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arxiv: 2605.17943 · v1 · pith:C62EDGVTnew · submitted 2026-05-18 · ✦ hep-ph

Branching ratios and CP violations of B torho (ω) γ decays in the modified perturbative QCD approach and the relevant dark photonic decays of Bto rho (ω) γ^prime

Shang Qi , Mao-Zhi Yang This is my paper

Pith reviewed 2026-05-20 10:11 UTC · model grok-4.3

classification ✦ hep-ph
keywords radiative B decaysdark photonperturbative QCDform factorsbranching ratiosCP violationinfrared cutoff
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0 comments X

The pith

By fitting soft form factors from data in modified pQCD, total form factors for B to rho or omega plus photon match light-cone sum rule results and yield upper limits on dark photon modes.

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

This paper studies the radiative decays B to rho or omega plus a photon using a modified perturbative QCD approach that retains transverse momenta of quarks and gluons and includes a Sudakov factor to control infrared behavior. An infrared momentum cutoff separates the contributions into hard parts computed perturbatively and soft parts treated as adjustable inputs. These soft inputs are fixed by requiring the calculated branching ratios to match existing experimental measurements for the standard photon final states. When the hard and soft pieces are added, the resulting form factors agree with independent nonperturbative calculations from light-cone sum rules. The same form factors are then applied without change to estimate upper bounds on the branching ratios of the corresponding decays that produce a dark photon from an extra U(1) gauge symmetry.

Core claim

In the modified perturbative QCD approach, an infrared cutoff scale divides the form factors of B → ρ(ω)γ into hard perturbative pieces and soft nonperturbative pieces; the soft pieces are determined by matching the predicted branching ratios to experimental data, after which the summed form factors reproduce light-cone sum rule results, and these same form factors supply upper limits on the branching ratios of B → ρ(ω)γ′ decays where γ′ is a dark photon.

What carries the argument

The critical infrared momentum cutoff that separates hard perturbative form factors from soft input form factors in the modified pQCD calculation of radiative B decays.

If this is right

  • The summed form factors agree with results from light-cone sum rules of QCD.
  • Upper limits can be placed on the branching ratios of the dark-photon decays B to rho or omega plus gamma prime.
  • CP-violating asymmetries in the standard radiative modes can be computed within the same framework.

Where Pith is reading between the lines

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

  • The same cutoff technique could be tested on other rare B decays that involve photons or missing-energy signatures.
  • If a dark photon is observed, the predicted branching-ratio bounds would translate into direct limits on the kinetic mixing parameter of the extra U(1) model.
  • Future lattice or sum-rule calculations of the soft form factors could replace the data-driven fit and provide an independent cross-check.

Load-bearing premise

The soft form factors extracted by fitting ordinary photon decays can be reused unchanged for the dark-photon channels.

What would settle it

An experimental measurement of the branching ratio for B to rho or omega plus dark photon that lies above the upper limit obtained from the fitted form factors would show the direct transfer of those form factors is invalid.

Figures

Figures reproduced from arXiv: 2605.17943 by Mao-Zhi Yang, Shang Qi.

Figure 1
Figure 1. Figure 1: FIG. 1. Contribution of operator [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Contribution of operator [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Diagrams in which the operator [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Diagrams in which the operator [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Annihilation diagrams in which the oper [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The other type of annihilation diagrams [PITH_FULL_IMAGE:figures/full_fig_p013_7.png] view at source ↗
read the original abstract

In this work we study the radiative decays of $B\to \rho (\omega)\gamma$ processes in the modified perturbative QCD approach, where the transverse momenta of the quark and gluons envolved in the interaction process are kept, and the Sudakov factor is incorporated in the theoretical calculation, which are helpful to suppress the infrared end-point contribution. A critical infrared momentum cutoff scale is introduced, which is used to separate the soft and hard contributions in QCD. Then the form factors envolved in the radiative decays should be separated as hard and soft form factors. The hard form factors can be calculated with the perturbative QCD approach, while the soft form factors should be viewed as soft input parameters. The soft form factors can be obtained by confronting the theoretical calculation of the branching ratios of the radiative decay of $B$ meson with the experimental data. Summing the soft and hard form factors, we find that the total form factors are in fine agreement with that obtained by nonperturbative theoretical method, such as the light-cone sum rules of QCD. We also study $B\to \rho (\omega) \gamma^\prime$ decays by using the form factors obtained in the $B\to \rho (\omega)\gamma$ decay processes, where $\gamma^\prime$ is the dark photon introduced by the extra $U(1)$ symmetry model. The upper limit of the branching ratios of thes decays are estimated.

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 applies a modified perturbative QCD framework to B → ρ(ω)γ decays, retaining transverse momenta and Sudakov factors while introducing an infrared cutoff scale to separate soft and hard form-factor contributions. Hard pieces are computed perturbatively; soft form factors are extracted by requiring the predicted branching ratios to match experimental data. The summed form factors are reported to agree with light-cone sum-rule results. The same numerical soft form factors are then inserted without modification into the amplitudes for B → ρ(ω)γ′ decays (γ′ a massive dark photon) to derive upper limits on those branching ratios.

Significance. If the kinematic extrapolation were validated, the work would illustrate a hybrid pQCD-plus-phenomenological approach to radiative B decays and supply rough sensitivity estimates for dark-photon searches. The present significance is reduced because the soft inputs are tuned to the very observables being computed and are reused for a kinematically distinct process without re-derivation or error propagation.

major comments (2)
  1. [Dark-photon section (after the LCSR comparison)] The soft form factors are determined by fitting the modified pQCD branching-ratio expressions for massless-photon B → ρ(ω)γ decays to data (see the paragraph beginning “The soft form factors can be obtained by confronting…”). These same numerical values are inserted unchanged into the B → ρ(ω)γ′ amplitudes. For m_γ′ > 0 the momentum transfer becomes q² = m_γ′², altering the hard-gluon kernel, the Sudakov suppression, the phase-space factor, and the optimal infrared cutoff; none of these adjustments are performed or estimated in the manuscript.
  2. [Form-factor comparison paragraph] The claim that the total form factors agree with LCSR results is obtained only after the soft pieces have been adjusted to reproduce the experimental B → ρ(ω)γ branching ratios. Consequently the reported agreement is not an independent cross-check but a consistency condition built into the fitting procedure.
minor comments (2)
  1. [Method section] The infrared cutoff scale is introduced as a free parameter but its numerical value and stability under variation are not tabulated or plotted.
  2. [Results for γ′ decays] No error budget or uncertainty from the fitted soft form factors is propagated into the quoted upper limits on the dark-photon branching ratios.

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 each major comment below. Where the concerns are valid we have revised the text or added discussion; in one case we provide a clarification of the method's intent while acknowledging its limitations.

read point-by-point responses

  1. Referee: [Dark-photon section (after the LCSR comparison)] The soft form factors are determined by fitting the modified pQCD branching-ratio expressions for massless-photon B → ρ(ω)γ decays to data (see the paragraph beginning “The soft form factors can be obtained by confronting…”). These same numerical values are inserted unchanged into the B → ρ(ω)γ′ amplitudes. For m_γ′ > 0 the momentum transfer becomes q² = m_γ′², altering the hard-gluon kernel, the Sudakov suppression, the phase-space factor, and the optimal infrared cutoff; none of these adjustments are performed or estimated in the manuscript.

    Authors: We agree that a complete re-calculation of the hard kernel, Sudakov factors and infrared cutoff at q² = m_γ′² would be preferable. Our present treatment uses the form factors extracted at q² = 0 as an approximation, motivated by the expectation that any dark-photon mass relevant for near-term searches remains small compared with the hard scale set by the B-meson mass. In the revised manuscript we will (i) state this approximation explicitly, (ii) provide a rough numerical estimate of the size of the omitted corrections by evaluating the leading q² dependence of the hard kernel for m_γ′ up to 300 MeV, and (iii) propagate a corresponding uncertainty into the quoted upper limits on the branching ratios. revision: partial

  2. Referee: [Form-factor comparison paragraph] The claim that the total form factors agree with LCSR results is obtained only after the soft pieces have been adjusted to reproduce the experimental B → ρ(ω)γ branching ratios. Consequently the reported agreement is not an independent cross-check but a consistency condition built into the fitting procedure.

    Authors: The referee correctly notes that the soft form factors are fixed by requiring the predicted branching ratios to match experiment. The subsequent comparison of the summed (hard + soft) form factors with LCSR results is therefore not an independent validation of the absolute normalization. It does, however, test whether the perturbatively computed hard contribution is of the magnitude and sign expected once the soft piece has been anchored to data. We will revise the relevant paragraph to make this distinction clear and to present the LCSR comparison as a consistency check on the hard-scattering kernel rather than as an independent cross-validation. revision: yes

Circularity Check

1 steps flagged

Soft form factors fitted to B→Vγ branching ratios reused unchanged for massive γ' without kinematic re-evaluation

specific steps
  1. fitted input called prediction [Abstract]
    "The soft form factors can be obtained by confronting the theoretical calculation of the branching ratios of the radiative decay of B meson with the experimental data. [...] We also study B→ρ(ω)γ′ decays by using the form factors obtained in the B→ρ(ω)γ decay processes, where γ′ is the dark photon [...] The upper limit of the branching ratios of these decays are estimated."

    Soft form factors are fixed by requiring the calculated BR(B→ρ(ω)γ) to reproduce experimental data under massless-photon kinematics. The identical numerical values are then substituted into the amplitude for the massive γ' case. The resulting BR upper limits are therefore not derived from first principles for the new kinematics but are direct consequences of the original data fit.

full rationale

The paper determines soft form factors by fitting the modified pQCD branching-ratio calculation (hard piece + soft input, with IR cutoff) for massless-photon B→ρ(ω)γ decays directly to experimental data. These numerical values are then inserted without adjustment into the B→ρ(ω)γ' amplitudes. Because the dark-photon case has q² = m_γ'² > 0, the form-factor argument, hard-gluon kernel, phase space, and Sudakov suppression all shift, yet no recalculation or refit is performed. This makes the quoted upper limits an unadjusted extrapolation of the original fit rather than an independent derivation. The core standard-decay results retain independent content from the perturbative hard form factors and the external LCSR comparison, so overall circularity is partial rather than total.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 1 invented entities

The central results rest on an ad-hoc infrared cutoff, fitted soft form factors, and the assumption that the same form factors apply to dark-photon final states. The dark photon itself is postulated without new evidence.

free parameters (2)
  • soft form factors
    Determined by fitting calculated branching ratios to experimental data for B→ρ(ω)γ
  • infrared momentum cutoff scale
    Introduced to separate soft and hard contributions in the modified pQCD calculation
axioms (2)
  • domain assumption Transverse momenta of quarks and gluons are retained and the Sudakov factor suppresses infrared end-point singularities
    Core assumption of the modified perturbative QCD approach used throughout
  • domain assumption Form factors factorize into independently calculable hard and soft pieces
    Required to isolate the perturbative hard contribution from the fitted soft input
invented entities (1)
  • dark photon γ' no independent evidence
    purpose: Hypothetical gauge boson from an extra U(1) symmetry used to model possible dark-sector interactions
    Postulated new particle whose decays are bounded using the fitted form factors; no independent evidence or prediction is supplied in the work

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Reference graph

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