Blocking Mesogenesis

This paper proposes a mechanism to circumvent stringent experimental constraints on Mesogenesis models—which explain baryon asymmetry and dark matter via meson decays—by utilizing a late-time phase transition to dynamically increase dark sector particle masses, thereby kinematically forbidding the decays that would otherwise violate proton lifetime limits and observed CP violation bounds.

The Gist

The Big Mystery: Why is there more stuff than anti-stuff?

Imagine the Big Bang as a giant cosmic baking oven. According to our best theories, it should have baked equal amounts of "matter" (the stuff we are made of) and "anti-matter" (its evil twin). When matter and anti-matter meet, they annihilate each other into pure energy, like a bomb going off.

If the universe had equal amounts of both, they would have all destroyed each other, leaving a universe made only of light and no stars, planets, or people. But here we are! There is a massive surplus of matter. Something must have tipped the scales early on to save the matter. This is called Baryon Asymmetry.

The Old Idea: "Mesogenesis" (The Messy Kitchen)

Scientists have proposed a theory called Mesogenesis. Imagine the early universe as a busy kitchen. In this kitchen, heavy particles called Mesons (like unstable cookies) were decaying (breaking apart).

Usually, when a cookie breaks, it makes two crumbs. But in Mesogenesis, these specific cookies were breaking in a weird way:

1. One crumb became a normal proton (matter).
2. The other crumb became a Dark Matter particle (invisible stuff).

This process created a little extra matter every time it happened. Over time, this built up the universe we see today.

The Problem:
This theory has two major "kitchen disasters":

1. The Proton Leak: If the invisible Dark Matter particle is too light, it could accidentally cause a normal proton to decay (break apart) today. We know protons are incredibly stable (they last forever), so if this theory predicts they should break, the theory is wrong.
2. The Too-Small Signal: To get enough matter to fill the universe, the "cookie breaking" (decay) needs to happen very often. But experiments at particle colliders (like the LHC) have looked for these specific cookies breaking and haven't seen them. The theory requires the cookies to break too often compared to what we can observe.

The New Idea: "Blocking Mesogenesis" (The Shape-Shifting Lock)

The authors of this paper propose a clever workaround. They suggest that the rules of the kitchen changed after the baking was done but before the universe cooled down completely.

They call this "Blocking Mesogenesis."

Here is the analogy:
Imagine you are trying to fit a large suitcase (the Dark Matter particle) through a small door (the decay process).

• In the Early Universe (Hot): The suitcase is made of soft foam. It is squishy and small. It fits easily through the door. The "cookie" breaks, creating matter and dark matter. The universe gets its extra matter.
• The Phase Transition (The Change): Suddenly, the temperature drops, and a "phase transition" happens (like water turning to ice). The suitcase suddenly freezes and expands. It becomes a giant, hard block of ice.
• Today (Cold): Now, the suitcase is too big to fit through the door. The door is blocked.

How This Solves the Problems

This "morphing" (changing shape) of the Dark Matter particle solves the two disasters mentioned earlier:

1. Solving the Proton Leak:

   • Before: The Dark Matter particle was light enough to cause protons to break apart.
   • After: The particle grew heavy (the suitcase expanded). Now, it is too heavy to interact with protons in a way that breaks them. The protons are safe, and our universe remains stable.

2. Solving the "Too-Small Signal" Problem:

   • Before: We needed the cookies to break all the time in the early universe to get enough matter. But if they broke that often, we should see them breaking in our labs today. We don't.
   • After: The cookies broke all the time in the early universe (when the suitcase was small). But today, the suitcase is too big, so the cookies cannot break anymore.
   • The Result: We can have a theory where the cookies broke frequently in the past (creating the universe) but don't break today (so experiments don't see them). It's like a factory that ran at full speed for one hour and then shut down forever.

The "Magic" Mechanism

How does the suitcase change size? The paper suggests a Dark Phase Transition.
Think of the Dark Sector (the invisible world) as having its own weather. At a specific moment in the universe's history, the "weather" changed (a phase transition, like water freezing). This change gave the Dark Matter particles a sudden "mass boost," making them heavier and blocking the decay channels.

Why This Matters

This paper is exciting because:

• It saves the theory: It allows the Mesogenesis idea to survive the strict rules of modern physics.
• It opens new doors: It suggests that we might be able to create these heavy Dark Matter particles in our particle colliders (like the LHC) by smashing things together at high energies, even though they don't appear in nature today.
• It predicts new signals: It suggests we might see rare decays of other particles (like Lambda baryons) that act as "smoking guns" for this theory.

Summary

The universe is full of matter because, long ago, a specific type of particle decay happened frequently. But if that decay still happened today, it would break protons and violate what we see in experiments.

This paper proposes that the "rules of the game" changed. The particles involved in that decay grew heavier over time, effectively locking the door on the decay process. This allows the universe to have been created by this process without breaking the laws of physics we see today. It's a brilliant "get out of jail free" card for a very promising theory.

Technical Summary

1. Problem Statement

The paper addresses two major constraints hindering the viability of Mesogenesis, a mechanism proposed to explain the Baryon Asymmetry of the Universe (BAU) and Dark Matter (DM) through the late-time decays of Standard Model (SM) mesons ($M$) into a baryon ($B$) and a dark sector fermion ($\psi$).

• Proton Decay Constraints: In standard Mesogenesis models, if the dark fermion $\psi$ is lighter than the proton ($m_\psi < m_p$), it induces proton decay via loop diagrams involving the mediator. This is particularly problematic for models utilizing $D$-mesons, where kinematic requirements for the decay $D \to B\psi$ force $m_\psi \lesssim 0.92$ GeV, well below the proton mass.
• CP Violation and Branching Ratio Tension: To reproduce the observed BAU ($Y_{obs} \approx 8.7 \times 10^{-11}$), the product of the branching ratio ($BR$) and CP asymmetry ($A_{CP}$) must satisfy specific thresholds.
  • For $B$-meson mixing, observed CPV limits are small ($|A_{mix}| \lesssim 2 \times 10^{-3}$), requiring a large branching ratio ($BR \gtrsim 10^{-3}$ to $0.1$). However, experimental searches for $B \to B + \text{missing energy}$ constrain $BR \lesssim 10^{-5}$.
  • For direct CPV, while theoretical limits are looser, the required branching ratios ($BR \sim 10^{-5}$) are approaching current experimental sensitivity, creating tension.

The core problem is that current terrestrial bounds on rare meson decays and proton stability seemingly rule out the parameter space required for Mesogenesis to work, especially for $D$-meson scenarios.

2. Methodology and Proposed Mechanism

The authors propose a novel mechanism dubbed "Blocking Mesogenesis." The central idea is to introduce a late-time phase transition (PT) in the dark sector that occurs after the reheating temperature ($T_R$) but before Big Bang Nucleosynthesis (BBN).

• Mass Morphing: During this phase transition, the masses of the dark sector particles ($\psi$ and its decay products) undergo a significant shift ("morphing").
  • Early Universe ($T > T_{PT}$): The mass $m_\psi$ is light enough to allow the decay $M \to B\psi$, generating the BAU.
  • Late Universe ($T < T_{PT}$): The mass shifts to $m'_\psi = m_\psi + \Delta m_\psi$ such that $m'_\psi > m_M - m_B$. This kinematically blocks the meson decay today.
  • Proton Stability: The mass shift also ensures $m'_\psi > m_p$, thereby suppressing proton decay in the current epoch.

Key Models:
The authors construct three benchmark scenarios based on different meson sources and CPV origins:

1. Mechanism A: $B^0_{d,s}$ decays with CPV from meson oscillations (mixing).
2. Mechanism B: $B$ decays with direct CPV from the dark sector.
3. Mechanism C: $D$ decays with direct CPV (previously ruled out by proton decay bounds).

Dark Sector Implementation:
Two specific dark sector models are proposed to realize the mass morphing:

• Strongly Interacting Sector: A confining non-Abelian gauge theory where a scalar operator acquires a Vacuum Expectation Value (VEV) below a critical temperature, inducing mass shifts via effective operators.
• Dark Abelian Higgs Model: A $U(1)_D$ gauge symmetry broken via a first-order phase transition. Mass shifts are induced through mixing between the dark fermion $\psi$ and a vector-like fermion $\psi_2$ that carries the $U(1)_D$ charge.

3. Key Contributions

• Relaxation of Proton Decay Bounds: By allowing $m_\psi < m_p$ in the early universe but $m_\psi > m_p$ today, the mechanism resurrects $D$-meson Mesogenesis, which was previously excluded.
• Decoupling of Early and Late Universe Constraints: The mechanism allows for large branching ratios ($BR \sim 0.1$) in the early universe to generate the BAU, while the branching ratio today is effectively zero. This bypasses the stringent $BR \lesssim 10^{-5}$ limits from current $B$-factory experiments (Belle, BaBar, LHCb).
• Compatibility with SM CPV: For Mechanism A, the reduced requirement on the branching ratio means the model can potentially be driven solely by the Standard Model's CP violation in $B$-meson mixing, rather than requiring large new physics CPV sources.
• New Phenomenological Signatures: The model predicts sub-TeV colored scalar mediators ($Y$) accessible at the LHC, as well as rare decays of heavy baryons (e.g., $\Lambda_c \to K + \text{missing energy}$) that are not kinematically blocked.

4. Results

The authors performed a comprehensive analysis of the parameter space ($m_Y$ vs. $m_\psi$) for the three mechanisms:

• Mechanism A (Mixing CPV):
  • The analysis shows that with the blocking mechanism, the full BAU can be generated even if the CP asymmetry is limited to the SM prediction (or slightly above).
  • The parameter space is consistent with LHC constraints on colored scalars ($m_Y \sim \text{TeV}$) and avoids proton decay limits.
• Mechanism B (Direct CPV in B):
  • Allows for successful BAU generation with $A_{dir} \sim 10^{-3}$.
  • Predicts a signal in the decay channel $\Xi^0_b \to D^0 + \text{missing energy}$.
• Mechanism C (Direct CPV in D):
  • Successfully generates the BAU for $D \to \Lambda \psi$.
  • Predicts a signal in $\Lambda_c \to K + \text{missing energy}$.
  • Crucially, this mechanism is only viable because the mass morphing prevents the proton decay that would otherwise occur if $m_\psi$ remained light today.

Phase Transition Viability:
The authors verified that the required mass shifts ($\Delta m_\psi \sim \mathcal{O}(100 \text{ MeV} - \text{GeV})$) can be achieved by both proposed dark sector models without violating BBN constraints or generating excessive gravitational waves (GW). The latent heat released is sufficient to modify particle masses but mild enough to avoid washing out the BAU or causing a period of inflation.

5. Significance

This work fundamentally alters the landscape of low-scale baryogenesis:

1. Revival of Excluded Models: It rescues Mesogenesis models based on $D$-mesons and those relying solely on SM CPV, which were previously considered dead ends due to experimental bounds.
2. New Experimental Targets: It shifts the search strategy from looking for rare meson decays (which are now blocked) to searching for direct production of sub-TeV colored scalars at colliders (LHC, FCC) and rare heavy baryon decays ($\Lambda_c, \Xi_c$).
3. Cosmological Consistency: It demonstrates a robust way to reconcile high-energy physics requirements (generating BAU) with low-energy precision constraints (proton stability, rare decays) through dynamical mass evolution in the early universe.
4. Gravitational Wave Potential: If the phase transition is first-order, the model predicts a stochastic gravitational wave background potentially detectable by future observatories, linking baryogenesis to multi-messenger astronomy.

In summary, "Blocking Mesogenesis" provides a theoretically consistent and phenomenologically rich framework that resolves the tension between the requirements for generating the matter-antimatter asymmetry and the stringent experimental limits on proton decay and rare meson decays.