Recognition: 2 theorem links
· Lean TheoremPrecise measurement of the CKM angle γ with a novel approach
Pith reviewed 2026-05-10 18:51 UTC · model grok-4.3
The pith
Combined electron-positron and proton-proton collision data measure the CKM angle gamma to 71.3 degrees with 5 degree uncertainty.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The CKM angle gamma is measured by applying a novel, unbinned, model-independent approach to datasets of electron-positron collisions and proton-proton collisions. The CP-violating phase gamma is determined from B to D to KS0 h prime plus h prime minus h decays, while the corresponding strong-phase parameters are measured using doubly tagged D to KS or L0 h prime plus h prime minus decays in the quantum-correlated D Dbar system. A joint fit to both datasets yields gamma equal to 71.3 degrees plus or minus 5.0 degrees. The result is the most precise to date and consistent with previous measurements and world averages.
What carries the argument
The joint unbinned fit that simultaneously extracts CP-violating observables from B meson decays and strong-phase parameters from quantum-correlated charm decays.
Load-bearing premise
The strong-phase parameters extracted from quantum-correlated charm decays can be transferred directly to the B meson decay analysis without additional model-dependent corrections.
What would settle it
An independent determination of the strong-phase parameters in D to KS h plus h minus decays that differs from those used in the joint fit would shift the extracted value of gamma outside the reported uncertainty.
Figures
read the original abstract
A measurement of the CKM angle $\gamma$ is performed by applying a novel, unbinned, model-independent approach to datasets of electron-positron collisions collected by the BESIII experiment and proton-proton collisions by the LHCb experiment, corresponding to integrated luminosities of 8 fb$^{-1}$ and 9 fb$^{-1}$, respectively. The $C\!P$-violating phase $\gamma$ is determined from ${B^{\pm}\rightarrow D(\rightarrow K_{\rm S}^{0} h^{\prime+}h^{\prime-}) h^{\pm}}$ decays in LHCb data, where $h^{(\prime)}$ is either a pion or kaon, while the corresponding strong-phase parameters are measured using doubly tagged ${D\rightarrow K_{\rm S/L}^0 h^{\prime+} h^{\prime-}}$ decays in the quantum-correlated $D\overline{D}$ system present in BESIII data. A joint fit to both datasets, which allows for a simultaneous determination of the associated $C\!P$-violating observables and strong-phase parameters, yields ${\gamma = (71.3\pm 5.0)^{\circ}}$. The result is the most precise to date and consistent with previous measurements and world averages.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The manuscript presents a novel unbinned model-independent measurement of the CKM angle γ via a joint fit combining BESIII quantum-correlated D Dbar → K_S/L^0 h'+ h'- decays (for strong-phase parameters) with LHCb B± → D(→ K_S^0 h'+ h'-) h± decays (for CP-violating observables), using 8 fb^{-1} and 9 fb^{-1} respectively. The fit yields γ = (71.3 ± 5.0)°, reported as the most precise to date and consistent with prior measurements and world averages.
Significance. If the transferability assumption holds, the result would meaningfully advance precision on γ, strengthening tests of CKM unitarity and new-physics searches. The joint unbinned fit is a genuine methodological advance that simultaneously constrains strong phases and CP observables without additional model dependence.
major comments (1)
- Abstract: the central claim that strong-phase parameters extracted from BESIII e+e- data can be directly transferred to the LHCb pp analysis with no additional model-dependent corrections or environment-specific biases is load-bearing for an unbiased γ. No cross-checks (separate vs. joint fits, or residual Dalitz-plot discrepancies) are described to confirm the shared parameters absorb all differences in production, boosts, acceptances, or efficiencies.
Simulated Author's Rebuttal
We thank the referee for their careful reading of the manuscript and for recognizing the methodological advance represented by the joint unbinned fit. We address the major comment on the transferability of strong-phase parameters below. We agree that additional explicit validation would strengthen the presentation and will incorporate the requested cross-checks in the revised version.
read point-by-point responses
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Referee: Abstract: the central claim that strong-phase parameters extracted from BESIII e+e- data can be directly transferred to the LHCb pp analysis with no additional model-dependent corrections or environment-specific biases is load-bearing for an unbiased γ. No cross-checks (separate vs. joint fits, or residual Dalitz-plot discrepancies) are described to confirm the shared parameters absorb all differences in production, boosts, acceptances, or efficiencies.
Authors: The strong-phase parameters are intrinsic properties of the D → K_S^0 h^+ h^- decay amplitudes and are therefore independent of the production mechanism (e^+e^- at BESIII versus pp at LHCb), the boost, or detector-specific acceptances and efficiencies. These differences are handled through experiment-specific efficiency maps and the unbinned likelihood, which directly incorporates the observed Dalitz-plot distributions from each dataset. The joint fit determines the strong-phase parameters simultaneously with the CP-violating observables, allowing the LHCb data to contribute directly to their constraint and ensuring internal consistency without external model-dependent corrections. We acknowledge that the original manuscript did not include explicit cross-checks such as a comparison of strong-phase parameters from a BESIII-only fit versus the joint fit, or an examination of residual Dalitz-plot discrepancies after efficiency correction. These will be added to the revised manuscript to demonstrate that the shared parameters describe both datasets adequately and that no significant environment-specific biases remain. revision: yes
Circularity Check
No significant circularity in the joint unbinned fit derivation
full rationale
The paper reports an experimental measurement of gamma via a joint unbinned fit to independent BESIII quantum-correlated D Dbar data (for strong-phase parameters) and LHCb B decay data (for CP observables). The abstract and description state that the fit simultaneously determines both sets of parameters from the combined datasets without pre-fixing one from the other or invoking self-citations that reduce the output to an input by construction. No equations are presented that equate the reported gamma value to a fitted input or rename a known result; the derivation remains data-driven and self-contained against external benchmarks.
Axiom & Free-Parameter Ledger
free parameters (1)
- gamma
axioms (1)
- domain assumption Quantum correlations in the D Dbar system at the psi(3770) resonance allow model-independent extraction of strong phases.
Lean theorems connected to this paper
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IndisputableMonolith/Foundation/ArithmeticFromLogic.leanLogicNat recovery and orbit embedding unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
For a Fourier expansion truncating at the order of M, a total of 2 × (2M + 1) weight functions are defined as wn(z) ≡ wopt(z) cos[k ϕ(z)] or sin[k ϕ(z)].
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.
Forward citations
Cited by 1 Pith paper
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Measurement of $\gamma$ using $B^{\pm}\rightarrow DK^{\pm}$ and $B^{\pm}\rightarrow D\pi^{\pm}$ decays with $D\rightarrow K_{\rm S}^{0}\pi^{+}\pi^{-}$ and $D\rightarrow K_{\rm S}^{0}K^{+}K^{-}$
The CKM angle γ is measured to be (68.1 ± 6.7)° from CP violation observed in the Dalitz plots of B± → DK± and B± → Dπ± decays with D → KS0π+π− and KS0K+K−.
Reference graph
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discussion (0)
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