Baryon and lepton asymmetry of the Universe in the left-right weak interaction model

This paper proposes that in a left-right weak interaction model, baryon and lepton asymmetries arise during the hadronization of quark-gluon plasma due to CP-violating differences in neutron and antineutron lifetimes caused by right-handed vector boson mixing, while sterile neutrinos account for dark matter and carry a compensating lepton asymmetry.

The Gist

The Big Mystery: Why is the Universe Made of Stuff?

Imagine the Big Bang as a giant explosion that created equal amounts of "matter" (the stuff we are made of) and "antimatter" (its evil twin). In a perfect world, when matter and antimatter meet, they annihilate each other, turning into pure energy (like a flash of light). If the universe started with equal amounts of both, they should have wiped each other out completely, leaving a universe filled only with light and no people, stars, or planets.

But here we are. The universe is full of matter. This means something happened in the very early universe to tip the scales, creating a tiny bit more matter than antimatter. This paper tries to explain how that happened.

The New Theory: A "Left-Right" Twist

The authors propose a new version of the "Left-Right Weak Interaction Model." Think of the weak force (one of the four fundamental forces of nature) as a pair of hands: a Left hand and a Right hand.

• The Standard Model (Old View): The universe mostly uses the Left hand. The Right hand is barely there.
• This Paper's View: The Right hand is there, but it's a bit mixed up with the Left hand.

The Key Twist: The authors suggest that this mixing works differently for "particles" (like neutrons) than it does for "antiparticles" (like antineutrons).

• Imagine a dance where the Left hand leads the male dancers and the Right hand leads the female dancers.
• In this new theory, the "mixing angle" (how much the hands overlap) is positive for the male dancers but negative for the female dancers.
• Because of this sign difference, the "Right hand" boson (a particle carrier) interacts differently with matter than with antimatter. This breaks the symmetry and creates CP Violation (a fancy way of saying the laws of physics treat matter and antimatter slightly differently).

How the Universe Got Its Matter (The Baryon Asymmetry)

The paper suggests this happened during the "Hadronization" phase, which is like the moment when a hot soup of quarks cooled down enough to freeze into solid chunks (protons and neutrons).

1. The Race: Imagine neutrons and antineutrons are runners in a race. They are both trying to survive.
2. The Uneven Track: Because of the "Left-Right" mixing described above, the track for neutrons is slightly different than the track for antineutrons.
3. The Result: Neutrons live just a tiny bit longer than antineutrons. It's a very small difference (like one runner finishing a race a fraction of a second before the other), but because there are so many runners, this tiny advantage adds up.
4. The Winner: The antineutrons die off slightly faster. The neutrons survive. When the universe expands and cools, the surviving neutrons become the protons and neutrons that make up our world today.

The authors calculate that this tiny difference in "lifespan" explains exactly how much extra matter we see in the universe today.

The Ghost Particles: Sterile Neutrinos and Dark Matter

The paper also tackles a second mystery: Dark Matter. We know there is invisible stuff holding galaxies together, but we don't know what it is.

The authors propose that this invisible stuff is made of Sterile Neutrinos.

• Active Neutrinos: These are like social butterflies; they interact with everything and are everywhere.
• Sterile Neutrinos: These are like ghosts. They barely interact with anything. They are "sterile" because they don't play by the usual rules of the weak force.

The Escape Plan:
In the early universe, these heavy sterile neutrinos were born. Because they are heavy and don't interact much, they didn't get "stuck" in the cosmic soup like the other particles. They escaped (or "thermalized" differently) and floated away.

• Dark Matter: These escaped sterile neutrinos are the dark matter. They form invisible gravitational wells that hold galaxies together.
• Lepton Asymmetry: When these ghosts left, they took some "lepton" (a type of particle) imbalance with them. This created a balance sheet where the excess of matter (baryons) is matched by an excess of "missing" lepton numbers, keeping the universe's overall math balanced.

The Evidence and The Future

The authors claim their theory fits the data we already have:

• Neutron Decay: They used measurements of how neutrons decay to find the "mixing angle" parameters.
• Meson Oscillations: They checked their math against experiments with K-mesons, D-mesons, and B-mesons (unstable particles that flip between matter and antimatter). Their theory predicts the observed "flips" correctly.

What Needs to Happen Next?
The paper concludes that while the theory looks good, the current measurements aren't precise enough to be 100% sure.

• They are calling for new, ultra-precise experiments (specifically at the PIK reactor in Russia) to measure neutron decay with much higher accuracy.
• If they can measure the "asymmetry" (the difference between matter and antimatter behavior) with 5 times more precision, they hope to prove this "Left-Right" theory is the correct explanation for why we exist.

Summary Analogy

Imagine a giant coin toss that happened at the beginning of time.

• Old Theory: The coin was perfectly fair. It should have landed 50/50, leaving us with nothing.
• This Paper's Theory: The coin was slightly bent (due to the "Left-Right" mixing). It wasn't a huge bend, just a tiny one. But because the universe is so big, that tiny bend meant that for every billion "tails" (antimatter) that disappeared, one "head" (matter) survived.
• The Ghosts: While the coins were being tossed, some "ghost coins" (sterile neutrinos) flew off the table entirely. They are now the invisible scaffolding (Dark Matter) holding the universe together, while the remaining coins formed the stars and us.

Technical Summary

Technical Summary: Baryon and Lepton Asymmetry in the Left-Right Weak Interaction Model

Problem Statement
The paper addresses the fundamental cosmological problem of baryon asymmetry: the observed predominance of matter over antimatter in the Universe. The Standard Model (SM) fails to explain this asymmetry, as it assumes symmetry between matter and antimatter. While A.D. Sakharov formulated three necessary conditions for generating baryon asymmetry (baryon number violation, C/CP violation, and non-stationarity), the SM provides insufficient CP violation and lacks a robust mechanism for baryon number violation under cosmological conditions. Furthermore, recent precision measurements of neutron decay and superallowed nuclear beta decays reveal deviations from the SM at the 3.7$\sigma$ level and a discrepancy in the CKM matrix unitarity, suggesting new physics. The authors propose that these anomalies can be reconciled within an extended left-right (LR) weak interaction model, which simultaneously offers a mechanism for generating both baryon and lepton asymmetries and a candidate for dark matter.

Methodology and Theoretical Framework
The authors utilize an extended left-right manifest model of weak interactions. A central feature of this model is the mixing of left ($W_L$) and right ($W_R$) vector bosons. Unlike standard LR models, this extended version introduces a specific asymmetry in the mixing scheme: the mixing angle $\zeta$ changes sign depending on the charge of the vector boson ($W^-$ vs. $W^+$).

• Mixing Scheme: The flavor states are related to mass states via a mixing matrix where the sign of the sine term ($\sin \zeta$) is positive for $W^-$ (particle) and negative for $W^+$ (antiparticle).
• Parameters: The model is constrained by precision neutron decay data, yielding optimal parameters: $\delta \approx 0.070$ (ratio of squared masses of $W_1$ and $W_2$) and $\zeta \approx -0.039$. This implies a right-handed boson mass $M_{W_R} \approx 304$ GeV, consistent with collider limits due to the suppressed resonance of the impurity state.
• CP Violation Mechanism: The sign difference in the mixing angle for $W^-$ and $W^+$ leads to different decay probabilities for particles and antiparticles. Specifically, the decay of a neutron (via $W^-$) and an antineutron (via $W^+$) proceeds with different lifetimes, creating a CP-violating asymmetry $A_{LR} \approx -2\delta\zeta \approx 5.5 \times 10^{-3}$.

Key Contributions and Results

1. Generation of Baryon Asymmetry:
   The paper proposes that baryon asymmetry arises during the hadronization of quark-gluon plasma (at temperatures $T < 150$ MeV).

   • Sakharov Conditions: The model satisfies all three conditions:
     • Baryon Number Violation: Achieved through the difference in neutron and antineutron decay rates ($\tau_n \neq \tau_{\bar{n}}$) during the rapid expansion of the Universe.
     • CP Violation: Inherent in the LR model due to the sign-dependent mixing of $W^\pm$.
     • Non-stationarity: The expansion rate of the Universe ($H \sim 10^3$ s$^{-1}$) exceeds the decay rate of neutrons ($\Gamma \sim 10^{-3}$ s$^{-1}$), preventing thermal equilibrium.
   • Quantitative Estimate: Using the derived asymmetry and the timescale of hadronization ($t \sim 10^{-3}$ s), the authors estimate a baryon-to-photon ratio $\eta \approx (5.3 \pm 2.6) \times 10^{-10}$. This is of the same order of magnitude as the observed value ($6.1 \times 10^{-10}$), suggesting the mechanism is viable.

2. Generation of Lepton Asymmetry and Dark Matter:
   The model incorporates sterile (right-handed) neutrinos ($m_4, m_5, m_6$) corresponding to electron, muon, and tau flavors.

   • Lepton Asymmetry: Sterile neutrinos do not thermalize with the cosmic plasma and escape, carrying away a lepton asymmetry with a sign opposite to the baryon asymmetry. This preserves the $B-L$ difference while disrupting the $B+L$ balance.
   • Dark Matter Formation: The paper presents a mechanism where heavy sterile neutrinos (in the keV range) form dark matter.
     • Light sterile neutrinos (eV scale) reach thermal equilibrium and cannot explain structure formation.
     • Heavy sterile neutrinos (keV scale) with small mixing angles do not thermalize. They separate from the plasma early ($10^{-6}$–$10^{-5}$ s), forming gravitational wells that seed galaxy formation.
     • The authors suggest that three sterile neutrino states could account for $\sim 27\%$ of the Universe's dark matter density, while the heaviest state ($m_6$) might contribute to dark energy dynamics via gravitational expansion.

3. Validation via Neutral Meson Oscillations:
   The authors apply the derived parameters ($\delta, \zeta$) to neutral meson systems ($K^0, D^0, B^0, B_s^0$).

   • The model predicts a CP-violating asymmetry $A_{LR} \approx 5.5 \times 10^{-3}$.
   • Calculations show that for $K^0$ and $D^0$ mesons, where the oscillation period is longer than the decay time, the integral asymmetry matches experimental data.
   • For $B_s^0$ mesons, rapid oscillations lead to a suppression of the integral asymmetry, consistent with current experimental limits.
   • The model successfully describes the time-dependent CP violation observed in $B^0$ decays, attributing the sign change of CP violation to the transition between $W^-$ and $W^+$ mediated processes.

Significance and Claims
The paper claims that the extended left-right model provides a unified explanation for several outstanding issues in particle physics and cosmology:

• It resolves the discrepancy between neutron decay data and CKM unitarity by introducing a sign-dependent mixing angle for vector bosons.
• It offers a concrete mechanism for the generation of baryon and lepton asymmetries that satisfies Sakharov's conditions without requiring GUT-scale physics, relying instead on the hadronization epoch and sterile neutrino dynamics.
• It proposes a specific dark matter candidate (keV sterile neutrinos) that naturally arises from the LR symmetry breaking scale.
• The model predicts that the nature of CP violation is tied to the presence of a right-vector boson admixture with opposite mixing signs for particles and antiparticles.

Future Directions and Experimental Verification
The authors emphasize that the validity of this model depends on increasing the precision of experimental measurements. They specifically cite the "Neutron Beta Decay" project at the PIK reactor (NRC KI), which aims to improve the measurement accuracy of neutron decay asymmetries by a factor of three (reaching $10^{-3}$ relative accuracy). Achieving a $5\sigma$ significance in these measurements would strongly support the left-right model. Additionally, they note the need for improved sensitivity in sterile neutrino searches (e.g., Neutrino-4 experiment) to constrain the mass and mixing parameters of the proposed dark matter candidates.