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Constraining $B$-Mesogenesis models with inclusive and exclusive decays

T0 review · 3 major / 5 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read By taking the ratio of inclusive and exclusive B decays so unknown couplings cancel, the paper turns the minimal B-Mesogenesis branching requirement into a mass bound that excludes dark particles above 3 GeV and leaves a small window…

desk verdict A clean coupling-independent ratio gives a genuinely new constraint on B-Mesogenesis, but the headline 3 GeV exclusion rests on a phase-space treatment that is internally inconsistent and more mass-scheme sensitive than the paper admits. read the letter →

arxiv 2412.14947 v1 pith:B2MENREY submitted 2024-12-19 hep-ph hep-ex

Alexander Lenz , Ali Mohamed , Zachary Wüthrich This is my paper · ORCID
classification hep-phhep-ex
keywords B-MesogenesisdarkmatterbaryogenesisBmesondecaysheavyquarkexpansioninclusivedecaywidthlight-conesumrulesantibaryon
topics Matter-Antimatter AsymmetryDark Matter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The B-Mesogenesis model tries to solve two cosmological problems at once: it generates the matter-antimatter asymmetry through CP violation in B meson mixing and supplies dark matter as a stable dark antibaryon produced in new b-quark decays. The authors' goal is to find how much room the model still has. They compute the inclusive rate for b -> d u psi at leading order in the heavy quark expansion and combine it with the existing light-cone sum-rule prediction for the exclusive decay B+ -> p+ psi. The ratio of the two rates eliminates the unknown new-physics couplings, which turns the model's minimal requirement Br(B+ -> psi BM) > $10^{-4}$ into a pure lower bound on Br(B+ -> p+ psi) as a function of the dark particle mass m_psi. Compared with the BABAR upper limit, this bound excludes m_psi above 3 GeV and leaves only a small window below 3 GeV that near-future experiments can test.

What carries the argument

The load-bearing object is the ratio in Eq. (3.10): $\mathrm{Br}(B^+ \to p^+ \psi) > 10^{-4}\, \Gamma(B^+ \to p^+ \psi)/\Gamma(b \to d u \psi)$. It converts the model's minimal inclusive requirement into an exclusive branching-fraction bound because the effective four-fermion couplings $|G_{(d)}|^2$ or $|G_{(b)}|^2$ appear identically in both widths and cancel. The inclusive width is the LO-QCD dimension-three heavy-quark-expansion result $\Gamma_3(b \to d u \psi) = |G|^2 m_b^5/(16\cdot 192\pi^3)\,(1 - 8\rho + 8\rho^3 - \rho^4 - 12\rho^2\log\rho)$ with $\rho = m_\psi^2/m_b^2$, which is the muon-decay phase-space function with the coupling rescaled; the exclusive width uses the LCSR form factors $F$ and $\tilde{F}$ from Ref. [5] extrapolated by a $z$-expansion. The comparison in Section 4.1 turns the ratio into a curve in $m_\psi$ that can be cut by the BABAR bound.

What would settle it

A future measurement is the cleanest check: if a B-factory search reaches the predicted lower bound and observes $B^+ \to p^+ \psi$ events with reconstructed $m_\psi$ above 3 GeV, the exclusion claim is wrong; conversely, excluding the surviving $m_\psi < 3$ GeV window would kill the model. On the theory side, computing the next perturbative or $1/m_b$ correction to $\Gamma(b \to d u \psi)$ and checking whether the central curve of Figure 5 moves by more than the LCSR form-factor uncertainty would settle whether the 3 GeV boundary is stable.

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is a coupling-independent mass bound. Requiring the B-Mesogenesis inclusive branching fraction Br(B+ -> psi BM) to exceed $10^{-4}$, and using the identity Br(B+ -> p+ psi) > $10^{-4}$ Gamma(B+ -> p+ psi)/Gamma(b -> d u psi), the unknown couplings G(d) or G(b) cancel. With the LO-QCD free-quark width Gamma_3(b -> d u psi) computed here and the LCSR exclusive width taken from the literature, the resulting lower bound on Br(B+ -> p+ psi) as a function of m_psi can be confronted with the BABAR 90% confidence upper limit. The authors conclude that dark antibaryon masses above 3 GeV are excluded, while a small allowed region below 3 GeV remains. They also find that the model's effect on tau(B+)/tau(Bd) is too small to be discriminated with current precision.

Load-bearing premise

The bound assumes that the leading-order free-quark heavy-quark-expansion width $\Gamma_3(b \to d u \psi)$ accurately equals the full inclusive rate $\Gamma(B^+ \to \psi BM)$, and that the light-cone-sum-rule form factors can be extrapolated reliably to the kinematic endpoint; the paper states the first as an expectation ("We expect the inclusive approach to hold at masses considerably lower than that bound") rather than a quantified error estimate.

Editorial extensions

If this is right

  • If the central bound is correct, dark antibaryon masses above 3 GeV are already ruled out, so viable B-Mesogenesis requires $m_\psi$ below 3 GeV.
  • The surviving parameter space is small and near current sensitivity, so a future B-factory dataset can either confirm or exclude the model without new theoretical input.
  • The lifetime ratio $\tau(B^+)/\tau(B_d)$ cannot discriminate the model at present: the predicted shift stays inside the Standard Model uncertainty for all $m_\psi$.
  • Because the couplings cancel in the ratio, the bound tightens automatically as the LCSR form factors and the inclusive width improve, independent of the unknown $G_{(d)}$ and $G_{(b)}$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The paper leaves implicit that the same ratio trick could be applied to other exclusive channels, such as $B \to \Lambda_c \psi$ or $\Lambda_b \to p \psi$, once light-cone-sum-rule predictions for them exist; each channel would provide an independent check of the $m_\psi = 3$ GeV boundary.
  • A testable extension not pursued here is a scan of the surviving $m_\psi < 3$ GeV region using the $m_\psi$ dependence of the predicted branching fraction, since a future measurement that resolves this dependence could distinguish the two operator versions of the model, whose form factors differ.
  • The authors do not spell out that, because the inclusive width has exactly the phase-space structure of muon decay, the boundary's sensitivity to $m_b$ is analytic: a future shift in the $b$-quark mass at the 3 GeV scale moves the excluded mass by a definite, calculable amount without a new QCD computation.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The manuscript examines constraints on the B-Mesogenesis model from the new b-quark decay channels b -> d u psi. It computes the leading-order free-quark inclusive width Gamma3(b -> d u psi) in Eq. (3.5), forms the coupling-independent ratio in Eq. (3.10) with the LCSR exclusive width for B+ -> p+ psi, and compares the resulting lower bound on Br(B+ -> p+ psi) with the BABAR upper limit. The paper concludes that dark-antibaryon masses above 3 GeV are excluded, leaving a small allowed window below 3 GeV that near-future experiments can test. It also evaluates dimension-six spectator contributions to tau(B+)/tau(Bd) and finds that lifetime ratios currently impose no additional constraints.

Significance. The construction of the ratio in Eq. (3.10) is clean and genuinely useful: the unknown couplings G(d) or G(b) cancel, turning a model-dependent exclusive prediction into a testable lower bound that depends only on m_psi and known inputs. The paper also provides a compact compendium of lifetime-ratio contributions for both operator types, which will be useful for future work. The headline 3 GeV exclusion is, however, built on a leading-order partonic phase-space treatment whose hadronic threshold behaviour and mass-scheme sensitivity are not quantified, and on an LCSR extrapolation whose uncertainty in the relevant kinematic region is not assessed. The result is therefore a plausible and interesting constraint rather than a demonstrated exclusion.

major comments (3)
  1. [Sec. 3.1, Eq. (3.5) and Sec. 4.1] The denominator of Eq. (3.10) is the leading-order free-quark width Gamma3(b -> d u psi) of Eq. (3.5), computed with massless d and u quarks. The text after Eq. (3.5) identifies the phase-space endpoint as m_B+ - m_p = 4341.14 MeV and says the inclusive approach is expected to hold 'at masses considerably lower than that bound,' i.e. below about 3 GeV. But Eq. (3.5) actually vanishes at m_psi = m_b, not at the hadronic threshold, and the 3 GeV boundary used for the exclusion lies outside the region where the authors state the inclusive approach should be trusted. The exclusion of m_psi > 3 GeV therefore rests on an unquantified expectation about the validity of Gamma3 in exactly the mass range where the bound is drawn. Please quantify the hadronic or higher-order HQE corrections, or model the physical threshold consistently at the hadronic level, before using the 3 GeV boundary as a firm exclusion.
  2. [Sec. 3.1, Eq. (3.5) and Table 1] The numerical value of Gamma3 in Eq. (3.5) is very sensitive to the b-quark mass scheme in the region near m_psi = 3 GeV. With m_b(3 GeV) = 4.47 GeV one has rho = m_psi^2/m_b^2 ≈ 0.45 and the phase-space factor is approximately 0.03; using a pole mass of about 4.78 GeV changes the factor to approximately 0.05, a change of order 60 percent in the denominator of Eq. (3.10). Since the lower bound on Br(B+ -> p+ psi) is inversely proportional to Gamma3, this shifts the crossing point with the BABAR upper limit and changes the excluded mass range. The paper should provide a scheme and scale variation of m_b, or justify why the low-scale MSbar mass is the appropriate choice for this phase-space region.
  3. [Sec. 3.2, Eqs. (3.8)-(3.10)] The exclusive width in Eq. (3.7) uses LCSR form factors whose z-expansion in Eq. (3.8) is fitted at low q^2. For the boundary value m_psi = 3 GeV one needs q^2 = 9 GeV^2, which is well above the LCSR fit region and corresponds to a non-negligible fraction of t_+ ≈ 38.7 GeV^2. The slope parameters in Table 1 carry uncertainties, but the uncertainties of the form-factor extrapolation into this kinematic region are not validated, for example by varying the truncation order of the z-expansion or comparing with an alternative parametrization. The lower bound in Eq. (3.10) inherits this unquantified extrapolation error, so the location of the 3 GeV boundary is not yet fully controlled.
minor comments (5)
  1. [Sec. 3.1] The phrase 'the LO-QCD term of the dimension 3 decay rate' is imprecise; this is the leading term Gamma3 of the HQE, not a 'dimension 3 decay rate.' Please reword.
  2. [Eq. (3.10)] The notation in Eq. (3.10) uses an equality sign after 'Br(B+ -> psi BM) > 10^-4'; the second line should be written as a separate definition of the lower bound, using '>' or '=' with a clarifying phrase, to avoid suggesting an exact identity.
  3. [Sec. 4.1 and Fig. 5] There are several presentation issues: 'The the remaining allowed region' is a typo; 'B-Mesogensis' should be 'B-Mesogenesis'; and the caption of Fig. 5 should distinguish clearly between the model lower bound (red) and the experimental upper limit (blue) as in the text.
  4. [Sec. 3.2] The function named 'Källen' should be spelled 'Källén'.
  5. [References] Reference [16] is the 2022 HFLAV arXiv preprint; consider citing the most recent published HFLAV update or the latest PDG value for the lifetime ratio.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the m_psi exclusion follows from a coupling-independent ratio of independently computed widths and an external experimental upper limit.

full rationale

The central bound in Eq. (3.10) is built as a ratio of the exclusive LCSR width (Eq. 3.7, with form factors from Ref. [5]) to the leading-order partonic width (Eq. 3.5, computed in this paper), multiplied by the externally imposed baryogenesis threshold Br(B -> psi B M) > 10^-4 from Ref. [1]. The unknown couplings |G(d)|^2 and |G(b)|^2 cancel algebraically in this ratio, so the resulting lower bound on Br(B+ -> p+ psi) depends only on m_psi and on external inputs: the LCSR form factors, the b-quark mass, and the BABAR upper limit. None of these inputs is fitted to the quantity being predicted. The inclusive width is a standard free-quark phase-space integral, explicitly noted to be identical to muon decay under the replacements |G(d)|^2/16 -> G_F^2, m_b -> m_mu, and m_psi -> m_e; using it as the denominator is a leading-order HQE approximation, not a restatement of the target observable. The self-citations to Refs. [19, 24, 30, 31] supply SM hadronic matrix elements and the SM lifetime ratio; these are separately published, independently computed inputs and are not used to define the B-Mesogenesis bound itself. The paper's caveat that the inclusive approach is expected to hold 'at masses considerably lower than that bound' is a reliability limitation near the hadronic threshold, not a circular step: it concerns the accuracy of Eq. (3.5), not an identity between input and output. No step in the derivation reduces by construction to its own input, and no fitted parameter is relabeled as a prediction.

Assumptions & free parameters 4 free parameters · 6 assumptions · 2 invented entities

The central bound inherits the baryogenesis threshold Br > 10^-4, the LCSR form factors and slope parameters from Ref. [5], the leading-order HQE truncation, and the assumption that only one operator type is active. These are external inputs or stated modeling choices, not derived in this paper. The unknown B-Mesogenesis couplings themselves cancel in the ratio that produces the main exclusion, so they are not free parameters of the paper's core claim.

free parameters (4)
  • b_B->pR^((d)) slope = 4.46 +0.97 -1.72 GeV^2
    Slope parameter from the z-expansion fit to LCSR results in Ref. [5], used in Eq. (3.8) for the exclusive B+ -> p+psi rate.
  • b_B->pL^((d)) slope = -2.27 +0.10 -0.08 GeV^2
    Slope parameter from the z-expansion fit in Ref. [5], entering the eF_B->pL form factor in Eq. (3.8).
  • b_B->pR^((b)) slope = -2.00 +1.58 -3.62 GeV^2
    Slope parameter for the (b)-type operator from Ref. [5], used in the exclusive rate.
  • b_B->pL^((b)) slope = -2.85 +0.17 -0.15 GeV^2
    Slope parameter for the (b)-type operator from Ref. [5], used in the exclusive rate.
assumptions (6)
  • domain assumption The baryogenesis requirement Br(B -> psi B M) > 10^-4 is a hard lower bound.
    Section 3.1, Eq. (3.10). The central bound is linearly proportional to this threshold, which is taken from Ref. [1] and not derived in this paper.
  • domain assumption The leading-order HQE term Gamma3 dominates the inclusive B-Mesogenesis width, with 1/m_b and QCD corrections negligible.
    Section 3.1 and footnote 2. The paper states 'we neglect QCD corrections' and 'We expect the inclusive approach to hold at masses considerably lower than that bound', so the inclusive normalization is a leading-order approximation.
  • domain assumption The LCSR predictions for B+ -> p+psi from Ref. [5] are reliable, including the z-expansion extrapolation and slope parameters.
    Section 3.2, Eqs. (3.7)-(3.9), Table 1. The exclusive rate and the 3 GeV boundary depend on these external hadronic inputs.
  • domain assumption Only one of the (d)-type or (b)-type operators is active at a time.
    Footnote 3, based on flavor constraints from Ref. [1]. This lets the paper treat the two operator versions separately.
  • domain assumption The four-quark operator matrix elements can be parametrized with Bag parameters from Ref. [19] or the vacuum insertion approximation.
    Section 3.3.3, Eqs. (3.32)-(3.33). The lifetime-ratio calculation inherits these external matrix elements.
  • domain assumption The Standard Model prediction for tau(B+)/tau(Bd) from Ref. [31] and the HQE framework are accepted as valid inputs.
    Section 1 and Section 3.3. The lifetime-ratio analysis compares BSM contributions against this external SM baseline.
invented entities (2)
  • Dark antibaryon psi independent evidence
    purpose: Dark matter candidate that couples to quarks via the Y scalar and appears as missing energy in B decays.
    Postulated in Refs. [1,44], not introduced in this paper. Independent falsifiable handle: BABAR's search for B+ -> p+psi [46] places an upper bound on its production rate.
  • Color-triplet scalar Y independent evidence
    purpose: Heavy mediator with baryon number -2/3 that connects b quarks to the dark antibaryon psi.
    Postulated in Refs. [1,44]. ATLAS and CMS searches for color-triplet scalars provide the coupling upper limits quoted in Tables 2 and 3, giving an external handle.

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Cite this review

Pith. "Pith review of Constraining $B$-Mesogenesis models with inclusive and exclusive decays." pith.science (2026). https://pith.science/paper/B2MENREY

@misc{pith2026241214947,
  author       = {Pith},
  title        = {Pith review of: Constraining $B$-Mesogenesis models with inclusive and exclusive decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/B2MENREY}},
  note         = {Machine review of arXiv:2412.14947}
}
abstract

The $B$-Mesogenesis model explains the matter-antimatter asymmetry and leads to the right amount of dark matter in the Universe. In particular, this model predicts new decay channels of the $b$ quark. We investigate the modification of inclusive $b$-hadron decay rates and of the lifetimes of different $B$ mesons due to these new decay channels and compare our results with available predictions for exclusive $B$ meson decays. We find a small surviving parameter space where the $B$-Mesogenesis model is working and which has not been excluded by experiment. Experimental investigations in the near future should be able to test this remaining parameter space and thus either exclude or confirm the $B$-Mesogenesis model.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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  3. Constraints on the mass of the dark antibaryon using $B_d\rightarrow \Lambda \psi_{DS}$ channel in light cone QCD

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Reviewed August 11, 2026 · model on record in the stance chip above.