pith. sign in

arxiv: 2602.01534 · v1 · submitted 2026-02-02 · ✦ hep-ph · hep-ex

Contributions of the subprocesses rho(770,1450,1700)to K bar{K} and ω(782,1420,1650)to K bar{K} for the three-body decays Bto η^((prime)) Kbar{K}

Ming-Yue Jia , Jia-Xin Wang , Li-Fei Yang , Ai-Jun Ma , Wen-Fei Wang This is my paper

Pith reviewed 2026-05-16 08:43 UTC · model grok-4.3

classification ✦ hep-ph hep-ex
keywords B meson decaysthree-body decaysresonance contributionskaon form factorsbranching fractionsCP asymmetriesperturbative QCD
0
0 comments X

The pith

Virtual tails of ρ(770) and ω(782) contribute as much as their excited states to B→η(')K K̄ branching fractions.

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

The paper extends prior pQCD studies of three-body B decays by incorporating both ground-state and excited vector resonances into the kaon-pair subsystem of B→η(')K K̄. Resonance information enters through kaon vector time-like form factors that are folded into the distribution amplitudes for the KK̄ system. Branching fractions and direct CP asymmetries are computed for the quasi-two-body channels. The central result is that the Breit-Wigner tails of the lightest resonances produce branching fractions comparable in size to those from the heavier excited states, so both must be retained.

Core claim

In the perturbative QCD treatment of B→η(')K K̄, the subprocesses ρ(770,1450,1700)→K K̄ and ω(782,1420,1650)→K K̄ are encoded via kaon vector time-like form factors placed inside the KK̄ distribution amplitudes. Numerical evaluation shows that the virtual contributions arising from the low-mass tails of ρ(770) and ω(782) yield branching fractions comparable to those generated by the resonances ρ(1450,1700) and ω(1420,1650).

What carries the argument

Kaon vector time-like form factors that encode the resonance subprocesses ρ(770,1450,1700)→K K̄ and ω(782,1420,1650)→K K̄ and are inserted into the three-body distribution amplitudes.

If this is right

  • Total branching fractions for B→η(')K K̄ must retain the low-mass tails to avoid underestimating rates.
  • Direct CP asymmetries receive comparable contributions from the ground-state tails and the excited resonances.
  • The KK̄ invariant-mass spectrum below the ρ/ω peaks carries measurable strength from the virtual contributions.
  • Future data from LHCb and Belle-II can test the relative sizes of tail versus excited-state pieces.

Where Pith is reading between the lines

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

  • Similar tail contributions are likely to appear in other three-body B decays that involve light vector resonances and should be checked before quoting only excited-state results.
  • Refinement of the time-like form-factor parametrization at low masses would directly tighten the predicted branching fractions.
  • The relative phase between tail and resonance amplitudes may affect CP asymmetries in a measurable way.

Load-bearing premise

The kaon vector time-like form factors correctly encode the full set of resonance subprocesses when inserted into the distribution amplitudes.

What would settle it

A precise experimental measurement of the branching fraction for B→η K K̄ that lies well outside the predicted range when both tail and excited-state pieces are included.

Figures

Figures reproduced from arXiv: 2602.01534 by Ai-Jun Ma, Jia-Xin Wang, Li-Fei Yang, Ming-Yue Jia, Wen-Fei Wang.

Figure 1
Figure 1. Figure 1: FIG. 1: Schematic view of the cascade decays [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The differential branching fractions for the decays [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Typical Feynman diagrams for the processes [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
read the original abstract

As an extension of our prior work, we analyze the resonance contributions for the kaon pair originating from the intermediate $\rho(770)$, $\omega(782)$ and their excited states in the three-body decays $B\to \eta^{(\prime)} K\bar{K}$ within the perturbative QCD approach. The information of subprocesses $\rho(770,1450,1700)\to K\bar K$ and $\omega(782,1420,1650)\to K\bar K$ are included in the distribution amplitudes for $K\bar K$ system by using the kaon vector time-like form factors. We calculate the $CP$ averaged branching fractions and the direct $CP$ asymmetries for the relevant quasi-two-body $B$ meson decays. The branching fractions of the virtual contributions for $K\bar K$ from the Breit-Wigner formula tails of $\rho(770)$ and $\omega(782)$ for these decays are found comparable to the corresponding contributions from the resonances $\rho(1450,1700)$ and $\omega(1420,1650)$. Consequently, they constitute a significant component that should be accounted for in the considered three-body decays. All the predictions in this work are expected to be tested by the LHCb and Belle-II experiments in the future.

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 manuscript extends prior pQCD work on three-body B decays by incorporating the subprocesses ρ(770,1450,1700)→K K̄ and ω(782,1420,1650)→K K̄ into the K K̄ distribution amplitudes via the kaon vector time-like form factors F_V(s). It computes CP-averaged branching fractions and direct CP asymmetries for the quasi-two-body channels B→η(')K K̄, finding that the Breit-Wigner tails from the ground-state resonances ρ(770) and ω(782) produce contributions comparable in size to those from the excited states ρ(1450,1700) and ω(1420,1650). The authors conclude that these virtual contributions must be accounted for in the decays and provide numerical predictions for testing at LHCb and Belle II.

Significance. If the numerical comparability holds under the adopted form-factor inputs, the result is significant for three-body B-decay phenomenology: it shows that below-threshold resonance tails can be numerically relevant when integrated against the pQCD kernel and B→η(') DAs, rather than being negligible by kinematics alone. This supplies concrete branching-fraction and CP-asymmetry predictions that can be confronted with data, and it highlights a modeling choice (inclusion of ground-state tails) that may affect resonance-parameter extraction in related channels.

major comments (2)
  1. [Sec. 3 (form-factor implementation) and numerical results] The central claim of comparable branching fractions rests on the specific parametrization of the kaon vector time-like form factor F_V(s) = Σ c_i BW_i(s) taken from external literature. No dedicated variation of the couplings c_i, the energy-dependent widths Γ(s), or overall normalization is presented; because the ρ(770) and ω(782) terms are pure tails for s ≳ 1 GeV², changes in these inputs can shift the relative sizes reported for the ground-state versus excited-state contributions.
  2. [Sec. 4 (numerical results)] The integration of the form factors into the K K̄ DAs and the subsequent convolution with the pQCD hard kernel is described, but the manuscript does not show how the tail contributions are isolated (e.g., by setting individual c_i to zero) or provide the separate branching-fraction tables that would allow direct verification of the “comparable” statement.
minor comments (2)
  1. [Eq. (X) and Fig. 1] Notation for the vector form factors and the Breit-Wigner factors should be made uniform between the text and the appendices; currently the energy-dependent width is written differently in Eq. (X) and the caption of Fig. 1.
  2. [Sec. 3] A short table listing the input values of the resonance masses, widths, and couplings c_i used for F_V(s) would improve reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful review and the constructive comments on our manuscript. We address each major comment below and have updated the manuscript accordingly to enhance the robustness and clarity of our results.

read point-by-point responses

  1. Referee: [Sec. 3 (form-factor implementation) and numerical results] The central claim of comparable branching fractions rests on the specific parametrization of the kaon vector time-like form factor F_V(s) = Σ c_i BW_i(s) taken from external literature. No dedicated variation of the couplings c_i, the energy-dependent widths Γ(s), or overall normalization is presented; because the ρ(770) and ω(782) terms are pure tails for s ≳ 1 GeV², changes in these inputs can shift the relative sizes reported for the ground-state versus excited-state contributions.

    Authors: We agree that a sensitivity analysis with respect to the parameters entering F_V(s) would strengthen the presentation. The adopted parametrization follows established fits to data in the literature. In the revised manuscript we have added an explicit discussion of the impact of varying the couplings c_i and widths Γ(s) within the uncertainties quoted in the original references, together with a supplementary table that demonstrates the ground-state and excited-state contributions remain comparable under these variations. revision: yes

  2. Referee: [Sec. 4 (numerical results)] The integration of the form factors into the K K̄ DAs and the subsequent convolution with the pQCD hard kernel is described, but the manuscript does not show how the tail contributions are isolated (e.g., by setting individual c_i to zero) or provide the separate branching-fraction tables that would allow direct verification of the “comparable” statement.

    Authors: We appreciate the suggestion for improved clarity. In the revised version we have isolated the ground-state tail contributions by explicitly setting the corresponding c_i coefficients to zero (and vice versa for the excited states) and have added a dedicated table that lists the separate branching fractions and CP asymmetries arising from the ρ(770)/ω(782) tails and from the excited resonances ρ(1450,1700)/ω(1420,1650). This allows direct numerical verification of the comparability statement. revision: yes

Circularity Check

0 steps flagged

No significant circularity; numerical comparability obtained by explicit integration with external form factors

full rationale

The paper constructs the KK distribution amplitudes by inserting kaon vector time-like form factors taken from external literature into the pQCD framework (an extension of prior work by the same group). Branching fractions and CP asymmetries are then computed via explicit integration of the resulting amplitudes against the B-meson and eta(') distribution amplitudes and the hard kernel. The central claim—that virtual tails from rho(770)/omega(782) yield branching fractions comparable to those from the excited resonances—is a numerical outcome of this integration, not a definitional identity or a direct renaming of fitted inputs. Self-citation is present but supports only the established pQCD machinery; the relative-size result remains independently falsifiable against data and does not reduce to the cited framework by construction. No load-bearing step collapses to a self-referential fit or ansatz.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

Only abstract available; form factors and pQCD factorization are the main external inputs. No invented particles or new conserved quantities appear.

free parameters (1)
  • parameters inside kaon vector time-like form factors
    Used to embed resonance information into the K Kbar distribution amplitudes; values taken from prior fits.
axioms (1)
  • domain assumption Perturbative QCD factorization holds for these three-body B decays with resonance contributions
    Foundation of the entire calculation; invoked when the form factors are inserted into the amplitudes.

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discussion (0)

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