Mesogenesis Framework: Baryogenesis & Dark Matter

• Mesogenesis is defined as a set of baryogenesis scenarios that connect cosmic baryon asymmetry with dark matter relic density via rare out-of-equilibrium meson decays.
• It employs low-scale decays, CP violation through dark-sector interactions, and TeV-scale mediators to produce observable signals in exotic B-meson and heavy baryon decays.
• The framework establishes a hard lower bound on branching ratios, setting the stage for near-future collider and underground experiments to scrutinize its predictions.

The Mesogenesis Framework encompasses a set of baryogenesis scenarios wherein the origin of the cosmic baryon asymmetry and the dark matter relic density are dynamically linked, typically via rare out-of-equilibrium decays of heavy neutral or charged mesons into Standard Model (SM) baryons and dark-sector states. Characteristically, these frameworks posit new baryon-number–carrying dark particles, minimal extensions of the SM flavor structure, and exploit SM or dark-sector CP violation to robustly connect cosmological parameters to measurable laboratory observables, notably rare B-meson (and baryon) decays with missing energy. A defining property is the direct testability by near-future collider and underground experiments at branching fractions and rates comfortably within reach of present or planned facilities.

1. Dynamical Origin and Core Mechanism

The archetypal Mesogenesis scenario unfolds in a low-scale, late-phase cosmology, where a long-lived scalar $\Phi$ (mass $m_\Phi \sim 10$–$100$ GeV) dominates the Universe's energy density and decays at temperatures $T_R \sim 5$–$80$ MeV, below the QCD transition but before BBN. The $\Phi$ decay injects high-energy $b\bar b$ quarks that hadronize into $B_{s,d}^0$, $B^\pm$, and $B_c^\pm$ mesons. These mesons, produced out of chemical equilibrium, decay nearly instantaneously compared to the Hubble time: $\Gamma_\Phi \ll \Gamma_B$, guaranteeing a purely decay-dominated system.

Crucially, the primary baryogenesis channel is the exotic decay: $B \to \mathcal{B}_{\rm SM} + \psi$ where $\mathcal{B}_{\rm SM}$ is a visible baryon (e.g., $p$, $\Lambda^0$) and $\psi^{\alpha}_\mathcal{B}$ is a dark-sector Dirac fermion (“dark baryon”) that carries SM baryon number. These decays are mediated by dimension-6 operators generated via exchange of a TeV-scale colored scalar mediator $Y$, e.g.,

$$\mathcal{O}_{bud} = \frac{\tilde y_{ij}\,y_{k\alpha}}{M_Y^2}\,\epsilon_{abc}\,d^{b}_{Ri} d^{c}_{Rj} u^{a}_{Rk} \psi^\alpha_{\mathcal{B}}$$

The visible–dark baryon transfer is kinematically allowed for $m_p + m_e < m_\psi < m_M - m_{B_{\rm SM}}$, enforcing proton stability and allowing exothermic decays of $B$ mesons into visible and dark baryons.

The CP violation necessary for baryon-number generation arises from complex phases in the dark-sector Yukawa couplings and/or species structure. For $N_\psi \geq 3$ flavors or in the presence of a light dark mediator, one-loop interference can yield order-one CP asymmetry parameters $\varepsilon_\alpha$.

The baryon asymmetry is set by the Boltzmann equation

$$\frac{d(n_B - n_{\bar B})}{dt} + 3H(n_B - n_{\bar B}) = 2 \Gamma_\Phi\,\text{Br}(\Phi \to M)\, n_\Phi \sum_\alpha \text{Br}(M \to B\,\psi^\alpha)\, \varepsilon_\alpha$$

leading upon integration to

$$Y_{\Delta B} \equiv \frac{n_B - n_{\bar B}}{s} \simeq \frac{\sum_\alpha \text{Br}(M \to B\,\psi^\alpha)\, \varepsilon_\alpha}{1.3\times 10^{-8} \left(\frac{T_R}{60\,\rm MeV}\right)\left(\frac{2 m_M}{m_\Phi}\right)} \qquad [2509.18246]$$

Matching the observed $Y_{\Delta B}^{\rm(obs)} \approx 8.7\times 10^{-11}$ sets the required product

$$(\text{Br} \times \varepsilon)_{\rm min} \simeq 1.3\times 10^{-8} \left(\frac{m_\Phi}{2 m_M}\right)\left(\frac{60\,\rm MeV}{T_R}\right)$$

In the most favorable scenario, for $T_R=60$ MeV, $m_\Phi=2 m_M\sim 20$ GeV, $$\text{Br} \times \varepsilon \gtrsim 1.3\times 10^{-8}$$, and for generically large $\varepsilon_\alpha$ this is a hard lower bound on the $B$ meson exotic branching fraction.

2. Operator Structure, Kinematic Constraints, and CP Asymmetry

The minimal UV completion implements the four-fermion operator through a TeV-scale colored scalar $Y$ (hypercharge $-1/3$ or $+2/3$): $$\mathcal{L}_{-1/3} = -y_{u_\alpha d_\beta}\,\epsilon_{ijk}\,Y^{*i}\,\bar u^j_{\alpha R}\,(d^c_{\beta R})^k -y_{\psi d_\gamma}\,Y^i\,\bar\psi\,(d^c_{\gamma R})^i + \text{h.c.}$$

After integrating out $Y$, the effective Hamiltonian mediates $b \to d\,u\,\psi$ with

$$\mathcal{H}_{\rm eff} = -G_{(d)}\,\overline{\mathcal{O}}_{(d)}\,\psi^c - G^*_{(d)}\,\bar\psi^c\,\mathcal{O}_{(d)}$$

where $G_{(d)} = y_{ub} y_{\psi d}/M_Y^2$, and $$\overline{\mathcal{O}}_{(d)} = i \epsilon_{ijk} (\bar u_R^i (b_R^c)^j)\bar d_R^k$$.

CP violation resides in relative phases of $y_{ub}$, $y_{\psi d}$, and dark-sector mass mixings. At least three flavors or new loop-induced interactions are required for a nonzero imaginary part and thus a non-vanishing decay asymmetry. The maximal attainable CP asymmetry per flavor is $\varepsilon_\alpha = O(1)$ when tree and loop amplitudes are comparable, which is generically allowed for suitable model parameters.

3. Quantitative Predictions and Irreducible Limits

The framework predicts a model-independent, irreducible lower bound on exotic $B$-meson branching fractions if it is to explain the cosmic baryon asymmetry: $$\text{Br}(B \to \mathrm{baryon} + \mathrm{MET}) \gtrsim 2.7\times 10^{-8}$$ where the quoted value adopts conservative $m_\Phi$ and $T_R$ parameters, or includes modest washout effects ($m_\Phi=100$ GeV, $T_R=20$ MeV).

This limit is independent of how indirect signatures are probed: any branching fraction below this cannot yield the observed $Y_{\Delta B}$, even with maximal $\varepsilon_\alpha$. For less optimal cosmologies, the required branching grows inversely with $T_R$ and decreases with $m_\Phi$.

Key theoretical assumptions are:

• $\Phi$ reheats only up to $T_R \lesssim 60$ MeV, preventing significant $B$–$\bar B$ annihilation or coherent oscillation washout.
• $\text{Br}_\Phi^M \simeq 1$: democratic/hardonic $\Phi$ decays supply the $B$-meson population.
• Negligible back-reaction or washout in the dark sector at $T \lesssim T_R$.

4. "Dark-Lepton" Variant and Leptogenesis Connection

An alternative is a “dark-lepton” realization, where the effective low-energy operator is

$$\mathcal{O} = \frac{1}{\Lambda^2}[\,\bar d\,\Gamma^\mu u\,][\,\bar\ell_d^a \Gamma_\mu \ell\,] + \text{h.c.}$$

This mediates $M^\pm \to \ell^\pm \ell^a_d$ decays, with $\ell^a_d$ a dark lepton carrying a conserved lepton number. CP violation in these two-body decays yields a dark-lepton asymmetry $Y_{L_d}$, relayed to the SM via $Y_L^{\rm SM} = -Y_{L_d}$ and processed into baryon number.

The net baryon asymmetry scales as

$$Y_{\Delta B} \sim \sum_{M^\pm}\text{Br}(M^\pm \to \ell \ell_d) A_{CP}^{\rm dark,\ell} \frac{T_R}{20\,\text{MeV}} \frac{10\,\text{GeV}}{m_\Phi} \times 10^{-6}$$

Physically, this enables baryogenesis via rare charged-meson decays from pions up to $B_c^\pm$, expanding the experimental window for discovery.

5. Collider and Low-Energy Search Roadmap

Major experimental implications are as follows:

Direct searches at $B$ factories (Belle, BaBar, Belle-II):

• Signature: SM baryon ($p$, $\Lambda^0$, $\Sigma$, $\Lambda_c^+$, $\dots$) $+$ large missing energy; full kinematic reconstruction and flavor tagging.
• Current exclusive bounds: $$\text{Br}(B^0 \to \Lambda^0 + MET),\,B^+ \to p + MET \sim 10^{-5}$$–$10^{-4}$.
• Expected Belle-II reach: $\sim10^{-7}$ or better. Sensitivity at $10^{-8}$ would decisively probe the entire Mesogenesis parameter space even for the smallest allowed CP-fraction.

Heavy-flavor hadron and baryon decays at LHCb and future hadron colliders:

• $B_c^+ \to$ beauty baryon $+$ MET; heavy baryons $\Lambda_b^0 \to \pi^0 + MET$, $\Lambda_b^0 \to D^0 + MET$, $\Xi_b \to K + MET$ and analogous modes.
• Expected sensitivity: branching fractions $10^{-6}$–$10^{-7}$ at HL-LHC datasets.

Indirect probes:

• EDM experiments: 2-loop diagrams generating dark CP asymmetry also induce the Weinberg three-gluon operator; predicted neutron EDMs remain below $10^{-26}e\cdot$cm for TeV-scale $Y$ and $\mathcal{O}(1)$ phases. Next-generation neutron EDM searches ($<10^{-28}e\cdot$cm) will begin probing the remaining parameter space.
• Nucleon decay/IND: Dark-matter–induced nucleon decay signals in detectors such as DUNE, Super-K, and Hyper-K probe overlapping parameter space with complementary sensitivity (Berger et al., 2023).

Exclusion/Discovery Roadmap:

1. Push all exotic $B$ decays to $p$, $\Lambda^0$, $\Lambda_c^+$, etc., $+$ MET below $\text{Br} \sim 10^{-8}$.
2. Search for heavy baryon $\to$ meson $+$ MET at LHCb to similar sensitivity.
3. In event of a signal, compare $B$ and $\bar B$ channels to extract $\varepsilon_\alpha$.
4. Null results to $\text{Br}<10^{-8}$ robustly exclude dark-baryon Mesogenesis (unless extreme mass "morphing" is invoked); remaining viable models are only "dark-lepton" variants.
5. A discovery in $10^{-8} \lesssim \text{Br} \lesssim 10^{-5}$, with a nonzero $\varepsilon$ and corroborative EDM or nucleon decay, would allow detailed reconstruction of the Mesogenesis mechanism.

6. Distinction from SM and Connection to Other Frameworks

The Mesogenesis framework differs fundamentally from conventional baryogenesis mechanisms in several salient respects:

• It is agnostic to the source of CP violation, allowing purely SM, purely dark, or hybrid SM–dark CPV scenarios (e.g., the full baryon asymmetry can be produced with SM CKM phases given appropriate dark-sector dynamics and time-dependent mediator mass shifts (Elor et al., 2024)).
• Observable consequences are dominantly in flavor physics (rare $B$ and heavy baryon decays), rather than high-temperature electroweak or GUT-scale signals.
• Irreducible model-independent laboratory observables exist: a hard lower bound on branching ratios, with order-one theoretical uncertainties in the exclusive rates from hadronic form factors, yet these are being ablated by rapid advances in lattice QCD and light-cone sum rules (Elor et al., 2022, Boushmelev et al., 2023).

The scenario makes sharp, falsifiable predictions for collider and intensity-frontier experiments in the next decade, offering a comprehensive approach rather than leaving open-ended parameter spaces.

7. Open Issues and Future Directions

Key open questions include:

• Precision determination of hadronic matrix elements for all relevant $B$ baryon and meson decay channels, including higher-twist and SU(3)-breaking effects.
• A full classification of possible dark-sector UV completions that accommodate $\mathcal{O}(1)$ CP phases without conflicting with flavor constraints.
• Definitive experimental exclusion or discovery at $B$ factories (Belle II, LHCb), and underground IND searches; the field is poised for critical progress as sensitivity to branching ratios at or below $10^{-8}$ is achieved.
• For "dark-lepton" variants, comprehensive inclusion of lepton-number–conserving operators and their interplay with weak sphaleron dynamics in the early Universe.
• The potential role of time-dependent or "morphing" mediator masses to evade otherwise stringent laboratory limits while enabling SM-only CPV–driven baryogenesis (Elor et al., 2024).

A plausible implication is that if the minimal predicted branching ratio is not observed at future $B$ factories or LHCb, essentially all minimal and even many non-minimal realizations of baryogenesis at the MeV scale via late out-of-equilibrium meson decays will be excluded, closing a unique class of low-scale baryogenesis models.

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In summary, the Mesogenesis Framework robustly correlates the cosmological baryon asymmetry with rare, testable $B$- and heavy baryon decay signatures. Its experimental exclusion or confirmation in the coming years would have fundamental implications for models of baryogenesis and for the interconnection of SM flavor physics, cosmology, and the dark sector (Elor, 22 Sep 2025, Lenz et al., 2024, Collaboration et al., 2023).