arxiv: 2510.00378 · v2 · submitted 2025-10-01 · ✦ hep-ph · hep-ex

bar{B}_{s,d}⁰ to J/psi μ⁺μ⁻ Decays in QCD Factorization

Xin-Qiang Li , Yan Shi , Ya-Dong Yang , Xing-Bo Yuan , Chun-Yang Zhao This is my paper

Pith reviewed 2026-05-18 11:17 UTC · model grok-4.3

classification ✦ hep-ph hep-ex

keywords QCD factorizationrare B decaysbranching ratiosJ/psi mu munon-factorizable correctionslight-cone distribution amplitudesB meson decays

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The pith

QCD factorization with NLO corrections predicts branching ratios of 2.88 x 10^{-10} for Bs0 to J/psi mu+ mu- and 1.07 x 10^{-11} for Bd0 above 1 GeV2 in q2.

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

The paper applies the QCD factorization formalism to the rare decays of neutral B mesons to a J/psi meson and a muon pair, motivated by initial LHCb searches. It computes the decay amplitudes by convoluting hard-scattering kernels, including both leading-order and next-to-leading-order QCD corrections, with the light-cone distribution amplitudes of the B and J/psi mesons. The non-factorizable one-loop vertex corrections are found to suppress the branching ratios by about an order of magnitude relative to the leading-order results. The resulting numerical predictions, along with distributions of helicity amplitudes and J/psi polarization fractions, furnish concrete targets for future measurements at LHCb and Belle II.

Core claim

Within the QCD factorization approach, the leading-order branching ratios integrated from q2 = 1 GeV2 to the kinematic endpoint reach up to 2.21 x 10^{-9} for the Bs decay and 7.69 x 10^{-11} for the Bd decay, depending on the model parameters chosen for the leading-twist B-meson LCDA. After the inclusion of non-factorizable one-loop vertex corrections, the integrated branching ratios are reduced to 2.88 x 10^{-10} for Bs0 -> J/psi mu+ mu- and 1.07 x 10^{-11} for Bd0 -> J/psi mu+ mu-.

What carries the argument

QCD factorization, which factorizes the decay amplitude into a convolution of perturbative hard-scattering kernels with the light-cone distribution amplitudes of the initial B meson and final J/psi meson.

If this is right

The dimuon invariant mass distributions of the individual and total helicity amplitudes squared become measurable observables.
The differential and integrated longitudinal polarization fractions of the J/psi meson provide additional quantities that future experiments can extract.
The same framework supplies predictions for the maximum branching ratios at leading order before vertex corrections are applied.
These results establish benchmarks against which deviations could signal contributions beyond the Standard Model.

Where Pith is reading between the lines

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

Confirmation of the predicted rates would support extending QCD factorization to other charmonium-containing B decays where the final-state meson is compact.
Significant experimental deviations might indicate the need to incorporate additional non-factorizable effects or alternative models for the B-meson LCDA.
The helicity and polarization information could be combined with angular analyses in related channels to test the factorization assumption more stringently.

Load-bearing premise

QCD factorization holds for these decays because the transverse size of the J/psi meson is small in the heavy quark mass limit.

What would settle it

A measurement of the Bs0 -> J/psi mu+ mu- branching ratio above 1 GeV2 in q2 that differs by more than a factor of a few from 2.88 x 10^{-10} would falsify the applicability of the QCD factorization calculation.

read the original abstract

Motivated by the first LHCb searches for the rare $\bar{B}_{s,d}^{0} \to J/\psi\mu^{+}\mu^{-}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $J/\psi$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist $B$-meson LCDA, the maximum branching ratios of $\bar{B}_{s}^{0}\to J/\psi\mu^{+}\mu^{-}$ and $\bar{B}_{d}^{0} \to J/\psi\mu^{+}\mu^{-}$, integrated over the dimuon invariant mass squared $q^2$ from $1\,\mathrm{GeV}^2$ to $(m_{B_{s,d}}-m_{J/\psi})^2$, can reach up to $2.21\times10^{-9}$ and $7.69\times10^{-11}$ at the leading order in $\alpha_s$, respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $\mathcal{B}(\bar{B}_{s}^{0} \to J/\psi\mu^{+}\mu^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=2.88\times10^{-10}$ and $\mathcal{B}(\bar{B}_{d}^{0} \to J/\psi\mu^{+}\mu^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=1.07\times10^{-11}$. In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $J/\psi$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data.

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.

Desk Editor's Note private letter to a colleague

This is a straightforward NLO QCD factorization calculation for two rare B decays that supplies concrete numbers but rests on an unquantified assumption about power corrections for the J/psi.

read the letter

The main thing to know is that the paper computes branching ratios for Bs0 and Bd0 to J/psi mu+ mu- at NLO in QCD factorization, finding values around 2.88 times 10 to the -10 and 1.07 times 10 to the -11 after the one-loop vertex corrections reduce the leading-order results by roughly an order of magnitude. It also gives differential helicity amplitude distributions and J/psi polarization fractions over the dimuon mass range starting at 1 GeV squared. This is the first detailed application to these exact modes, motivated by the recent LHCb searches, so the kernels and numerical outputs are new within the existing formalism. The perturbative hard-scattering parts are handled cleanly and the reduction from LO to NLO is shown explicitly. The differential results look like they could be compared to future data from LHCb or Belle II. The soft spots are the dependence on specific model choices for the leading-twist B-meson LCDA, which sets the central values without a full uncertainty breakdown visible here, and the lack of any explicit check on the size of 1/m_c power corrections. The justification for factorization is the usual statement that the J/psi transverse size becomes small in the heavy-quark limit, but with physical charm mass this suppression is not obviously strong, and no scaling estimate or bound is supplied. That makes the quoted branching ratios more illustrative than definitive. This is for b-physics phenomenologists who track rare decays and factorization applications. A reader who needs updated predictions or helicity distributions for these channels would get direct use out of it. The work is solid enough on its own terms to deserve a serious referee, even if the power-correction issue needs attention in review. I would send it out rather than desk reject.

Referee Report

2 major / 2 minor

Summary. The manuscript applies QCD factorization to the rare decays B̄_{s,d}^0 → J/ψ μ⁺μ⁻. It computes leading-order and next-to-leading-order hard-scattering kernels, convolves them with the leading-twist light-cone distribution amplitudes of the B meson and J/ψ, and reports numerical branching ratios integrated for q² ≥ 1 GeV² together with differential distributions and J/ψ longitudinal polarization fractions. The central results are that NLO vertex corrections reduce the branching ratios by roughly one order of magnitude relative to the LO maxima, yielding B(B̄_s^0 → J/ψ μ⁺μ⁻) = 2.88 × 10^{-10} and B(B̄_d^0 → J/ψ μ⁺μ⁻) = 1.07 × 10^{-11}.

Significance. If the leading-twist factorization formula remains dominant for physical charm mass, the NLO calculation supplies the first quantitative predictions for these modes that can be confronted with future LHCb and Belle II data. The explicit inclusion of one-loop non-factorizable vertex corrections is a technical advance over existing LO estimates and demonstrates the feasibility of higher-order work in this channel.

major comments (2)

[Abstract] Abstract: The LO branching ratios are presented as model-dependent maxima (2.21 × 10^{-9} and 7.69 × 10^{-11}), while the NLO results are quoted as definite central values without stating which LCDA model parameters are used or providing a sensitivity range. Because the final numbers are obtained by convolution with the B-meson LCDA, the absence of an uncertainty breakdown or explicit parameter choice undermines the robustness of the quoted NLO branching ratios.
[Abstract and Introduction] Abstract and Introduction: The applicability of QCD factorization is justified solely by the statement that the transverse size of the J/ψ becomes small in the heavy-quark limit. No scaling argument, numerical estimate, or bound is supplied for the size of Λ/m_c or higher-twist corrections at the physical charm mass. Since the central numerical claims rest on the leading-twist factorization formula capturing the dominant contribution, a quantitative assessment of the expected suppression of power corrections is required.

minor comments (2)

[Abstract] The integration range q² ≥ 1 GeV² is stated in the abstract; confirm that the same lower cut and the explicit upper limit (m_B − m_J/ψ)² are used uniformly in all numerical results and plots in the main text.
Consider adding a short table or paragraph that lists the specific model parameters adopted for the B-meson LCDA in the NLO numerics, together with the values of the other input parameters (decay constants, quark masses, etc.).

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 and describe the revisions we will implement.

read point-by-point responses

Referee: [Abstract] Abstract: The LO branching ratios are presented as model-dependent maxima (2.21 × 10^{-9} and 7.69 × 10^{-11}), while the NLO results are quoted as definite central values without stating which LCDA model parameters are used or providing a sensitivity range. Because the final numbers are obtained by convolution with the B-meson LCDA, the absence of an uncertainty breakdown or explicit parameter choice undermines the robustness of the quoted NLO branching ratios.

Authors: We agree that the abstract should more explicitly identify the LCDA parameters underlying the central NLO values. The NLO branching ratios are obtained with a specific choice of the leading-twist B-meson LCDA (detailed in Section 3 of the manuscript). We will revise the abstract to state the adopted parameters and to note the sensitivity of the results to reasonable variations of these parameters, with a corresponding uncertainty discussion added to the numerical results section. revision: yes
Referee: [Abstract and Introduction] Abstract and Introduction: The applicability of QCD factorization is justified solely by the statement that the transverse size of the J/ψ becomes small in the heavy-quark limit. No scaling argument, numerical estimate, or bound is supplied for the size of Λ/m_c or higher-twist corrections at the physical charm mass. Since the central numerical claims rest on the leading-twist factorization formula capturing the dominant contribution, a quantitative assessment of the expected suppression of power corrections is required.

Authors: We acknowledge that a more quantitative discussion of power corrections would improve the manuscript. A complete higher-twist calculation lies beyond the scope of the present work. We will add a scaling argument in the introduction noting that power corrections are suppressed by factors of order (Λ/m_c)^2. With m_c ≈ 1.5 GeV and Λ ≈ 0.5 GeV this yields an estimated O(10%) effect, supporting the expectation that the leading-twist formula captures the dominant contribution at the physical charm mass. revision: partial

Circularity Check

0 steps flagged

No significant circularity in the QCD factorization derivation

full rationale

The paper computes perturbative hard-scattering kernels at LO and NLO within the QCD factorization framework and convolves them with external model LCDAs for the B meson and J/ψ to obtain numerical branching ratios. These outputs explicitly depend on chosen model parameters for the leading-twist B-meson LCDA, as stated in the abstract, but the kernels themselves are derived from first-principles QCD diagrams rather than fitted to the target observables. The applicability of factorization is justified by the standard heavy-quark limit argument that the J/ψ transverse size becomes small, which is an external theoretical expectation and not a self-referential definition, self-citation, or ansatz imported from the authors' prior work. No load-bearing step reduces a claimed prediction to an input by construction, nor invokes uniqueness theorems or renames known results. The derivation chain is therefore independent and self-contained against the stated external inputs and benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central numerical results rest on the applicability of QCD factorization and on specific models chosen for the leading-twist B-meson LCDA; no new particles or forces are postulated.

free parameters (1)

model parameters for leading-twist B-meson LCDA
Numerical branching ratios are stated to depend on these parameters; different choices produce a range up to the quoted maximum values.

axioms (1)

domain assumption QCD factorization holds because the transverse size of the J/psi is small in the heavy quark mass limit
Explicitly invoked in the abstract to justify applying the formalism to these decays.

pith-pipeline@v0.9.0 · 5957 in / 1381 out tokens · 16452 ms · 2026-05-18T11:17:58.357249+00:00 · methodology

discussion (0)

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unclear
Relation between the paper passage and the cited Recognition theorem.

We perform a detailed study of these processes within the QCD factorization formalism... hard-scattering kernels... convoluted with the light-cone distribution amplitudes

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
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contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
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Reference graph

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