Mesogenesis through the Ephemeral Dark Decay of Beauty

This paper proposes a mechanism for generating the Universe's baryon asymmetry via mesogenesis, where an ultralight scalar and early-Universe thermal muons temporarily enable dominant $B$ meson decays into dark sectors, satisfying current flavor constraints while predicting observable signals in future collider, flavor, and astrophysical experiments.

The Gist

The Big Mystery: Where Did All the Matter Come From?

Imagine the Big Bang as a massive explosion that created equal amounts of "stuff" (matter) and "anti-stuff" (antimatter). In a perfect world, these two should have cancelled each other out immediately, leaving behind only empty energy. But they didn't. We exist, which means there was a tiny bit more matter than antimatter left over. This leftover is called the Baryon Asymmetry.

Physicists have long struggled to explain how this imbalance happened. Usually, they look for new, exotic laws of physics to explain it. This paper, however, suggests we might have been looking in the wrong place. It argues that the Standard Model of physics (our current best rulebook) actually does have the secret ingredient needed to create this imbalance, but it was hidden inside a specific type of particle decay that only happened in the very early universe.

The Problem: The "Forbidden" Door

The paper focuses on a process called Mesogenesis. Think of a B-meson (a heavy particle made of a "beauty" quark) as a delivery truck. In the early universe, this truck was supposed to drop off a package of "dark matter" and a regular particle, creating an imbalance between matter and dark matter.

However, there is a major problem:

1. The Door is Locked Today: If we try to make these trucks drop off their packages now, the door is locked. Experiments at particle accelerators (like the LHC and Belle-II) have looked for these specific decay patterns and found nothing. The "branching fraction" (the chance of this happening) is currently too small to explain the universe.
2. The Mass Mismatch: For the truck to drop off the package, the package (a dark fermion called $\psi_B$) needs to be light enough to fit through the door. Today, this package is too heavy.

The Solution: A "Magic" Temperature Switch

The authors propose a clever workaround. Instead of trying to force the door open today, they suggest the door was only unlocked for a very short time in the past.

Here is the mechanism, explained with an analogy:

The Invisible Thermostat
Imagine the early universe was a hot room filled with a specific type of gas: muons (a type of subatomic particle, like a heavy electron).

• The Scalar Field ($\phi$): Think of this as a "magic thermostat" that floats through the universe. It is incredibly light and invisible.
• The Connection: This thermostat is connected to the muons in the room. When the room is hot and full of muons, the thermostat gets pushed into a specific position.
• The Effect: When the thermostat is in this position, it acts like a weight-lifter for the dark package ($\psi_B$). It temporarily makes the package much lighter, allowing the B-meson truck to drop it off.

The Timeline:

1. Early Universe (The Hot Room): The universe was hot ($\sim 10$ MeV). There were tons of muons. The thermostat was pushed, making the dark package light. The B-mesons decayed rapidly, creating the matter/antimatter imbalance we see today.
2. The Cooling Down: As the universe expanded, it cooled down. The muons disappeared (they "froze out").
3. The Lock Engages: Without the muons pushing the thermostat, the thermostat snapped back to its resting position. Suddenly, the dark package became heavy again (heavier than the B-meson truck). The door slammed shut.
4. Today: The decay channel is now "kinematically forbidden." It's physically impossible for the truck to drop off the package because the package is too heavy. This is why our current experiments don't see it, and why the theory is safe from current data.

The "Heavy" Truck Driver (The Mediator)

To make this work, the theory needs a "mediator" particle (a color-triplet scalar, named $Y$) to help the B-meson talk to the dark sector.

• The Constraint: Usually, these mediators must be very heavy (over 1,000 GeV) to avoid being caught by the LHC.
• The Loophole: The authors show that if this mediator interacts with other particles (like top quarks) very strongly, it changes how it behaves in the LHC detectors. It becomes a "broad resonance" (a blurry signal rather than a sharp spike), making it harder to detect. This allows the mediator to be lighter (around 600 GeV), which is necessary for the math to work, without breaking current LHC rules.

What Can We Look For?

Even though the main "door" is closed today, the paper suggests we might still see footprints of this theory in three ways:

1. Ghostly Three-Body Decays: Even if the main package is too heavy to fit, the B-meson might still try to drop off a "ghost" version of the package (an off-shell particle) along with other debris. This is a very rare event, but future flavor experiments might catch a glimpse of it.
2. Long-Range Muon Forces: The "magic thermostat" (the ultralight scalar) interacts with muons. If we could build a super-sensitive detector, we might feel a new, incredibly weak force acting between muons over long distances.
3. Neutron Star Mergers: Neutron stars are dense balls of matter containing huge numbers of muons. If two neutron stars crash into each other, the intense environment might briefly reactivate the thermostat, potentially changing how the stars behave or how they emit gravitational waves.

Summary

The paper argues that the universe's matter imbalance was created by a "temporary glitch" in the laws of physics. In the hot, early universe, a sea of muons temporarily lightened a dark particle, allowing a specific decay to happen. As the universe cooled, the muons vanished, the particle got heavy again, and the decay stopped. This explains why we see the result (our existence) but can't see the process happening today. The theory is consistent with current data but offers specific targets for future experiments to prove it.

Technical Summary

1. Problem Statement

The origin of the Baryon Asymmetry of the Universe (BAU) remains an open question. While the Sakharov conditions require CP violation, the Standard Model (SM) CP violation (via the CKM phase) is generally considered insufficient to generate the observed asymmetry.

• Mesogenesis Proposal: A specific mechanism, Mesogenesis, suggests that the SM CP violation in $B$-meson decays could generate the BAU if these decays proceed into a dark sector (specifically, $B \to \bar{\psi}_B + B_{SM}$, where $\psi_B$ is a dark fermion carrying anti-baryon number).
• The Conflict: To generate the observed BAU using only SM CP violation, the branching fraction for these exotic $B$-meson decays must be near unity ($\mathcal{O}(1)$) in the early Universe. However, current experimental data from $B$-factories (Belle-II, BaBar) and the LHC constrain these branching fractions to be extremely small ($\lesssim 10^{-4}$).
• Previous Limitations: A prior model (Ref. [7]) attempted to resolve this by having the mediator particle's mass change over time (via domain walls). However, this mechanism risks violating Big Bang Nucleosynthesis (BBN) constraints due to inhomogeneities in the baryon asymmetry before BBN.

2. Methodology and Model Construction

The authors propose a new mechanism where the mass of the dark fermion ($\psi_B$), rather than the mediator, evolves cosmologically. This allows the decay to be kinematically allowed in the early Universe but forbidden today.

A. Cosmological Mass Evolution

• Mechanism: The mass of the dark fermion $\psi_B$ is coupled to an ultralight scalar field ($\phi$).
  $$m_{\psi} = m^0_{\psi} + g_{\psi} \phi$$
• Source of $\phi$: The scalar field $\phi$ acquires a non-zero expectation value in the early Universe due to its coupling with the thermal population of charged leptons (specifically muons, $\mu$, at temperatures $T \sim 10$ MeV).
  $$\mathcal{L} \supset g_{\ell} \phi \bar{\ell}\ell + g_{\psi} \phi \bar{\psi}_B \psi_B$$
• Temporal Dynamics:
  • Early Universe ($T \sim 10$ MeV): The thermal density of muons sources a large value for $\phi$, effectively lowering the mass of $\psi_B$ to $\lesssim 1$ GeV. This allows $B$-mesons to decay into $\bar{\psi}_B + B_{SM}$.
  • Late Universe (Today): As the Universe cools and the muon density drops, $\phi$ oscillates and redshifts. The mass of $\psi_B$ rises to its vacuum value ($m^0_{\psi} \gtrsim 5$ GeV), kinematically forbidding the two-body $B$-meson decay.
• Scalar Parameters: The model requires an ultralight scalar with mass $m_{\phi} \sim \mathcal{O}(10^{-13})$ eV (Compton wavelength $\sim 10^3$ km) to ensure oscillations begin after Mesogenesis but before BBN issues arise.

B. Mediator and LHC Constraints

• Mediator: The interaction is mediated by a color-triplet scalar $Y$ (mass $M_Y$).
• Constraint Challenge: Successful Mesogenesis requires $M_Y \lesssim 600$ GeV. However, LHC searches for single production of color-triplet scalars typically exclude masses up to $\sim 900$ GeV.
• Solution: The authors introduce multiple interaction terms in the Lagrangian to dilute the branching fraction of $Y$ into the specific $B$-meson decay channel ($Y \to c\bar{b}$).
  • They introduce a large coupling to the top quark ($y_{tb} \sim 5$) while keeping $y_{cb}$ and $y_{\psi s}$ smaller.
  • This suppresses the $Y \to c\bar{b}$ branching ratio to $<5\%$, relaxing LHC constraints enough to allow $M_Y \sim 600$ GeV.
  • The large coupling to the top quark broadens the resonance width, further reducing the signal-to-background ratio in collider searches, making the model viable.

3. Key Contributions

1. Novel Mass Evolution Mechanism: Instead of modifying the mediator mass (which led to BBN issues in previous models), the authors shift the mass of the dark sector fermion using an ultralight scalar coupled to SM leptons.
2. Resolution of Experimental Tension: The model successfully reconciles the need for $\mathcal{O}(1)$ branching fractions in the early Universe with the stringent $\lesssim 10^{-4}$ limits observed today by making the decay channel "ephemeral" (active only when muon density is high).
3. LHC Viability: The paper demonstrates that a light color-triplet scalar ($M_Y \sim 600$ GeV) can survive current LHC constraints by utilizing flavor structure (large $y_{tb}$) to suppress the specific decay channels targeted by current searches.
4. Phenomenological Predictions: The model outlines distinct signatures for future experiments beyond standard collider searches.

4. Results and Constraints

• Parameter Space: The benchmark model uses:
  • $m_{\phi} \approx 9 \times 10^{-14}$ eV.
  • $m^0_{\psi} \approx 7$ GeV (vacuum mass).
  • Couplings: $g_{\mu} \sim 10^{-24}$, $g_{\psi} \sim 10^{-13}$.
  • Yukawa couplings: $y_{tb} \sim 5$, $y_{cb} \sim 1$.
• BBN Safety: The model ensures that the scalar field oscillations begin after the BAU generation but before BBN, avoiding the inhomogeneity problems associated with domain wall annihilation in previous models.
• Proton Decay: The mass of $\psi_B$ remains $> 1$ GeV in all relevant environments (including neutron stars), preventing proton decay via $\psi_B$ mediation.
• Dark Matter: The dark fermion $\psi_B$ decays rapidly into stable dark matter ($\phi, \xi$) via a separate interaction, ensuring the asymmetry is transferred to the dark sector without washing out.

5. Significance and Future Signals

The paper provides a robust, testable framework for generating the BAU using only Standard Model CP violation, a scenario previously thought to be ruled out by flavor data.

Potential Signals for Future Detection:

1. Exotic B Decays (Off-shell): While the two-body decay is shut off today, three-body decays ($B \to \xi \phi + B_c$) via an off-shell $\psi_B$ may still occur. These could be probed by future flavor experiments (Belle-II) if the coupling $y_{\psi}$ is sufficiently large ($\gtrsim 10^{-2}$).
2. Long-Range Forces: The ultralight scalar $\phi$ mediates a new long-range force coupled to muons. This could be detected by:
   • Precision tests of the equivalence principle.
   • Gravitational Wave Observations: Neutron star mergers contain high densities of muons ($N_{\mu} \sim 10^{55}$). The presence of the scalar force could alter the merger dynamics or gravitational wave signal, potentially detectable by LIGO/Virgo.
3. LHC Discovery: The color-triplet scalar $Y$ is predicted to be within the reach of future LHC runs (mass $\sim 600$ GeV), particularly if dedicated searches for broad resonances with specific flavor patterns are conducted.

In conclusion, this work revitalizes the Mesogenesis scenario by introducing a cosmological "switch" for dark sector masses, offering a solution to the baryon asymmetry problem that is consistent with current high-energy and flavor constraints while predicting unique signals for astrophysics and future colliders.