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arxiv: 1906.09387 · v2 · pith:72WA2NGEnew · submitted 2019-06-22 · ✦ hep-ph

Quasi-two-body decays B_((s)) to P D₀^*(2400) to P D π in the perturbative QCD approach

Bo-Yan Cui , Ying-Ying Fan , Fu-Hu Liu , Wen-Fei Wang This is my paper

Pith reviewed 2026-05-25 18:35 UTC · model grok-4.3

classification ✦ hep-ph
keywords B meson decaysquasi-two-body decaysperturbative QCDbranching fractionsD0*(2400) resonanceCKM suppressionSU(3) symmetryBs decays
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The pith

Perturbative QCD calculations predict branching fractions of 10^{-9} to 10^{-4} for B_{(s)} decays to light mesons and the D_0^*(2400) resonance.

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

The paper applies the perturbative QCD factorization approach to quasi-two-body decays B_{(s)} to P D_0^*(2400) to P D pi, where P stands for pi, K, eta or eta prime. It computes branching fractions across a wide range and shows how a strong CKM suppression factor of order lambda^4 produces large differences between modes with D_0^* and anti-D_0^* intermediates. Ratios of specific branching fractions are extracted and found to agree with expectations from flavor SU(3) symmetry. A reader would care because the results supply concrete, testable numbers for experiments to check the framework on broad resonances.

Core claim

In the perturbative QCD factorization approach, the branching fractions for the considered quasi-two-body decays lie in the range 10^{-9} to 10^{-4}. The CKM suppression factor R_CKM approximately lambda^4 (rho-bar^2 + eta-bar^2) approximately 3 times 10^{-4} produces the great difference between decays with D_0^* and bar D_0^* as intermediate states. The ratio R_bar D_0^{*0} is about 0.091^{+0.003}_{-0.005}, consistent with the flavour-SU(3) symmetry result, while the ratios between B_s and B decay modes are found to be 1.10^{+0.05}_{-0.02} and 1.03^{+0.06}_{-0.07}.

What carries the argument

The perturbative QCD factorization approach applied to quasi-two-body decays mediated by the broad D_0^*(2400) resonance decaying to D pi.

If this is right

  • Branching fractions for modes with D_0^* intermediates are orders of magnitude larger than those with bar D_0^* intermediates because of the CKM factor of approximately 3 times 10^{-4}.
  • The ratio between B^0 to bar D_0^{*0} K^0 to D^- pi^+ K^0 and B^0 to bar D_0^{*0} pi^0 to D^- pi^+ pi^0 equals 0.091 with small theoretical uncertainty.
  • The ratio of branching fractions B_s^0 to D_0^{*+} K^- to D^0 pi^+ K^- over B^0 to D_0^{*+} pi^- to D^0 pi^+ pi^- equals 1.10^{+0.05}_{-0.02}.
  • The ratio of B_s^0 to bar D_0^{*0} bar K^0 to D^- pi^+ bar K^0 over twice B^0 to bar D_0^{*0} pi^0 to D^- pi^+ pi^0 equals 1.03^{+0.06}_{-0.07}.

Where Pith is reading between the lines

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

  • If the ratios hold experimentally, they would support extending the same calculational method to other broad scalar resonances in B decays.
  • Precision measurements of these modes could help determine whether the D_0^*(2400) is best described as a conventional quark-antiquark state or requires additional components.
  • Agreement with SU(3) symmetry in the presence of a broad resonance suggests the symmetry relations remain useful even when the intermediate state has a large width.

Load-bearing premise

The perturbative QCD factorization approach remains valid and factorizable for these quasi-two-body decays involving the broad D_0^*(2400) resonance.

What would settle it

An experimental measurement of any branching fraction lying well outside the 10^{-9} to 10^{-4} range or a ratio R_bar D_0^{*0} differing substantially from 0.091 would falsify the central predictions.

Figures

Figures reproduced from arXiv: 1906.09387 by Bo-Yan Cui, Fu-Hu Liu, Wen-Fei Wang, Ying-Ying Fan.

Figure 1
Figure 1. Figure 1: Inspired by the generalized parton distribution in hard exclus [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

We study the quasi-two-body decays $B\to P D^{\ast}_0(2400) \to P D\pi $ with $P=(\pi, K, \eta, \eta^{\prime})$ in the perturbative QCD factorization approach. The predicted branching fractions for the considered decays are in the range of $10^{-9}$-$10^{-4}$. The strong Cabibbo-Kobayashi-Maskawa (CKM) suppression factor $R_{CKM}\approx \lambda^4 (\bar{\rho}^2 + \bar{\eta}^2) \approx 3\times 10^{-4}$ results in the great difference of the branching ratios for the decays with $D_0^*$ and $\bar{D}_0^*$ as the intermediate states. The ratio $R_{\bar{D}_0^{*0}}$ between the decays $B^0 \to \bar{D}_0^{*0} K^0\to D^-\pi^+K^0$ and $B^0 \to \bar{D}_0^{*0}\pi^0 \to D^-\pi^+\pi^0$ is about $0.091^{+0.003}_{-0.005}$, consistent with the flavour-$SU$(3) symmetry result. The ratio for the branching fractions is found to be $1.10^{+0.05}_{-0.02}$ between $\mathcal{B}(B_s^0\to D_0^{*+}K^-\to D^0\pi^+K^-)$ and $\mathcal{B}(B^0\to D_0^{*+} \pi^-\to D^0\pi^+ \pi^-)$ and to be $1.03^{+0.06}_{-0.07}$ between $\mathcal{B}(B_s^0\to\bar{D}_0^{*0} \bar{K}^0\to D^-\pi^+ \bar{K}^0)$ and $2\mathcal{B}(B^0\to \bar{D}_0^{*0}\pi^0\to D^-\pi^+\pi^0)$. The predictions in this work can be tested by the future experiments.

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 / 1 minor

Summary. The manuscript calculates branching fractions for the quasi-two-body decays B_{(s)} → P D_0^*(2400) → P D π (P = π, K, η, η') in the perturbative QCD factorization approach. It reports values in the range 10^{-9}–10^{-4}, attributes large differences between D_0^* and bar{D}_0^* modes to CKM suppression (R_CKM ≈ 3×10^{-4}), and gives ratios R_bar{D}_0^{*0} ≈ 0.091^{+0.003}_{-0.005} (consistent with SU(3)), 1.10^{+0.05}_{-0.02} for B_s^0 vs B^0 modes, and 1.03^{+0.06}_{-0.07} for another pair, all intended as testable predictions.

Significance. If the results hold, the work supplies concrete, falsifiable predictions for rare B decays that can be confronted with data from LHCb or Belle II, thereby testing both the applicability of pQCD factorization to quasi-two-body channels with broad resonances and the validity of flavor-SU(3) relations. The explicit numerical outputs with quoted uncertainties constitute a strength that allows direct experimental comparison.

major comments (2)
  1. [Abstract] Abstract: the central numerical claims (branching fractions 10^{-9}–10^{-4} and the three quoted ratios with asymmetric errors) are presented without reference to the explicit pQCD convolution integrals, the resonance distribution amplitude, or the error budget from non-perturbative inputs, rendering the results impossible to reproduce or stress-test from the given text.
  2. [Abstract] Abstract and introduction: the entire set of predictions rests on the assumption that the pQCD factorization formula remains valid when the intermediate state is the broad D_0^*(2400) resonance (width ~300 MeV); no dedicated justification, scale-separation argument, or sensitivity study to non-factorizable contributions or modified resonance lineshape is supplied, which directly affects the reliability of all quoted branching fractions and ratios at the level of the reported uncertainties.
minor comments (1)
  1. [Abstract] Abstract: the two ratios labeled R_D0*0 and R_bar{D}_0^{*0} are introduced without an explicit definition of the numerator and denominator channels, which could be clarified for readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed comments on our manuscript. We address each major comment below and will revise the manuscript to improve clarity and strengthen the discussion of the pQCD applicability.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central numerical claims (branching fractions 10^{-9}–10^{-4} and the three quoted ratios with asymmetric errors) are presented without reference to the explicit pQCD convolution integrals, the resonance distribution amplitude, or the error budget from non-perturbative inputs, rendering the results impossible to reproduce or stress-test from the given text.

    Authors: The abstract provides a concise summary of the key numerical results. The explicit pQCD convolution integrals, the resonance distribution amplitude for the D_0^*(2400), and the full error budget (including variations from meson wave functions, hard scales, and CKM parameters) are detailed in Sections II and III, with references to our prior pQCD works on quasi-two-body decays. To address the concern, we will add a short phrase in the abstract referencing the pQCD factorization approach and the Breit-Wigner treatment of the resonance. revision: partial

  2. Referee: [Abstract] Abstract and introduction: the entire set of predictions rests on the assumption that the pQCD factorization formula remains valid when the intermediate state is the broad D_0^*(2400) resonance (width ~300 MeV); no dedicated justification, scale-separation argument, or sensitivity study to non-factorizable contributions or modified resonance lineshape is supplied, which directly affects the reliability of all quoted branching fractions and ratios at the level of the reported uncertainties.

    Authors: We agree that an explicit justification strengthens the presentation. The pQCD approach for quasi-two-body decays with broad resonances has been validated in multiple prior applications (e.g., B → Kρ(770) → Kπ and similar channels), where hard-gluon exchange ensures factorization and the resonance is incorporated via an effective distribution amplitude with Breit-Wigner lineshape. Non-factorizable contributions are suppressed by the same power-counting arguments as in two-body decays. We will add a dedicated paragraph in the introduction and Section II discussing scale separation, citing supporting literature, and noting that the quoted uncertainties already incorporate lineshape variations. revision: yes

Circularity Check

0 steps flagged

No significant circularity in pQCD derivation chain

full rationale

The paper applies the perturbative QCD factorization approach to compute branching fractions and ratios for the quasi-two-body decays, presenting numerical results in the range 10^{-9}–10^{-4} and specific ratios such as R≈0.091 that are compared to but not forced by SU(3) symmetry. No equations or sections in the provided text reduce the central predictions to self-definitions, fitted inputs renamed as predictions, or load-bearing self-citations whose validity is unverified within the work. The framework inputs (e.g., distribution amplitudes, CKM elements) are standard and externally constrained, leaving the derivation self-contained against external benchmarks with independent calculational content.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available; no explicit free parameters, axioms, or invented entities can be extracted or audited.

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