit to the same observable or a re-labeling of an input parameter. No self-citations are invoked to justify the central premise, no uniqueness theorem is imported, and the parameter δ_LIV remains free to be bounded by data. The chain therefore contains independent content and does not reduce to its own inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The central claim rests on introducing one new scale parameter and one preferred direction without independent evidence; all other structure is taken from the Standard Model.

free parameters (2)
  • δ_LIV
    Dimensionless coefficient setting the strength of the Lorentz violation term in the Z dispersion relation.
  • n^μ
    Unit four-vector that picks out the preferred direction of the violation.
axioms (1)
  • domain assumption Standard Model Lagrangian for Z boson production and decay in Drell-Yan
    The paper modifies only the dispersion relation while keeping the rest of the SM interaction vertices unchanged.
invented entities (1)
  • LIV term δ_LIV (p·n)^2 no independent evidence
    purpose: To encode a minimal breaking of Lorentz invariance in the Z propagator
    Postulated ad hoc to generate the predicted mass shift and sidereal modulation; no independent evidence or falsifiable prediction outside this model is supplied.

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Reference graph

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