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Taming Penguins: Towards High Precision Measurements in $\phi_d$ and $\phi_s$

T0 review · 2 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Penguin control sets B-meson CP phases at 45.6 and -3.72 degrees.

desk verdict Solid proceedings-style update of the SU(3) penguin-control framework with new LHCb/Belle-II data; the numbers are plausible but the SU(3)-breaking systematic remains a hand-assigned prior rather than a derived uncertainty. read the letter →

arxiv 2501.09414 v1 pith:OZTDBCTP submitted 2025-01-16 hep-ph

Kristof De Bruyn , Robert Fleischer , Eleftheria Malami This is my paper · ORCID
classification hep-ph PACS 13.25.Hw11.30.Hv
keywords penguintopologiesSU(3)flavoursymmetryCPviolationB-mesonmixingphasescontrolmodesJ/psiK_S^0decaysphiD_s^+D_s^-
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

These proceedings show how to remove the hadronic 'penguin' pollution that currently limits how accurately the B-meson mixing phases $\phi_d$ and $\phi_s$ can be extracted from CP-asymmetry measurements. The method uses the approximate SU(3) flavour symmetry of the strong force to connect the three 'golden' channels $B_d^0\to J/\psi K_S^0$, $B_s^0\to J/\psi\phi$, and $B_s^0\to D_s^+ D_s^-$ to control channels in which penguin effects are enhanced, and then fits all seven channels simultaneously. With the latest CP-asymmetry measurements included, the corrected phases become $\phi_d=(45.6^{+1.1}_{-1.0})^\circ$ and $\phi_s=(-3.72^{+1.09}_{-0.97})^\circ$, with an extra systematic from SU(3) breaking of $0.3^\circ$ and $0.11^\circ$, respectively. These phases are among the cleanest probes of new physics, and the penguin shift was becoming the leading obstacle to using them at full precision.

What carries the argument

The machinery is the amplitude decomposition $A = \mathcal{N}\left(1 + \epsilon a e^{i\theta} e^{i\gamma}\right)$, where $\epsilon\approx0.052$ is a known ratio of Cabibbo-like factors, $a$ and $\theta$ parametrise the size and strong phase of the penguin topology relative to the tree, and $\gamma$ is the unitarity-triangle angle. Its key property is that the CP asymmetries are ratios of amplitudes, so the normalisation $\mathcal{N}$ drops out and all factorisable SU(3) breaking cancels. The paper then uses SU(3) symmetry to identify $a$ and $\theta$ for each golden mode with the corresponding parameters in its control mode(s), turning a fit of seven CP-asymmetry measurements into a simultaneous determination of $\phi_d$, $\phi_s$, and the three penguin pairs; non-factorisable SU(3) breaking is folded in as external Gaussian corrections with means $x=1.2$, $y=20^\circ$ and widths $0.2$, $20^\circ$.

What would settle it

A first-principles lattice QCD computation of the ratio of penguin-over-tree matrix elements in a control mode relative to its golden mode, returning $x>1.4$ or $|y|>40^\circ$, would shift the fitted phases by more than the quoted $0.3^\circ$ and $0.11^\circ$ systematics; alternatively, separate high-statistics fits of the two $J/\psi$ control modes that yield mutually incompatible $(a,\theta)$ values would break the SU(3) link.

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Extended reading notes

Core claim

This paper establishes that the hadronic phase shifts $\Delta\phi_d$ and $\Delta\phi_s$ produced by penguin topologies in the golden decays can be pinned down from data rather than treated as theory errors. Writing each decay amplitude as $A = \mathcal{N}\left(1 + \epsilon a e^{i\theta} e^{i\gamma}\right)$ with $\epsilon\approx0.052$, and using a simultaneous fit to the direct and mixing-induced CP asymmetries in all seven channels, it obtains penguin parameters $a_{J/\psi P}=0.14^{+0.14}_{-0.09}$ with strong phase $\theta_{J/\psi P}=(167^{+21}_{-32})^\circ$, $a_{J/\psi V}=0.052^{+0.092}_{-0.045}$ with $\theta_{J/\psi V}=(317^{+38}_{-120})^\circ$, and $a_{DD}=0.007^{+0.054}_{-0.007}$ with $\theta_{DD}=(350^{+10}_{-350})^\circ$. Subtracting the implied shifts from the measured effective phases then yields the state-of-the-art values $\phi_d=(45.6^{+1.1}_{-1.0})^\circ$ and $\phi_s=(-3.72^{+1.09}_{-0.97})^\circ$; the additional SU(3)-breaking systematic, estimated by injecting Gaussian factors $x=1.2\pm0.2$ and $y=(20\pm20)^\circ$, is $0.3^\circ$ and $0.11^\circ$.

Load-bearing premise

The control modes and the golden modes are supposed to share the same penguin-to-tree ratio of hadronic matrix elements under the approximate SU(3) flavour symmetry, with non-factorisable symmetry-breaking corrections small enough to be covered by the assumed Gaussian factors.

Editorial extensions

If this is right

  • The corrected values in Eq. (7), not the raw effective phases of Eq. (8), are the ones to compare against Standard Model predictions.
  • Updating the penguin control modes is projected to reduce the $\phi_d$ uncertainty by up to a factor of two beyond golden-mode-only improvements, with an additional 15-30% gain for $\phi_s$.
  • The new SU(3)-breaking systematics of $0.3^\circ$ ($\phi_d$) and $0.11^\circ$ ($\phi_s$) are small enough that the bottleneck for reaching the planned sub-degree precision is the control-mode measurements themselves.
  • The fitted penguin parameters $a$ and $\theta$ are physical outputs that can be cross-checked with model calculations or used in other $B$-decay channels carrying the same topology.

Reading between the lines

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

  • The near-zero fitted value $a_{DD}=0.007^{+0.054}_{-0.007}$ suggests that $B_s^0\to D_s^+D_s^-$ may already be almost free of penguin contamination, and if this persists with more data it could become a nearly clean anchor for $\phi_s$.
  • Leaving the angle $\gamma$ free in the same simultaneous fit would turn this penguin-control analysis into an independent determination of the unitarity-triangle angle, at the cost of larger uncertainties.
  • A dedicated calculation of the non-factorisable SU(3)-breaking ratios, for example on the lattice, would convert the assumed Gaussian systematics into a first-principles uncertainty and directly test the 0.3°/0.11° assignments.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 4 minor

Summary. The paper presents an updated extraction of the penguin parameters and the CP-violating mixing phases phi_d and phi_s from a global fit to CP asymmetries in seven B-meson decay channels: the golden modes B_d -> J/psi K_S, B_s -> J/psi phi, B_s -> D_s^+ D_s^- and their SU(3)-related control modes. Using the GammaCombo framework and fixing the CKM angle gamma to the HFLAV value, the authors obtain a_JpsiP = 0.14+0.14-0.09, a_JpsiV = 0.052+0.092-0.045, a_DD = 0.007+0.054-0.007, and the corrected phases phi_d = (45.6+1.1-1.0) degrees and phi_s = (-3.72+1.09-0.97) degrees, quoted with additional SU(3)-breaking systematics of 0.3 degrees and 0.11 degrees (Eqs. (7), (9), (10)). The paper also presents projections for the end of the HL-LHC and Belle-II programmes.

Significance. If the quoted uncertainties are reliable, the results are a valuable step toward precision tests of the CKM picture in B decays: the data-driven SU(3) control-mode strategy is well established, and the inclusion of the new LHCb B->DD and Belle-II B->J/psi pi0 measurements sharpens the constraints on penguin pollution. The statistical procedure is standard and uses the public GammaCombo framework. The main limitation is that the dominant systematic (non-factorisable SU(3) breaking) is estimated from hypothetical Gaussian pulls rather than derived from QCD, and the paper does not show how the result depends on the assumed size or correlation of the breaking. The future projections are informative but appear to include only experimental uncertainties.

major comments (2)
  1. [Sec. 3, Eqs. (9)-(10)] The SU(3)-breaking systematic is assigned from a single hypothetical scenario (x_SU(3)=1.2±0.2, y_SU(3)=(20±20) degrees) applied identically to the penguin parameters a and theta in all three sectors. This is not a derived estimate of non-factorisable breaking, and the paper does not test how phi_d and phi_s shift as a function of x and y, under larger breaking, or under mode-dependent or correlated breaking. The statement that there is "almost no impact" for the tested choices does not bound the true error. Since these systematics enter the headline results in Eqs. (9)-(10), the authors should either provide a QCD-based estimate of the non-factorisable breaking for each sector or scan a physically motivated range of x and y (including correlations) and report the resulting shifts.
  2. [Sec. 3, Eq. (3) and surrounding discussion] The claim that factorisable SU(3) breaking "necessarily drop[s] out" because the CP asymmetries are ratios of decay amplitudes is too strong. The normalisation N in Eq. (3) cancels in the CP asymmetry of a single decay, but the SU(3) relation between a golden mode and its control mode involves the relative size of tree and penguin hadronic matrix elements; factorisable breaking can enter that ratio (e.g., through different decay constants or form factors in the two modes) and thereby modify a. The manuscript should specify how factorisable breaking is treated in the amplitude relations and, if it is neglected, include it in the systematic uncertainty.
minor comments (4)
  1. [Eq. (8)] The value of phi_eff_s is written as (3.50±0.80) degrees, but -0.061 rad corresponds to -3.50 degrees; a minus sign is missing.
  2. [Sec. 2, Eqs. (4)-(6)] The fitted parameter theta_DD has a huge uncertainty (350^{+10}_{-350} degrees), spanning nearly the full angular range; the paper should comment on whether this indicates that the DD sector barely constrains the penguin phase.
  3. [Sec. 3, Fig. 3] The caption of Fig. 3 does not define the correction factors x and y; the reader should not have to consult the text to understand the scenarios.
  4. [Abstract and Sec. 1] The abstract calls B_d -> J/psi K_S and B_s -> J/psi phi the "golden modes", but the paper also treats B_s -> D_s^+ D_s^- as a golden mode; this terminology should be made consistent.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the corrected phi_d and phi_s are outputs of a global fit to external CP-asymmetry measurements, and the SU(3)-breaking systematics are external sensitivity priors, not fitted inputs.

full rationale

The paper's central derivation is a simultaneous GammaCombo fit to the direct and mixing-induced CP asymmetries in seven B-decay channels, with the penguin parameters (a_J/psiP, theta_J/psiP, a_J/psiV, theta_J/psiV, a_DD, theta_DD) and the phases (phi_d, phi_s) as fit parameters. The inputs are independent experimental measurements from Belle-II, LHCb, and HFLAV, plus the externally taken CKM angle gamma. The system has more observables than unknown parameters, so the resulting phases are constrained estimates rather than quantities imposed by construction. The quoted corrected values in Eqs. (7), (9), and (10) are therefore not predictions drawn from the same fitted values; they are the maximum-likelihood outputs of an over-constrained fit. The SU(3)-breaking systematic is estimated in Sec. 3 by comparing the nominal fit with hypothetical Gaussian pulls x=1.2+/-0.2 and y=(20+/-20) degrees; the text explicitly says these are 'hypothetical scenarios' and 'not free parameters in the model,' so the resulting 0.3 degree and 0.11 degree uncertainties are sensitivity estimates based on an external assumption, not a fitted input renamed as a prediction. The self-citations to Refs. [5,8,9,13] introduce the amplitude parametrization in Eq. (3) and the control-mode strategy, but the numerical content of the paper is grounded in external data, and no uniqueness theorem or unverified prior result is invoked as the load-bearing justification. No specific equation or step in the paper reduces, by construction, to its own input.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central results depend on six penguin parameters fitted to data, plus the SU(3) symmetry and amplitude-parametrization assumptions inherited from the framework. No new particles or entities are introduced.

free parameters (6)
  • a(J/psi P) = 0.14 +0.14 -0.09
    Relative penguin amplitude for B_d -> J/psi K_S and its control modes, fitted in the extended fit (Eq. 4).
  • theta(J/psi P) = (167 +21 -32) deg
    Strong phase of penguin amplitude for the J/psi P class, fitted in the extended fit (Eq. 4).
  • a(J/psi V) = 0.052 +0.092 -0.045
    Relative penguin amplitude for B_s -> J/psi phi, fitted in the extended fit (Eq. 5).
  • theta(J/psi V) = (317 +38 -120) deg
    Strong phase of penguin amplitude for the J/psi V class, fitted in the extended fit (Eq. 5).
  • a(DD) = 0.007 +0.054 -0.007
    Relative penguin amplitude for B_s -> D_s+ D_s-, fitted in the extended fit (Eq. 6).
  • theta(DD) = (350 +10 -350) deg
    Strong phase of penguin amplitude for the DD class, fitted in the extended fit (Eq. 6).
assumptions (4)
  • domain assumption SU(3) flavour symmetry relates hadronic matrix elements of the golden modes and control modes.
    Invoked in Sec. 2 and 3 to transfer penguin parameters from control modes to the final-state classes.
  • domain assumption Factorisable SU(3) breaking cancels in CP asymmetries.
    Sec. 3: 'Because the CP asymmetries are ratios of decay amplitudes, any factorisable SU(3)-breaking effects, which impact the normalisation N in Eq. (3), necessarily drop out.'
  • domain assumption The decay amplitudes are parametrized by a single dominant tree plus one penguin term (Eq. 3), with other topologies neglected.
    Sec. 2 introduces Eq. (3); the analysis ignores exchange, annihilation, and other sub-sub-leading contributions.
  • domain assumption The UT angle gamma is taken from external HFLAV average as input.
    Sec. 2: 'The UT angle gamma = (65.6 +2.9 -3.0) deg is taken as external input.'

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Cite this review

Pith. "Pith review of Taming Penguins: Towards High Precision Measurements in $\phi_d$ and $\phi_s$." pith.science (2026). https://pith.science/paper/OZTDBCTP

@misc{pith2026250109414,
  author       = {Pith},
  title        = {Pith review of: Taming Penguins: Towards High Precision Measurements in $\phi_d$ and $\phi_s$},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OZTDBCTP}},
  note         = {Machine review of arXiv:2501.09414}
}
abstract

Experimentally, the phases $\phi_d$ and $\phi_s$ are determined from CP asymmetry measurements in the "golden modes" $B_d^0\to J/\psi K_{\mathrm{S}}^0$ and $B_s^0\to J/\psi\phi$. At leading order, the theoretical interpretation of these measurements is straightforward. However, to reach high precision determinations of $\phi_d$ and $\phi_s$, which is essential in view of the searches for signs of beyond the SM physics, corrections from next-to-leading order effects need to be accounted for. These corrections primarily originate from so-called penguin topologies. Using the $SU(3)$ flavour symmetry, these corrections can be determined using suitably chosen control modes. Recent new CP asymmetry measurements from LHCb in $B\to DD$ and Belle-II in $B_d^0\to J/\psi\pi^0$ decays greatly improve our knowledge on the parameters describing the contribution from penguin topologies. These proceedings will discuss the current constraints on the penguin parameters in $B\to J/\psi X$ and $B\to DD$ decays, provide corrected determinations for $\phi_d$ and $\phi_s$, and highlight what can be expected at the end of the HL-LHC and Belle-II programmes.

Figures

Figures reproduced from arXiv: 2501.09414 by the authors.

Figure 1
Figure 1. Schematic overview of the seven considered decay channels and their interdependence. 2. Fit for the penguin parameters The impact on the determination of 𝜙𝑑 and 𝜙𝑠 from the penguin topologies in the 𝐵 0 𝑑 → 𝐽/𝜓𝐾0 S , 𝐵 0 𝑠 → 𝐽/𝜓𝜙 and 𝐵 0 𝑠 → 𝐷 + 𝑠 𝐷 − 𝑠 decays is determined following the framework described in Refs. [5, 13]. For each of the three decays, the decay amplitude is parametrised as 𝐴(𝐵 0 𝑞 → 𝑓 ) = N  1 +… view at source ↗
Figure 2
Figure 2. Two-dimensional confidence regions of the fit for the penguin parameters, 𝜙𝑑 and 𝜙𝑠 from the measured CP asymmetries in the 𝐵 → 𝐽/𝜓𝑋 and 𝐵 → 𝐷𝐷 decays. Note that the contours for Adir CP and Amix CP are added for illustration only. They include the best fit solutions for 𝜙𝑑, 𝜙𝑠 and 𝛾 as Gaussian constraints. In the first scenario we expect an improvement in the determination of 𝜙𝑑 by approximately 30% compared to to… view at source ↗
Figure 3
Figure 3. Two-dimensional confidence regions of the fit for 𝜙𝑑 and 𝜙𝑠 from the measured CP asymmetries in the 𝐵 → 𝐽/𝜓𝑋 and 𝐵 → 𝐷𝐷 decays, assuming different 𝑆𝑈(3)-breaking scenarios. The 𝑆𝑈(3)-breaking effects are included as Gaussian constraints in the fit, and not free parameters in the model [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Two-dimensional confidence regions of the fit for the penguin parameters, 𝜙𝑑 and 𝜙𝑠 from potential future CP asymmetry measurements in the 𝐵 → 𝐽/𝜓𝑋 and 𝐵 → 𝐷𝐷 decays. Comparison between the two future scenarios for the expected situation after the end of the Belle-II a…

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