Baryogenesis and Dark Matter from non-thermally produced WIMPs

This paper proposes a unified scenario where non-thermally produced WIMP-like particles, generated during an early matter-dominated epoch, simultaneously account for the observed baryon asymmetry and dark matter abundance while remaining within the detectable mass range of colliders.

The Gist

Imagine the early Universe as a giant, chaotic kitchen right after the Big Bang. For a long time, physicists have been trying to solve two massive mysteries about what happened in that kitchen:

1. The Missing Antimatter: Why is our universe made almost entirely of "matter" (like us, stars, and planets) and almost no "antimatter"? If they were created equally, they should have canceled each other out, leaving nothing but empty light.
2. The Invisible Stuff: What is "Dark Matter"? We know it's there because it holds galaxies together with gravity, but we can't see it or touch it.

Usually, scientists think these two things happened separately. But this paper proposes a deliciously simple idea: What if both the matter we see and the invisible Dark Matter were cooked up by the same recipe, using the same special ingredient?

Here is the story of their discovery, broken down into everyday concepts.

The Problem: The "Standard Recipe" Didn't Work

Imagine trying to bake a cake (the matter in our universe) using a standard oven (the standard history of the Universe). The authors tried to bake this cake using a specific type of heavy particle called a WIMP (Weakly Interacting Massive Particle).

In the "standard recipe," these particles were cooked in a hot, dense soup. The problem? The oven was too efficient. The particles annihilated each other (destroyed themselves) too quickly, or they didn't stick around long enough to create the right amount of "matter" vs. "antimatter." It was like trying to make a specific flavor of ice cream, but the freezer was so cold that the mixture froze before it could get the right taste. The result was a universe with almost no matter.

The Twist: The "Early Matter Domination"

To fix this, the authors changed the history of the Universe's kitchen. They proposed a scenario called Early Matter Domination (EMD).

Think of the early Universe not as a hot soup, but as a slow-cooking stew.

• The Exotic Ingredient (The Mother Particle): Imagine a giant, heavy, invisible blob of dough (let's call it $\Psi$) that took over the kitchen. For a while, this dough dominated the energy of the universe, slowing everything down.
• The Slow Cook: Because this dough was so heavy and slow, the universe expanded differently. It wasn't a hot, fast explosion; it was a slow, gentle simmer.
• The Release: Eventually, this giant dough blob decayed (broke apart). When it did, it didn't just disappear; it exploded into a fresh batch of our special WIMP particles.

Because this happened after the universe had cooled down a bit, the new particles didn't get destroyed immediately. They had a chance to survive.

The Magic Trick: One Particle, Two Jobs

Now, here is the clever part of the recipe. The paper suggests that when this giant dough blob ($\Psi$) broke apart, it created a specific heavy particle (let's call it $X_2$). This particle is the "Mother" of everything.

This Mother particle has a split personality:

1. The Matter Maker: It decays in a way that is slightly unfair. It produces a tiny bit more "matter" than "antimatter." Over time, this tiny unfairness adds up to create all the stars and galaxies we see today.
2. The Dark Matter Parent: It also decays into a different, invisible particle (let's call it $X_{DM}$). This invisible particle is our Dark Matter.

The Analogy: Imagine a factory machine (the Mother particle) that drops out two types of toys: Red Blocks (Matter) and Invisible Ghosts (Dark Matter).

• In the old "Standard Recipe," the machine was broken, and it dropped out too few toys.
• In this new "Slow Cook" recipe, the machine is fed by the giant dough blob. It drops out the perfect number of Red Blocks to fill the universe, and it also drops out the perfect number of Invisible Ghosts to hold the galaxies together.

Why This is a Big Deal

The authors did the math (using complex equations called Boltzmann equations, which track how particles move and change) and found something exciting:

• The Mass is Just Right: In many other theories, the particles needed to be impossibly heavy (trillions of times heavier than a proton), making them impossible to detect. But in this "Slow Cook" scenario, the particles can be much lighter—light enough that we might actually be able to create them in particle colliders like the Large Hadron Collider (LHC) soon!
• A Common Origin: It solves two of the biggest mysteries in physics with one single event. The reason we exist (matter) and the reason galaxies don't fly apart (dark matter) are two sides of the same coin.

The Conclusion

The paper argues that if the early Universe had a "slow cooker" phase (dominated by a heavy, exotic field) before it became the hot radiation-filled universe we know, then:

1. We would have just the right amount of matter to exist.
2. We would have just the right amount of Dark Matter to hold the universe together.
3. The particles responsible for this are light enough that we might be able to catch them in our labs.

It's a beautiful, unified story: The universe didn't need two separate miracles to explain what we see and what we can't see. It just needed one special, slow-cooked event to bake them both at the same time.

Technical Summary

1. Problem Statement

The paper addresses two fundamental mysteries in cosmology: the origin of the baryon asymmetry of the universe (BAU) and the nature of Dark Matter (DM).

• The Challenge: Standard thermal WIMP (Weakly Interacting Massive Particle) scenarios for baryogenesis often fail to generate sufficient baryon asymmetry. This is because the CP-violating asymmetry generated in particle decays is typically very small. To compensate, the mother particle must have a very large thermal abundance, which often requires unfeasibly heavy mass scales (beyond collider reach) or leads to overproduction of DM.
• The Goal: The authors propose a unified framework where both the baryon asymmetry and Dark Matter are generated simultaneously via the non-thermal decay of a heavy mother particle, produced during an Early Matter Domination (EMD) phase. This approach aims to lower the required mass scales to the TeV range, making them accessible to current or future colliders.

2. Methodology

The authors employ a simplified model extending the Standard Model (SM) and utilize numerical solutions to coupled Boltzmann equations to track particle abundances.

A. The Simplified Model

• Field Content:
  • Two massive Majorana fermions, $X_1$ and $X_2$ (with $M_{X_2} > M_{X_1}$).
  • A scalar field $\Phi$ (mass $M_\Phi$).
  • Interactions are governed by a Yukawa-like Lagrangian involving quark fields ($Q, U, D$) and the new scalars/fermions.
• Mechanism:
  • Baryogenesis: The heaviest particle, $X_2$, decays out of equilibrium. The presence of both $B$-violating and $B$-conserving decay channels (mediated by $\Phi$ and $X_1$) generates a non-zero CP asymmetry ($\epsilon_{CP}$).
  • Non-Thermal Production: Instead of thermal freeze-out, the universe undergoes an Early Matter Domination (EMD) phase driven by a metastable scalar field $\Psi$ (mass $M_\Psi = 10^6$ GeV). $\Psi$ decays non-thermally into $X_2$ particles, significantly enhancing their abundance compared to the standard thermal scenario.

B. Cosmological Evolution

• Standard Scenario: The authors first solve the standard Boltzmann equations for a radiation-dominated universe. They find that for TeV-scale masses, the thermal abundance of $X_2$ is insufficient to overcome the small CP asymmetry, failing to reproduce the observed baryon asymmetry ($Y_{B-L}^{obs} \approx 10^{-10}$).
• EMD Scenario: They introduce a modified cosmological history where $\Psi$ dominates the energy budget before decaying at a reheating temperature $T_R$.
  • The system of equations is extended to include the energy density of $\Psi$ ($\rho_\Psi$) and the radiation bath ($\rho_R$).
  • The Hubble expansion rate $H$ is modified to account for the matter-dominated era ($H \propto a^{-3/2}$ vs $a^{-2}$ in radiation).
  • The evolution of particle yields ($Y = n/s$) is tracked from the decay of $\Psi$ through the freeze-out and decay of $X_2$.

C. Dark Matter Incorporation

Two scenarios for DM are proposed:

1. Direct Decay: A Majorana fermion $X_{DM}$ is produced directly from the decay of $X_2$.
2. Dark Sector (U(1)$_D$): A vector-like fermion $X_{DM}$ charged under a new $U(1)_D$ gauge symmetry. It interacts with $X_2$ via a scalar mediator $\Sigma$. This allows for $X_2 X_2 \to X_{DM} X_{DM}$ annihilation, linking the DM abundance to the baryogenesis sector.

3. Key Contributions

1. Resolution of the Mass Scale Problem: The paper demonstrates that non-thermal production via EMD allows for successful baryogenesis with particle masses in the TeV range (specifically $O(100 \text{ GeV}) - O(10 \text{ TeV})$), whereas standard thermal scenarios often require much heavier scales.
2. Analytical Approximation: The authors derive an analytical estimate for the final baryon yield in the EMD scenario:
   $$Y_{B-L} \approx 1.2 \times 10^{-11} \lambda^2 B_{X_2} \left(\frac{M_{X_2}}{100 \text{ GeV}}\right)^2 \left(\frac{1 \text{ TeV}}{M_\Phi}\right)^2 \left(\frac{T_R}{1 \text{ GeV}}\right) \left(\frac{10^6 \text{ GeV}}{M_\Psi}\right)$$
   This highlights the linear dependence on the reheating temperature $T_R$, a crucial lever for tuning the asymmetry.
3. Unified Origin: The model provides a common origin for baryon asymmetry and Dark Matter, where both are generated from the decay of the same mother particle ($X_2$) or its non-thermal precursor ($\Psi$).
4. Collider Viability: By lowering the mass scale to the TeV range, the proposed particles ($X_1, X_2, \Phi$) fall within the potential detection reach of the LHC or future colliders.

4. Results

• Standard vs. Non-Standard: Numerical integration of the Boltzmann equations confirms that the standard thermal history fails to produce the observed $Y_{B-L}$ for TeV-scale masses. However, the EMD scenario successfully reproduces the observed baryon abundance for a wide range of parameters.
• Parameter Dependence:
  • Reheating Temperature ($T_R$): The baryon yield increases with $T_R$ until $T_R$ approaches the thermal freeze-out temperature of $X_2$ ($\sim M_{X_2}/20$). Beyond this point, the non-thermal advantage diminishes as the decay products thermalize.
  • Coupling ($\lambda$): There is an optimal coupling value. Too low $\lambda$ results in insufficient CP asymmetry; too high $\lambda$ leads to efficient annihilation of $X_2$, reducing the available mother particles for decay.
• Dark Matter Relic Density:
  • In the direct decay scenario, the correct DM relic density is achieved with a very small branching ratio ($B_{DM} \sim 10^{-6} - 10^{-5}$).
  • In the $U(1)_D$ scenario, the DM abundance is sensitive to the gauge coupling $g_D$. The authors show that for specific benchmarks ($M_{X_{DM}} \sim 500 \text{ GeV} - 1 \text{ TeV}$), the correct relic density is obtained for $g_D \approx 0.35 - 0.5$.
  • The DM abundance in the $U(1)_D$ case follows a "non-thermal production with chemical equilibrium" behavior, where the relic density scales inversely with the cube of the reheating temperature relative to the standard freeze-out temperature.

5. Significance

This work offers a compelling alternative to standard thermal WIMP baryogenesis. By invoking an Early Matter Domination phase, it decouples the required particle mass scales from the magnitude of the CP asymmetry.

• Phenomenological Impact: It revitalizes the search for WIMP-like baryogenesis at colliders, suggesting that the particles responsible for the matter-antimatter asymmetry could be light enough to be produced and detected.
• Theoretical Framework: It provides a robust, simplified model that unifies the solutions to the baryon asymmetry and Dark Matter problems without requiring complex UV completions or extremely heavy new physics scales.
• Future Directions: The paper sets the stage for more systematic studies of the parameter space and specific collider signatures (e.g., displaced vertices from long-lived $X_2$ decays) that could test this non-thermal cosmological history.