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arxiv: 2606.00513 · v1 · pith:4M2SRN73new · submitted 2026-05-30 · ✦ hep-ph · hep-ex

Explaining the B to Kμ^+μ^- Anomaly in the Left-Right Inverse Seesaw Model

David Delepine , Shaaban Khalil This is my paper

Pith reviewed 2026-06-28 18:46 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords B to K mu mu anomalyLeft-Right Inverse SeesawWilson coefficientsflavor physicsheavy neutrinoscharged scalarBs mixing
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The pith

The left-right inverse seesaw model generates the observed B to K mu mu anomaly via a non-decoupling charged-scalar and heavy-neutrino box diagram.

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

The paper shows that in the Left-Right Inverse Seesaw model a box diagram with a charged scalar and heavy neutrinos produces the pattern seen in global fits to B to s mu mu data. Right-handed couplings yield an unsuppressed negative shift in the vector Wilson coefficient while a matching left-handed Dirac Yukawa coupling cancels the axial coefficient. A GIM-like phase structure in the right-handed quark mixing matrix suppresses the otherwise large effect on Bs mixing by several orders of magnitude. Numerical scans locate a viable parameter region that satisfies all current flavor and collider bounds, including a comfortable margin on the b to s gamma constraint.

Core claim

A charged-scalar/heavy-neutrino box diagram in the LRIS model naturally generates this pattern through a non-decoupling mechanism: the right-handed coupling produces a contribution to ΔC9 that is unsuppressed in the heavy-neutrino limit, while the simultaneous presence of a comparable left-handed Dirac Yukawa coupling ensures the automatic cancellation ΔC10 ≈ 0. The otherwise large contribution to Bs–B̄s mixing is suppressed by several orders of magnitude through a GIM-like phase structure in the right-handed quark mixing matrix. A numerical scan over the model parameter space identifies a viable region consistent with all current flavor and collider constraints.

What carries the argument

charged-scalar/heavy-neutrino box diagram whose right-handed couplings remain non-decoupling while a GIM-like phase structure in the right-handed quark mixing matrix suppresses Bs mixing

If this is right

  • The diagram produces ΔC9 ≈ -1 with ΔC10 remaining consistent with zero.
  • Bs-Bsbar mixing receives a contribution suppressed by several orders of magnitude.
  • The b to s gamma constraint holds throughout the viable band with two orders of magnitude margin.
  • A viable region of parameter space exists that satisfies all flavor and collider limits.
  • The scenario predicts correlated signals for the charged scalar and heavy right-handed neutrinos at the LHC.

Where Pith is reading between the lines

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

  • The same non-decoupling box could be checked against data on other rare b to s transitions such as B to K* mu mu angular observables.
  • Because the model already incorporates the inverse seesaw for neutrino masses, the same heavy neutrinos may produce additional testable signatures in lepton-flavor violation.
  • Future high-luminosity LHCb runs could distinguish this contribution from other explanations by measuring the precise correlation between ΔC9 and any small residual ΔC10.
  • Extensions that relax the assumed phase structure while retaining the non-decoupling feature could be explored to enlarge the viable space.

Load-bearing premise

The right-handed quark mixing matrix possesses a GIM-like phase structure that suppresses the contribution to Bs-Bsbar mixing by several orders of magnitude.

What would settle it

A measurement of Bs-Bsbar mixing significantly larger than the suppressed value predicted by the model, or the absence of both the charged scalar and heavy neutrinos in LHC searches, would rule out the proposed explanation.

Figures

Figures reproduced from arXiv: 2606.00513 by David Delepine, Shaaban Khalil.

Figure 1
Figure 1. Figure 1: FIG. 1. Summary of the LRIS phenomenology and constraints. (a) Allowed region in the [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
read the original abstract

We investigate the long-standing anomaly in the rare decay B into Kll within the Left-Right Inverse Seesaw (LRIS) model. Global analyses of the B into s mu mu data consistently indicate a significant negative shift in the vector Wilson coefficient, $\Delta C{9} \approx -1$, while the axial coefficient $\Delta C{10}$ remains consistent with zero. We show that a charged-scalar/heavy-neutrino box diagram in the LRIS model naturally generates this pattern through a \emph{non-decoupling} mechanism: the right-handed coupling produces a contribution to $\Delta C{9}$ that is unsuppressed in the heavy-neutrino limit, while the simultaneous presence of a comparable left-handed Dirac Yukawa coupling ensures the automatic cancellation $\Delta C{10} \approx 0$. The otherwise large contribution to $B_s$--$\bar{B}_s$ mixing is suppressed by several orders of magnitude through a GIM-like phase structure in the right-handed quark mixing matrix. A numerical scan over the model parameter space identifies a viable region, consistent with all current flavor and collider constraints. The $b \to s\gamma$ constraint is satisfied with two orders of magnitude to spare throughout the viable band. These results motivate correlated searches for the charged scalar and the heavy right-handed neutrinos at the LHC and future high-luminosity experiments.

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 / 1 minor

Summary. The manuscript proposes an explanation for the B → Kμ⁺μ⁻ anomaly within the Left-Right Inverse Seesaw (LRIS) model. It argues that a charged-scalar/heavy-neutrino box diagram produces a non-decoupling contribution to ΔC9 ≈ −1 while automatically canceling ΔC10 through comparable left- and right-handed couplings. The large contribution to Bs–B̄s mixing is claimed to be suppressed by a GIM-like phase structure in the right-handed quark mixing matrix, with a numerical scan identifying a viable parameter region consistent with constraints.

Significance. If the central mechanism holds, the result would be significant as it offers a model-specific resolution to the observed pattern in b→sℓℓ data (ΔC9 negative, ΔC10 zero) without conflicting with Bs mixing or b→sγ constraints. The non-decoupling feature and automatic cancellation are potentially attractive features, and the motivation for LHC searches for the charged scalar and heavy neutrinos is a positive aspect.

major comments (2)
  1. [Abstract] Abstract: The suppression of the Bs–B̄s mixing contribution by 'several orders of magnitude through a GIM-like phase structure in the right-handed quark mixing matrix' is presented as a key feature, but the abstract provides no derivation showing how this phase structure emerges from the LRIS Lagrangian or whether it requires tuning of the free parameters (right-handed Yukawa couplings, heavy neutrino masses, right-handed quark mixing phases). This assumption is load-bearing for the viability claim.
  2. [Abstract] Abstract: No explicit equations or derivation steps are provided for the box diagram contributions to the Wilson coefficients or the mixing suppression, making it impossible to verify the non-decoupling mechanism or the automatic ΔC10 cancellation from the given text.
minor comments (1)
  1. The abstract mentions a numerical scan but does not specify the scanned parameters or the range, nor any error analysis or fit quality metrics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thoughtful comments on our manuscript. The points raised concern the level of detail provided in the abstract regarding the GIM-like suppression mechanism and the box-diagram derivations. We agree these aspects of the abstract can be strengthened for clarity while preserving its summary nature, and we have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The suppression of the Bs–B̄s mixing contribution by 'several orders of magnitude through a GIM-like phase structure in the right-handed quark mixing matrix' is presented as a key feature, but the abstract provides no derivation showing how this phase structure emerges from the LRIS Lagrangian or whether it requires tuning of the free parameters (right-handed Yukawa couplings, heavy neutrino masses, right-handed quark mixing phases). This assumption is load-bearing for the viability claim.

    Authors: We agree the abstract is too concise on this point. The phase structure originates directly from the right-handed quark mixing matrix defined by the LRIS Lagrangian (see Section 3), where the GIM-like cancellations arise from the specific texture of the right-handed Yukawa couplings without additional tuning. The numerical scan in Section 5 confirms the suppression holds generically in the viable region. We will revise the abstract to briefly note the Lagrangian origin of the phase structure and reference the relevant section. revision: yes

  2. Referee: [Abstract] Abstract: No explicit equations or derivation steps are provided for the box diagram contributions to the Wilson coefficients or the mixing suppression, making it impossible to verify the non-decoupling mechanism or the automatic ΔC10 cancellation from the given text.

    Authors: The abstract is a high-level overview and omits equations by design. The explicit box-diagram expressions for ΔC9 and ΔC10 (including the non-decoupling limit and left-right cancellation), the relevant Feynman rules, and the loop functions are derived in Section 2. The Bs mixing suppression is quantified with explicit formulas in Section 4. To improve accessibility, we will update the abstract to include a short reference to these sections for the key mechanisms. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on explicit model calculations and parameter scan.

full rationale

The paper calculates contributions to Wilson coefficients from a specific box diagram in the LRIS model, attributes ΔC9 generation to non-decoupling right-handed couplings, and notes ΔC10 cancellation when left-handed Yukawa is comparable (a parameter choice within the scanned space). Bs mixing suppression is ascribed to phases in the right-handed quark mixing matrix, also part of the scanned parameters. No quoted equation or step reduces a claimed prediction to an input by construction, nor does any load-bearing claim rest solely on unverified self-citation. The viable region is identified numerically rather than forced by definition. This is a standard model accommodation analysis.

Axiom & Free-Parameter Ledger

3 free parameters · 2 axioms · 2 invented entities

The central claim rests on the LRIS model framework, the existence of suitable right-handed couplings and phases, and the validity of the numerical scan over parameter space; these are not derived from first principles in the abstract.

free parameters (3)
  • right-handed Yukawa couplings
    Adjusted to produce the required unsuppressed ΔC9 contribution in the heavy neutrino limit.
  • heavy neutrino masses
    Taken in the non-decoupling regime to maintain the box diagram contribution.
  • right-handed quark mixing phases
    Chosen to implement the GIM-like suppression of Bs mixing.
axioms (2)
  • domain assumption The Left-Right Inverse Seesaw model is a valid extension of the Standard Model.
    The entire analysis is performed inside this framework.
  • domain assumption Numerical scan over model parameters can identify regions consistent with all constraints.
    The viable region is reported from such a scan.
invented entities (2)
  • charged scalar no independent evidence
    purpose: Mediates the box diagram contributing to the Wilson coefficients.
    Introduced as part of the LRIS model to generate the anomaly pattern.
  • heavy right-handed neutrinos no independent evidence
    purpose: Participate in the non-decoupling box diagram and inverse seesaw mechanism.
    Core component of the LRIS model used for the explanation.

pith-pipeline@v0.9.1-grok · 5790 in / 1672 out tokens · 30731 ms · 2026-06-28T18:46:49.461059+00:00 · methodology

discussion (0)

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Forward citations

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