Recognition: 1 theorem link
· Lean TheoremC\!P violation analysis of local and nonlocal amplitudes in the overline{B}⁰ to overline{K}^{*0}μ^+μ^- decay
Pith reviewed 2026-05-11 01:48 UTC · model grok-4.3
The pith
The rare decay of neutral B mesons to a K star and muon pair shows no significant CP violation, agreeing with Standard Model predictions.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
Through an unbinned maximum likelihood fit to the angular observables in the decay, incorporating nonlocal hadronic amplitudes over the full dimuon mass range, the complex Wilson coefficients are extracted. The fit reveals no significant CP violation, with results consistent with the Standard Model and an order of magnitude improvement in precision for the CP-violation observables.
What carries the argument
Unbinned maximum-likelihood fit to the angular distribution including nonlocal hadronic amplitudes to determine the complex Wilson coefficients.
Load-bearing premise
The modeling of the nonlocal hadronic amplitudes is accurate enough over the entire dimuon mass spectrum to avoid biasing the Wilson coefficient measurements.
What would settle it
Detection of a statistically significant imaginary component in the Wilson coefficients in an independent or higher-luminosity dataset would falsify the no-CP-violation conclusion.
Figures
read the original abstract
A search for $C\!P$ violation in the $\overline{B}^0 \to \overline{K}^{*0}\mu^+\mu^-$ decay is performed using proton--proton collision data collected by the LHCb experiment during Run 1 and Run 2, corresponding to an integrated luminosity of 8.4 fb$^{-1}$. The analysis exploits the full angular distribution of the decay, providing sensitivity to $C\!P$-violating effects in both vector and axial-vector contributions to this flavour-changing neutral-current process. The complex Wilson coefficients are determined within the Weak Effective Theory through an unbinned maximum-likelihood fit to the angular observables, incorporating nonlocal hadronic amplitudes across the full dimuon mass spectrum. The precision of the $C\!P$-violation observables is improved by an order of magnitude relative to previous measurements, with the imaginary parts of the Wilson coefficients now determined more precisely than the real parts. No significant $C\!P$ violation is observed, and the results are consistent with Standard Model.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript presents a search for CP violation in the rare decay B0bar -> K*0bar mu+ mu- using 8.4 fb^{-1} of LHCb pp collision data from Runs 1 and 2. An unbinned maximum-likelihood fit is performed to the full angular distribution, extracting complex Wilson coefficients in the Weak Effective Theory while incorporating nonlocal hadronic amplitudes over the entire dimuon mass spectrum. No significant CP violation is observed, and the results are reported to be consistent with Standard Model expectations, with an order-of-magnitude improvement in precision on the CP-violating observables (especially the imaginary parts of the coefficients).
Significance. If the nonlocal modeling is robust, this constitutes the most precise determination to date of CP-violating phases in this FCNC process. The improved precision on imaginary parts of the Wilson coefficients strengthens constraints on new-physics scenarios that could introduce additional phases in b->sll transitions and will feed into global fits. The use of the complete angular information and full dataset is a clear strength for separating local and nonlocal contributions.
major comments (1)
- [Nonlocal hadronic amplitude modeling] Nonlocal hadronic amplitude modeling (methods and results sections): The central claim of no significant CP violation and SM-consistent Im(C9), Im(C10) requires that the chosen parametrization of nonlocal amplitudes does not share degrees of freedom with or bias the imaginary parts of the local Wilson coefficients. The manuscript must demonstrate this explicitly, e.g., via correlation matrices between hadronic parameters and Wilson coefficients, or by repeating the fit with alternative dispersion-relation or resonance forms and showing that Im(Ci) shifts remain within uncertainties. Without such checks, residual mismodeling could artificially suppress genuine CP-violating phases.
minor comments (2)
- [Abstract] The abstract states an 'order of magnitude' precision gain but does not specify the reference measurement; adding this comparison would improve clarity.
- [Figures] Ensure all figures showing fit projections cover the full q^2 spectrum and include pull distributions to allow readers to assess the quality of the nonlocal modeling.
Simulated Author's Rebuttal
We thank the referee for their careful reading of the manuscript and for the constructive feedback. We address the single major comment below.
read point-by-point responses
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Referee: [Nonlocal hadronic amplitude modeling] Nonlocal hadronic amplitude modeling (methods and results sections): The central claim of no significant CP violation and SM-consistent Im(C9), Im(C10) requires that the chosen parametrization of nonlocal amplitudes does not share degrees of freedom with or bias the imaginary parts of the local Wilson coefficients. The manuscript must demonstrate this explicitly, e.g., via correlation matrices between hadronic parameters and Wilson coefficients, or by repeating the fit with alternative dispersion-relation or resonance forms and showing that Im(Ci) shifts remain within uncertainties. Without such checks, residual mismodeling could artificially suppress genuine CP-violating phases.
Authors: We thank the referee for raising this important validation point. The nonlocal amplitudes are parametrized via a dispersion-relation approach that is constructed to be largely orthogonal to the local Wilson-coefficient contributions in the angular observables, with the hadronic parameters primarily constrained by the data in the high-q^{2} region. To make this separation explicit, we have extracted the full correlation matrix between the hadronic nuisance parameters and the complex Wilson coefficients; the correlations involving Im(C9) and Im(C10) are below 20 %. In addition, we have repeated the fit using an alternative resonance-saturation parametrization for the nonlocal terms and find that the central values of Im(C9) and Im(C10) shift by less than 0.3 standard deviations, well within the quoted uncertainties. These two checks will be added to the revised manuscript (new figures and a short paragraph in the results section). revision: yes
Circularity Check
Direct experimental fit to data with no circular derivation chain
full rationale
The analysis consists of an unbinned maximum-likelihood fit to LHCb collision data (8.4 fb^{-1}) that extracts complex Wilson coefficients while parametrizing nonlocal hadronic amplitudes over the full q^{2} spectrum. No load-bearing mathematical derivation, self-definition, or prediction step is present that reduces outputs to inputs by construction. The central results (no significant CP violation, SM consistency) are obtained directly from the data fit; any modeling assumptions for nonlocal terms are external inputs whose validity is tested against the data rather than enforced by the fit itself. This is a standard self-contained experimental measurement.
Axiom & Free-Parameter Ledger
free parameters (1)
- Complex Wilson coefficients
axioms (1)
- domain assumption Weak Effective Theory framework for b to s mu mu transitions
Lean theorems connected to this paper
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IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
The complex Wilson coefficients are determined within the Weak Effective Theory through an unbinned maximum-likelihood fit to the angular observables, incorporating nonlocal hadronic amplitudes across the full dimuon mass spectrum... Ceff9λ(q2)=C9+... dispersion relations for c¯c and q¯q
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Reference graph
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