Resonant Enhancement for the transfer of baryon number from a CP-violating hidden sector

This paper proposes a mechanism for generating the observed baryon asymmetry via a CP-violating hidden sector portal that sequesters equal and opposite baryon numbers, demonstrating that while top quark decays suffice for generic parameters, bottom quark decays and mesogenesis scenarios require resonant enhancement to achieve maximal efficiency and are potentially testable with improved branching ratio measurements.

The Gist

The Big Mystery: Why Are We Here?

Imagine the universe as a giant party that started with a perfect balance: exactly as many guests (matter) as there were empty chairs (antimatter). According to the laws of physics, when a guest meets an empty chair, they should cancel each other out and disappear.

If the universe started perfectly balanced, everything should have vanished, leaving only light. But we are here. There is a massive surplus of "guests" (matter) and almost no "empty chairs" (antimatter). This is the Baryon Asymmetry. The Standard Model of physics (our best rulebook for how particles behave) can't explain why this imbalance happened.

The Proposed Solution: The "Secret Room"

The authors of this paper propose a new scenario to explain the imbalance. Imagine the universe has two rooms:

1. The Visible Room: This is our world, filled with the matter we see (protons, neutrons, electrons).
2. The Hidden Room: A secret, invisible sector of the universe that we can't see directly.

The theory suggests that the universe didn't create new matter out of nothing. Instead, it acted like a tug-of-war.

• In the early universe, a "portal" (a doorway) opened between the two rooms.
• Through a process involving a specific type of physics violation (called CP violation, which means nature treats left and right, or matter and antimatter, slightly differently), the universe shuffled the balance.
• It moved an equal amount of "matter" into the Visible Room and an equal amount of "anti-matter" into the Hidden Room.
• The Result: The total balance of the whole house is still zero, but our Visible Room is now full of guests, while the Hidden Room is full of empty chairs. We see the guests; the empty chairs are hidden away.

The Problem: The "Leaky Bucket"

For this plan to work, the shuffling had to happen at just the right time.

• If it happened too early (when the universe was very hot), a cosmic "cleanup crew" called sphalerons would have washed the imbalance away, resetting the score to zero.
• If it happened too late, the universe would have already cooled down too much for the process to work.

The authors focus on a specific time window: just after the "cleanup crew" stopped working, but while the universe was still warm enough for heavy particles to exist. They look at two scenarios for how the shuffling happens:

1. Top Quarks: Heavy particles that decay early.
2. Bottom Quarks: Slightly lighter particles that decay later.

The Challenge: The "Weak Signal"

Here is the catch. In physics, creating an imbalance usually requires a "loop" in the math (a complex interaction). This makes the process naturally very slow and inefficient—like trying to fill a swimming pool with a teaspoon.

• For Top Quarks: The authors found that even with this slow "teaspoon" method, there is enough time and enough particles to fill the pool. No special tricks are needed. However, the "doorway" (the portal) would be so weak that we probably couldn't detect it with current experiments.
• For Bottom Quarks: This is where it gets tricky. The "doorway" is much more restricted by experimental rules (we know bottom quarks don't decay strangely very often). Because the doorway is so small, the "teaspoon" method is far too slow to fill the pool before the universe cools down. The math says this scenario should fail.

The Solution: The "Resonant Amplifier"

The paper's main discovery is a way to fix the Bottom Quark problem. They propose using Resonant Enhancement.

The Analogy: Imagine you are trying to push a heavy swing.

• Normal Pushing: If you push at random times, the swing barely moves. This is the "loop-suppressed" method.
• Resonant Pushing: If you wait until the swing is at the exact peak of its arc and push just then, a tiny push creates a massive swing. This is resonance.

In the paper's model, they introduce two "portal particles" (the messengers between the rooms) that have almost exactly the same mass.

• When these two particles are nearly identical in weight, the quantum mechanics of the universe allow them to "mix" in a way that acts like that perfectly timed push.
• This Resonant Enhancement boosts the efficiency of the shuffling process from a "teaspoon" to a "firehose."

The Results

The authors used complex math and computer simulations (Monte Carlo studies) to prove that:

1. It Works Naturally: You don't need to fine-tune the universe with impossible precision. If you pick random numbers for the particle interactions (within reasonable limits), the "resonance" naturally happens about 10% of the time, creating a massive boost in efficiency.
2. The Bottom Line: With this boost, the "Hidden Room" scenario using Bottom Quarks becomes a viable explanation for why we exist.

The "Final Test"

The paper concludes with a challenge for experimental physicists.

• Currently, we know that Bottom Quarks don't decay into these hidden particles more than 1 in 100,000 times ($10^{-5}$).
• The theory predicts that if this scenario is true, we should see these rare decays happening about 1 in 100 million times ($10^{-8}$).
• The Verdict: If future experiments (like Belle-II) improve their sensitivity by 2 or 3 orders of magnitude and still don't see these rare decays, this entire "Hidden Room" theory will be proven wrong. If they do see them, it could be the smoking gun that explains why the universe is full of matter.

Summary

The paper argues that the universe might have hidden its antimatter in a secret sector. While this usually seems too inefficient to work, the authors show that if two invisible particles are nearly identical in mass, a "resonant" effect acts like a megaphone, amplifying the process enough to create the matter-filled universe we see today. This theory can be fully confirmed or ruled out by looking for very rare decays of bottom quarks in the near future.

Technical Summary

Technical Summary: Resonant Enhancement for the Transfer of Baryon Number from a CP-Violating Hidden Sector

Problem Statement
The Standard Model (SM) fails to account for the observed baryon asymmetry of the universe (OBA), quantified by the baryon-to-entropy ratio $Y_B \approx 8.7 \times 10^{-11}$. While Sakharov's conditions (B-violation, C/CP-violation, and out-of-equilibrium dynamics) are necessary, the SM lacks sufficient CP-violation (CPV) and B-violation mechanisms to generate this asymmetry without violating constraints.

This paper investigates a scenario where the OBA arises from a portal coupling between the SM and a CP-violating hidden sector (HS), without explicit violation of baryon ($B$) or lepton ($L$) number in either sector. In this framework, the net $B$-number of the universe remains zero; instead, equal and opposite baryon numbers are sequestered between the SM and the HS. A critical constraint is that this transfer must occur below the electroweak scale ($T \lesssim 100$ GeV) to avoid washout by sphaleron processes, yet above the Big Bang Nucleosynthesis (BBN) scale.

The central challenge addressed is the efficiency of this transfer. When generated via SM particle decays (specifically top or bottom quarks), CPV typically arises from the interference between tree-level and loop-level diagrams, resulting in a suppression factor of $\sim 10^{-3}$. For top quark decays, this generic efficiency is sufficient to generate the OBA. However, for bottom quark decays—relevant to the "mesogenesis" scenario where the universe reheats to low temperatures and bottom quarks are produced non-thermally—existing experimental bounds on rare bottom decays ($Br \lesssim 10^{-5}$) combined with loop suppression render the generic efficiency insufficient. The paper asks whether a resonant enhancement can boost the CPV efficiency to $\mathcal{O}(1)$, thereby making the mesogenesis scenario viable despite tight experimental constraints.

Methodology
The authors construct a minimal benchmark model to facilitate resonant enhancement:

1. Portal Interaction: The SM is coupled to the HS via a dimension-6 "baryon portal" operator involving right-handed up and down quarks: $\mathcal{L}_{eff} \supset \frac{1}{M^2} (\psi^c u^c)(d^c d^c)$. This arises from integrating out a heavy color-triplet scalar $\Phi$ with hypercharge $-2/3$.
2. Hidden Sector: The HS contains two nearly mass-degenerate Dirac fermions $\Psi_{1,2}$ (the portal mediators), a Majorana fermion $\chi$, and a scalar $S$ with baryon number $B=+1$. The $\Psi$ particles decay into the stable HS states ($\chi, S$), which carry the sequestered baryon number.
3. Resonant Mechanism: CPV is generated through the interference of tree-level and one-loop diagrams involving the $\Psi$ propagators. The loop diagram includes a propagator mixing insertion between the nearly degenerate $\Psi_1$ and $\Psi_2$. When the mass splitting $\Delta m_\Psi = |m_{\Psi_1} - m_{\Psi_2}|$ is comparable to the decay width $\Gamma_\Psi$, the propagator goes on-shell, leading to a resonant enhancement of the CPV parameter $A_{CP}$.
4. Analytical and Numerical Analysis:
   • Top Decays: The authors solve Boltzmann equations for top quark decays at $T \sim 100$ GeV to determine the required coupling strengths.
   • Bottom Decays (Mesogenesis): They analyze the constraints from BaBar/Belle experiments on rare bottom meson decays.
   • Monte Carlo Study: To verify that resonant enhancement does not require fine-tuned flavor structures, the authors perform a Monte Carlo simulation. They randomly sample coupling magnitudes (consistent with perturbativity and experimental bounds) and CP phases, fixing the mass splitting $\Delta m_\Psi$ near the resonance condition ($\Delta m_\Psi \sim \Gamma$).

Key Contributions and Results

1. Top Quark Decays: The study confirms that for top quark decays, the generic loop-suppressed CPV ($A_{CP} \sim 10^{-3}$) is sufficient to generate the observed OBA. The required couplings are extremely small ($\mathcal{O}(10^{-19})$ branching ratios), making this specific realization difficult to test experimentally but theoretically consistent.
2. Bottom Quark Decays and Resonance: For bottom quark decays, the paper demonstrates that the generic efficiency is insufficient given current experimental limits on rare decays. However, by utilizing the resonant enhancement mechanism, the CPV efficiency $A_{CP}$ can be boosted to $\mathcal{O}(1)$.
   • Analytical calculations show that $A_{CP}$ peaks when $\Delta m_\Psi \sim \Gamma_\Psi$.
   • The Monte Carlo study reveals that an $A_{CP} > 0.5$ is achieved in approximately 10% of random parameter configurations without fine-tuning of phases or magnitudes. Only a tiny fraction ($\sim 10^{-4}$) of configurations yield non-resonant (generic) values.
3. Experimental Viability:
   • Direct Searches: For top-decay scenarios, the new physics is largely unconstrained by current LHC searches due to tiny couplings, though the scalar mediator $\Phi$ could be pair-produced if its mass is near the LHC limit ($M_\Phi \gtrsim 1.2$ TeV). For bottom-decay scenarios, the larger couplings required for OBA generation are constrained by rare decay searches ($Br \lesssim 10^{-5}$).
   • EDM Constraints: The paper calculates contributions to the neutron electric dipole moment (nEDM) arising from 3-loop diagrams. These contributions are suppressed by $M_\Phi^4$ and are found to be orders of magnitude below current experimental bounds, posing no conflict with the model.

Significance and Claims
The paper claims to establish that the "mesogenesis" scenario, assisted by a CP-violating hidden sector, remains a viable solution to the baryon asymmetry puzzle, provided that resonant enhancement is active.

The authors frame this as a "final stand" for the mesogenesis mechanism:

• If experimental searches for rare bottom meson decays can improve their sensitivity by 2–3 orders of magnitude (reaching $Br \sim 10^{-8}$), the parameter space for this scenario will be fully tested.
• If the branching ratio limits are pushed below $1.3 \times 10^{-8}$, even a maximally efficient ($A_{CP} \sim 1$) resonant enhancement would fail to generate the OBA, effectively ruling out mesogenesis as the source of the asymmetry.
• Conversely, if the mechanism is correct, it predicts the existence of rare bottom decay channels with branching ratios close to the projected limits of future experiments (e.g., Belle II).

The work underscores that while resonant enhancement is a generic feature of models with nearly degenerate mediators, its realization in the context of baryogenesis offers a concrete, falsifiable prediction for upcoming flavor physics experiments.