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arxiv: 2604.19612 · v2 · submitted 2026-04-21 · ✦ hep-ph · hep-ex

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QCD-factorization amplitudes from flavour symmetries: beyond the SU(3) symmetric case

Wen-Sheng Fang , Tobias Huber , Xin-Qiang Li , Eleftheria Malami , Gilberto Tetlalmatzi-Xolocotzi
Authors on Pith no claims yet

Pith reviewed 2026-05-10 02:13 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords B meson decaysSU(3) breakingQCD factorizationcharmless decaysCP asymmetriesnon-leptonic decaysflavour symmetriesannihilation amplitudes
0
0 comments X

The pith

Data-driven fits with SU(3) breaking in form factors and constants produce QCD-factorization amplitudes that match dynamical predictions for B to PP decays.

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

The paper performs a fit to measured branching ratios and CP asymmetries in charmless B decays to two light pseudoscalars. SU(3) flavour symmetry breaking is introduced only through transition form factors, decay constants, and phase-space factors rather than in the amplitudes themselves. The resulting best-fit amplitudes show central values that align closely with those obtained from full QCD-factorization calculations. The fit finds no indication that annihilation amplitudes are larger than the naive power-counting expectation of order Lambda_QCD over m_b. This framework is then applied to several long-standing flavour puzzles in non-leptonic B physics.

Core claim

Implementing flavour-SU(3) breaking at the level of transition form factors, decay constants and phase space factors, we find a good fit to the current experimental data. Our best-fit point materializes in QCD-factorization amplitudes whose central values resemble many features of the dynamical predictions obtained within the QCD factorization framework. Moreover, we do not find any strong indications that the size of annihilation amplitudes is numerically enhanced beyond the naïve ΛQCD/mb scaling.

What carries the argument

The data-driven extraction of QCD-factorization amplitudes from experimental branching ratios and CP asymmetries, with SU(3) breaking inserted only in form factors, decay constants, and phase space.

If this is right

  • The fitted amplitudes can be used directly for predictions in additional charmless B decay channels.
  • Standard power counting for annihilation topologies receives support from the absence of numerical enhancement.
  • Long-standing flavour puzzles in non-leptonic B decays become addressable within a single consistent framework.
  • The approach supplies a hybrid symmetry-plus-dynamical template that can be tested against future data.

Where Pith is reading between the lines

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

  • Repeating the fit with updated experimental inputs would test whether the resemblance to QCD-factorization amplitudes persists.
  • Extending the same breaking prescription to related processes such as B to PV decays could reveal whether the pattern is universal.
  • If the fitted annihilation terms remain small, this would favour theoretical models that keep annihilation suppressed by the heavy-quark mass.

Load-bearing premise

That all relevant SU(3) breaking effects in the data are captured by modifications to form factors, decay constants and phase space alone, without further breaking needed inside the amplitudes.

What would settle it

New precision measurements of branching fractions or CP asymmetries in B to PP modes that lie systematically outside the range allowed by varying the fitted parameters within their quoted uncertainties.

read the original abstract

Using experimental information on branching ratios as well as direct and mixing-induced CP asymmetries, we perform a data-driven analysis of charmless non-leptonic $B \to PP$ decays, where $P$ is any of the light pseudoscalar mesons. Implementing flavour-$SU(3)$ breaking at the level of transition form factors, decay constants and phase space factors, we find a good fit to the current experimental data. Our best-fit point materializes in QCD-factorization amplitudes whose central values resemble many features of the dynamical predictions obtained within the QCD factorization framework. Moreover, we do not find any strong indications that the size of annihilation amplitudes is numerically enhanced beyond the na\"ive $\Lambda_{\textrm{QCD}}/m_b$ scaling. Subsequently, we address a number of phenomenological applications, among which are various flavour puzzles that have been persisting in non-leptonic $B$ decays for quite some time.

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 / 2 minor

Summary. The paper conducts a data-driven analysis of charmless non-leptonic B → PP decays by fitting branching ratios and CP asymmetries while incorporating SU(3) flavour breaking only through transition form factors, decay constants, and phase-space factors. The resulting best-fit amplitudes are reported to closely resemble central values from QCD factorization (QCDF) calculations, with no strong evidence found for annihilation amplitudes exceeding the naive Λ_QCD/m_b scaling. The work then applies these amplitudes to longstanding flavour puzzles in B decays.

Significance. If the fit is demonstrably well-constrained and the resemblance to QCDF holds under explicit error propagation, the approach would provide a useful symmetry-based bridge to dynamical predictions, helping quantify the size of annihilation contributions and potentially resolving patterns in non-leptonic B data without invoking large non-factorizable effects.

major comments (2)
  1. [§4 (best-fit results and annihilation discussion)] The claim that annihilation amplitudes show no strong enhancement beyond naïve scaling (abstract and §4) rests on the best-fit point obtained after implementing SU(3) breaking solely via form factors, decay constants and phase space. However, with multiple topological amplitudes still related by approximate SU(3) and only a small number of free parameters reported, it is unclear whether the data tightly bound the annihilation magnitude or whether values several times larger remain compatible within the allowed parameter volume.
  2. [§3 (amplitude extraction) and §5 (comparison)] The reported resemblance between the fitted amplitudes and QCDF predictions is obtained by fitting directly to the same experimental branching ratios and CP asymmetries used to define the amplitudes. This introduces a circularity risk: the agreement may be driven by the fit rather than providing an independent test of QCDF features.
minor comments (2)
  1. [§3] Explicitly state the total number of free parameters, the χ²/dof value, the precise data set (including which measurements are included or excluded), and the treatment of experimental and theoretical uncertainties.
  2. [§2] Clarify the precise implementation of SU(3) breaking in the form factors and decay constants, including any assumed relations or additional parameters introduced beyond the minimal set.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We address the two major points raised below and have revised the manuscript to strengthen the presentation of our results and clarify the methodology.

read point-by-point responses

  1. Referee: [§4 (best-fit results and annihilation discussion)] The claim that annihilation amplitudes show no strong enhancement beyond naïve scaling (abstract and §4) rests on the best-fit point obtained after implementing SU(3) breaking solely via form factors, decay constants and phase space. However, with multiple topological amplitudes still related by approximate SU(3) and only a small number of free parameters reported, it is unclear whether the data tightly bound the annihilation magnitude or whether values several times larger remain compatible within the allowed parameter volume.

    Authors: We agree that the constraints on the annihilation amplitudes deserve explicit demonstration beyond the best-fit point. Our fit employs a modest number of free parameters under the approximate SU(3) relations, and the data on branching ratios together with CP asymmetries across multiple channels do constrain the annihilation contributions. In the revised manuscript we have added a discussion of the fit uncertainties on the annihilation amplitudes and a short parameter scan showing that values several times larger than the naive scaling lead to a significant deterioration in fit quality. This makes the bounds explicit and addresses the concern about the allowed parameter volume. revision: yes

  2. Referee: [§3 (amplitude extraction) and §5 (comparison)] The reported resemblance between the fitted amplitudes and QCDF predictions is obtained by fitting directly to the same experimental branching ratios and CP asymmetries used to define the amplitudes. This introduces a circularity risk: the agreement may be driven by the fit rather than providing an independent test of QCDF features.

    Authors: We acknowledge the referee's point on potential circularity. Our extraction determines the topological amplitudes solely from flavour-SU(3) relations (with breaking implemented only through form factors, decay constants and phase space) and does not assume any dynamical content from QCD factorization. The QCDF predictions, by contrast, arise from an independent perturbative framework with its own non-perturbative inputs. The observed agreement is therefore a non-trivial consistency check between a symmetry-based data analysis and a dynamical model. We have revised the text in §§3 and 5 to emphasize this distinction and to present the comparison explicitly as a test of whether the data-driven amplitudes align with QCDF expectations. revision: partial

Circularity Check

0 steps flagged

No circularity: data-driven fit yields amplitudes compared to independent QCDF framework

full rationale

The paper performs a fit of a flavour-SU(3) parametrization (with breaking inserted only via form factors, decay constants and phase space) directly to external experimental inputs consisting of branching ratios, direct CP asymmetries and mixing-induced CP asymmetries. The best-fit point is then inspected and observed to produce amplitude values whose central numbers resemble features of separate QCD-factorization calculations. This resemblance is a post-hoc comparison between two distinct approaches (symmetry-based fit versus dynamical QCDF), not a reduction of one to the other by construction. The statement that annihilation amplitudes show no strong enhancement beyond naive scaling is likewise a direct consequence of the fit not requiring large values, without any self-referential loop or fitted parameter being relabelled as a prediction. No equation or claim equates the output to the input; the derivation chain remains self-contained against the external data benchmark.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on a multi-parameter fit to branching ratios and CP asymmetries, with SU(3) symmetry as the organizing principle and QCD factorization used only for post-fit comparison.

free parameters (2)
  • SU(3) breaking parameters in form factors and decay constants
    Introduced to account for quark-mass differences and fitted to data.
  • Annihilation amplitude magnitudes
    Constrained by the global fit but not forced to be enhanced.
axioms (2)
  • domain assumption SU(3) flavor symmetry is a good approximate symmetry for light pseudoscalar mesons, broken primarily by quark masses
    Standard assumption in flavor physics invoked to organize the amplitudes.
  • domain assumption QCD factorization provides a valid dynamical framework for comparison of extracted amplitudes
    Used to interpret the best-fit point but not derived within the paper.

pith-pipeline@v0.9.0 · 5477 in / 1410 out tokens · 70813 ms · 2026-05-10T02:13:02.467809+00:00 · methodology

discussion (0)

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Forward citations

Cited by 2 Pith papers

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    Anomalies in b to c u-bar q transitions remain puzzling as proposed new physics scenarios involving SU(2) doublets are not significantly relaxed by collider dilution or factorization breakdown.

  2. CP asymmetries in charged meson decay to two pions

    hep-ph 2026-05 unverdicted novelty 4.0

    CP asymmetries for B+ to pi+ pi0, D+ to pi+ pi0, and K+ to pi+ pi0 are estimated in the Standard Model at roughly 3 times 10 to the -3, 10 to the -5, and 10 to the -6 using a unified formalism for isospin violation.

Reference graph

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