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Method to study $CP$ violation in $B_s^0\to K_S K^\pm \pi^\mp$ decays

T0 review · 0 major / 3 minor · reviewed 2026-06-28 · grok-4.3

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Pith's one-line read A method relates amplitudes across conjugate final states to allow a single tagged time-dependent Dalitz analysis of B_s^0 to K_S K pi decays.

desk verdict This paper sets out a workable method for a simultaneous tagged time-dependent Dalitz fit on the two charge states of Bs to Ks K pi, relating the amplitudes, and shows via pseudoexperiments that decent precision on phi_s^eff is reachable with existing LHCb data. read the letter →

arxiv 2606.06446 v1 pith:TOC3MDJZ submitted 2026-06-04 hep-ph hep-ex

Chen Chen , Tim Gershon , Thomas Latham This is my paper · ORCID
classification hep-phhep-ex
keywords CPviolationB_smesondecaysDalitzplotanalysistime-dependentweakphasemeasurementLHCbexperimentpseudoexperimentsthree-body
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out a procedure for extracting CP-violating phases from B_s^0 decays to K_S K^± π^∓ by running one simultaneous tagged decay-time-dependent Dalitz fit on both charge states. The procedure works by linking the resonant amplitudes that appear in the two final states. Feasibility is shown through pseudoexperiments that track the uncertainty on the effective weak phase φ_s^eff between the mixed and unmixed B_s^0 to K_S K*(892)^0 channels. A reader would care because these decays offer a new window on possible sources of CP violation beyond the Standard Model and the method is already coded for use with real LHCb data.

What carries the argument

The relation that ties resonant amplitudes in the two opposite-charge final states together so one fit can be performed on both at once.

What would settle it

Performing the full analysis on the actual LHCb Runs 1-3 dataset and obtaining an uncertainty on φ_s^eff substantially larger than the pseudoexperiment prediction would show the claimed sensitivity does not hold.

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Extended reading notes

Core claim

The amplitudes for decays to resonances in the K_S K^+ π^- and K_S K^- π^+ final states can be related to each other, making a single simultaneous tagged time-dependent Dalitz analysis valid; pseudoexperiments then show that this analysis reaches good precision on the weak phase difference φ_s^eff with a dataset matching LHCb Runs 1-3.

Load-bearing premise

The amplitudes for decays to resonances in the two final states can be related to each other so that a single simultaneous tagged time-dependent Dalitz analysis is valid.

Editorial extensions

If this is right

  • Good precision on φ_s^eff is reachable with LHCb Runs 1-3 data.
  • Sensitivity improves further with data from future LHCb runs.
  • The same amplitude-relation technique applies to other multibody decays that have multiple final states.
  • The method is already implemented inside the Laura++ Dalitz-plot analysis package.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The approach could be tested on other b to s transition modes where separate analyses of charge states have previously been required.
  • If the amplitude relations hold in data, the method may reduce the impact of certain reconstruction efficiencies that differ between the two final states.
  • Future high-statistics samples could use the same framework to search for direct CP violation in individual resonant contributions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The paper proposes a method for a simultaneous tagged time-dependent Dalitz-plot analysis of B_s^0 → K_S K^+ π^- and B_s^0 → K_S K^- π^+ decays to extract the effective weak phase φ_s^eff between B_s^0 → K_S K*(892)^0 and its charge conjugate, including mixing effects. Amplitudes for resonances in the two final states are related to each other as part of the framework; feasibility is shown via pseudoexperiments, with projected sensitivity to φ_s^eff using LHCb Run 1-3 data (and improvement with future datasets). The method is implemented in the Laura++ package and is intended to be applicable to other multibody decays.

Significance. If the proposed amplitude relations and pseudoexperiment setup hold under realistic conditions, the work enables the first such analysis in this channel, providing a new probe of CP violation in B_s decays that can test the Standard Model and search for new physics. Credit is due for the explicit demonstration of sensitivity via pseudoexperiments and the public implementation in Laura++.

minor comments (3)
  1. The description of the amplitude relations (in the section outlining the method) should include an explicit statement of which resonance parameters are shared versus allowed to float independently, to clarify the degrees of freedom in the simultaneous fit.
  2. Pseudoexperiment results (likely in §4 or the results section) report achievable precision on φ_s^eff but do not tabulate the input values used for background fractions, efficiency parametrization, or resonance model assumptions; adding these would strengthen reproducibility.
  3. The abstract states that the method 'can be applied to other multibody decays,' but the main text does not provide a concrete example or checklist of conditions under which the amplitude relations would generalize; this would aid readers.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, including the significance of the proposed method and the explicit demonstration via pseudoexperiments. The recommendation for minor revision is noted. No specific major comments were provided in the report.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; method proposal is self-contained

full rationale

The paper proposes a tagged time-dependent Dalitz analysis method for B_s^0 → K_S K^± π^∓ decays, relating amplitudes between the two final states as an explicit part of the framework. Feasibility is shown via pseudoexperiments that incorporate these relations by design. No equations reduce a claimed prediction to a prior fit, no self-citation chain supports a load-bearing uniqueness claim, and the sensitivity result on φ_s^eff is obtained from simulation rather than by construction from input parameters. The derivation chain is independent of the target result.

Assumptions & free parameters 0 free parameters · 1 assumptions · 0 invented entities

The central claim rests on standard particle-physics assumptions about resonance amplitudes and B_s mixing; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

assumptions (1)
  • domain assumption Amplitudes for resonances in the two final states can be related by isospin or other standard symmetries
    The method description in the abstract relies on this relation to enable the simultaneous analysis.

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Cite this review

Pith. "Pith review of Method to study $CP$ violation in $B_s^0\to K_S K^\pm \pi^\mp$ decays." pith.science (2026). https://pith.science/paper/TOC3MDJZ

@misc{pith2026260606446,
  author       = {Pith},
  title        = {Pith review of: Method to study $CP$ violation in $B_s^0\to K_S K^\pm \pi^\mp$ decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TOC3MDJZ}},
  note         = {Machine review of arXiv:2606.06446}
}
abstract

The $B_s^0\to K_S K^\pm \pi^\mp$ decays are of interest to test the Standard Model and search for new sources of $CP$ violation. A full study of these decays requires a tagged decay-time-dependent Dalitz-plot analysis performed simultaneously in the two final states. Such an analysis has never previously been performed. The method to carry out such an analysis, relating the amplitudes for decays to resonances in the two final-states to each other, is set out and its feasibility is demonstrated using pseudoexperiments. The sensitivity to the weak phase difference, $\phi_s^{\rm eff}$, between $B_s^0 \to K_S K^*(892)^0$ decays with and without $B_s^0$-$\bar{B}_s^0$ mixing is studied. Good precision on $\phi_s^{\rm eff}$ is found to be achievable with a dataset corresponding to LHCb Runs 1-3, with further improvement expected with datasets to be collected in future. The method is implemented in the Laura++ Dalitz-plot analysis package, and can be applied to other multibody decays with multiple final states.

Figures

Figures reproduced from arXiv: 2606.06446 by the authors.

Figure 1
Figure 1. The SM (a) loop and (b) tree diagrams contributing to the [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Real and imaginary parts of the amplitude coefficients obtained from fits to pseu [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
Figure 3
Figure 3. Distributions of ϕ eff s and phases of ∆c0 and ∆c¯0 determined from fits to pseudoexperi￾ments in Scenario 4 (b), where ∆c¯0 = −0.2, as listed in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Uncertainties on ϕ eff s for a selected set of model configurations listed in [PITH_FULL_IMAGE:figures/full_fig_p012_4.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

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