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arxiv: 2606.07398 · v1 · pith:POEVULCMnew · submitted 2026-06-05 · ✦ hep-ph · hep-ex· hep-lat

Correlating lepton flavor violating b to s and leptonic decay modes in a minimal abelian extension of the Standard Model

Pith reviewed 2026-06-27 21:45 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-lat
keywords lepton flavor violationb to s transitionsZ' bosonabelian extensionbranching ratiosflavor non-universalcorrelationsStandard Model extension
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The pith

In a minimal U(1)' extension of the Standard Model, current bounds on lepton flavor violating decays constrain branching ratios of LFV B(s) decays in a specific hierarchical order.

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

The paper examines a minimal abelian extension of the Standard Model that introduces a new U(1)' symmetry and an associated Z' boson with generation-dependent couplings to fermions. These couplings are controlled by three rational parameters that are identical for all fermions of each generation and sum to zero to cancel anomalies. The shared parameters create direct links between quark and lepton processes, allowing tree-level lepton flavor violating decays. Analysis of the resulting correlations shows that existing experimental upper limits on decays such as tau to three muons and muon to electron photon tightly restrict the allowed rates for lepton flavor violating b to s transitions. The restrictions appear in a clear hierarchical pattern across different B decay modes.

Core claim

In the ABCD model, the neutral Z' boson mediates tree-level lepton flavor violating decays, leading to correlations between LFV b to s ell1 ell2 transitions and purely leptonic LFV processes. The current experimental upper bounds for the rates of tau minus to mu minus mu plus mu minus, mu minus to e minus gamma, mu minus to e minus e plus e minus, and mu minus to e minus conversion in nuclei constrain branching ratios of LFV B(s) decays in hierarchical order.

What carries the argument

Three rational parameters epsilon 1, 2, 3 that set the generation-dependent couplings of the Z' boson to all Standard Model fermions, with each parameter identical across an entire generation and required to sum to zero.

If this is right

  • Lepton flavor violating b to s transitions are directly correlated with purely leptonic flavor violating decays through the shared coupling parameters.
  • Lepton flavor conserving processes exhibit only small deviations from Standard Model predictions because of the mutual constraints between quark and lepton sectors.
  • The hierarchical constraints from lepton data place stronger limits on some LFV B decay channels than on others.
  • Tree-level mediation by the Z' boson permits LFV rates that remain consistent with present bounds but could become accessible with improved experimental sensitivity.

Where Pith is reading between the lines

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

  • Improved limits on muon to electron conversion in nuclei would further tighten the allowed window for specific LFV B decay modes.
  • The model predicts that the strongest constraints on B meson LFV will come from the lepton channels already under tight experimental control.
  • Future measurements of multiple LFV B channels could test whether the observed rates respect the same hierarchy derived from lepton data.

Load-bearing premise

Each of the three parameters applies uniformly to every fermion in its assigned generation.

What would settle it

Measurement of a lepton flavor violating B decay branching ratio that falls outside the hierarchical ordering imposed by the current experimental limits on tau to three muons, muon to electron gamma, and related processes.

Figures

Figures reproduced from arXiv: 2606.07398 by Davide Milillo.

Figure 1
Figure 1. Figure 1: Predictions for the 𝑃-observables in 𝐵¯ → 𝐾¯ ∗ (𝐾𝜋)𝜇 +𝜇 − . The blue curves represent the SM central value, while the cyan band represents NP deviations in the ABCD model for 𝑀𝑍′ = 1 TeV. The experimental data points correspond to the combined Run 1 and 2016 measurements from the LHCb collaboration [22]. Furthermore, we investigate the correlations between LFC 𝐵(𝑠) decays and their LFV counter￾parts, findi… view at source ↗
Figure 2
Figure 2. Figure 2: Correlations between the branching ratios of (left) 𝐵𝑠 → 𝜇 − 𝜇 + and 𝐵𝑠 → 𝜇 − 𝜏 + and of (right) 𝐵¯ → 𝐾¯ ∗𝜇 − 𝜇 + and 𝐵¯ → 𝐾¯ ∗𝜇 − 𝜏 + for 𝑀𝑍′ = 1 TeV obtained after imposing Δ𝐹 = 2 constraints. The shaded vertical band corresponds to the experimental world averages [21]. Finally, we examine the correlations between LFV 𝑏 → 𝑠 transitions and the purely leptonic decay modes. We find that the leptonic modes … view at source ↗
Figure 3
Figure 3. Figure 3: Correlations between branching ratios of LFV 𝐵(𝑠) and leptonic decays. The shaded gray band represents the experimental upper bound quoted in [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Correlations between branching ratios of LFV 𝐵(𝑠) decays when the constraints from LFV lepton decays are successively imposed. The results are shown for 𝑀𝑍′ = 1 TeV (left panel) and 3 TeV (right panel). Acknowledgements D.M. thanks the coauthors of Ref. [2], and A.J. Buras for insightful discussions and valuable advices. This study has been carried out within the INFN project (Iniziativa Specifica) SPIF. 6… view at source ↗
read the original abstract

We examine possible correlations between $b \to s \ell_1^- \ell_2^+$ transitions -- both in the lepton flavor conserving ($\ell_1=\ell_2$) and violating case ($\ell_1 \neq \ell_2$) -- and purely leptonic flavor violating decays within the ABCD model [1], a minimal abelian extension of the Standard Model (SM) introducing a new $\text{U}(1)'$ symmetry. The associated neutral $Z'$ boson has generation-dependent, flavor non-universal couplings to SM fermions, governed by three rational parameters $\epsilon_{1,2,3}$, which sum to zero to ensure gauge anomaly cancellation. Each $\epsilon_i$ is common to all fermions of a given generation, thus inducing correlations among quark and lepton observables. For lepton flavor conserving (LFC) processes, only small deviations from SM predictions were found [2], reflecting the mutual constraints between the quark and lepton sectors, which preclude large discrepancies. On the other hand, the model allows tree-level lepton flavor violating (LFV) decays, yielding correlations between LFV $b\to s$ transitions and charged lepton decays. The analysis of such correlations shows that the current experimental upper bounds for the rates of $\tau^- \to \mu^-\mu^+\mu^-$, \ $\mu^-\to e^- \gamma$, \ $\mu^- \to e^- e^+e^-$ and $\mu^- \to e^-$ conversion in nuclei constrain branching ratios of LFV $B_{(s)}$ decays in hierarchical order [2].

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

1 major / 2 minor

Summary. The paper claims that in the ABCD model, a minimal U(1)' extension of the SM with a Z' boson whose couplings to fermions are governed by three parameters ε1, ε2, ε3 (summing to zero for anomaly cancellation), the fact that each εi is the same for all fermions of a generation leads to correlations between LFV b→s decays and leptonic LFV decays. Consequently, current experimental upper bounds on decays like τ−→μ−μ+μ−, μ−→e−γ, μ−→e−e+e−, and μ−→e− conversion in nuclei constrain the branching ratios of LFV B(s) decays in a hierarchical order.

Significance. If the correlations hold, the work is significant for providing a mechanism to link lepton and quark flavor violation in a minimal model, allowing bounds from well-measured leptonic processes to limit less constrained hadronic ones. The model is minimal and the parameters are rational, which is a strength. The results build on previous papers [1] and [2], so the incremental value is in highlighting the correlations.

major comments (1)
  1. [Abstract] Abstract: The hierarchical constraints on LFV B(s) decays are asserted to follow from the analysis in [2], but the manuscript provides neither the explicit branching-ratio expressions (in terms of the εi) nor the numerical hierarchy. This is load-bearing for the central claim that the leptonic bounds 'constrain branching ratios ... in hierarchical order.'
minor comments (2)
  1. [Abstract] Abstract: The statement that LFC processes yield 'only small deviations from SM predictions' is referenced to [2] without any quantitative comparison or table of values in the present text.
  2. [Abstract] Abstract: Adding a short table or explicit ordering of the constrained LFV B(s) branching ratios would improve readability and allow the reader to assess the hierarchy without consulting [2].

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and the recommendation for minor revision. We address the single major comment below.

read point-by-point responses
  1. Referee: [Abstract] Abstract: The hierarchical constraints on LFV B(s) decays are asserted to follow from the analysis in [2], but the manuscript provides neither the explicit branching-ratio expressions (in terms of the εi) nor the numerical hierarchy. This is load-bearing for the central claim that the leptonic bounds 'constrain branching ratios ... in hierarchical order.'

    Authors: We agree that the manuscript asserts the hierarchical constraints on the basis of the analysis in Ref. [2] without reproducing the explicit branching-ratio expressions in terms of ε1, ε2, ε3 or the associated numerical hierarchy. In the revised version we will add these expressions (derived from the Z' couplings in the ABCD model) together with a short numerical illustration of the resulting hierarchy, either in the main text or as an appendix. This will render the central claim self-contained while leaving the overall scope and conclusions unchanged. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper introduces the ABCD model from [1] with the explicit ansatz that each ε_i is assigned identically to all fermions of a given generation (with ε1 + ε2 + ε3 = 0). This model feature produces tree-level Z' mediated correlations between b → s ℓ1ℓ2 and leptonic LFV processes by construction of the shared couplings; the hierarchical constraints on branching ratios then follow directly from applying experimental bounds to those shared parameters. Self-citations to [1] and [2] serve only to reference the model definition and prior LFC results; they do not substitute for an independent derivation or create a load-bearing self-referential loop. No fitted parameter is renamed as a prediction, no uniqueness theorem is invoked from overlapping authors, and the central claim remains a straightforward model implication rather than a reduction to its own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

Based on abstract only; ledger entries extracted from stated model features.

free parameters (1)
  • ε1, ε2, ε3
    Three rational parameters controlling generation-dependent couplings; sum to zero for anomaly cancellation.
axioms (1)
  • domain assumption Gauge anomaly cancellation requires ε1 + ε2 + ε3 = 0
    Explicitly stated as necessary for the U(1)' extension to be consistent.
invented entities (1)
  • Z' boson no independent evidence
    purpose: Mediator of new U(1)' interactions with flavor non-universal couplings
    Postulated in the ABCD model; no independent evidence or falsifiable prediction outside the model provided in abstract.

pith-pipeline@v0.9.1-grok · 5827 in / 1271 out tokens · 26751 ms · 2026-06-27T21:45:55.025691+00:00 · methodology

discussion (0)

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Reference graph

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