Leptogenesis and Neutrino Masses Via Pseudo-Dirac Gauginos

This paper proposes a $U(1)_{R-L}$-symmetric supersymmetric model where pseudo-Dirac bino and wino gauginos generate light neutrino masses via a hybrid inverse seesaw mechanism and simultaneously produce the observed baryon asymmetry through $CP$-violating bino oscillations and decays, requiring a decoupled spectrum with TeV-scale binos, multi-TeV sfermions, and a high messenger scale that yields distinctive displaced vertex signals at the LHC.

The Gist

Imagine the universe as a giant, cosmic kitchen. When the universe was born, the recipe called for equal amounts of "matter" (the ingredients we are made of) and "antimatter" (the mirror-image ingredients). If the recipe had been followed perfectly, they would have met, canceled each other out, and left behind a universe filled only with light and energy.

But we are here. The universe is full of matter and almost no antimatter. Something went wrong with the recipe, or rather, something tipped the scales. This paper tries to explain how that tipping happened and, at the same time, explains why tiny particles called neutrinos have mass.

Here is the story, broken down into simple parts using everyday analogies.

1. The Mystery of the Missing Antimatter

Scientists have three rules (called "Sakharov conditions") that must be met to create an imbalance between matter and antimatter:

1. Break the rules: You need a way to violate the "law of conservation" that says matter and antimatter must always be equal.
2. Bias the coin: You need a mechanism that prefers matter over antimatter (CP violation).
3. Act fast: This process must happen while the universe is cooling down and things are out of balance, not when everything is settled and calm.

The Standard Model (our current best theory of physics) tries to do this, but it's like a chef who forgets the salt; it's not enough to explain why we exist. We need a new recipe.

2. The New Ingredients: "Pseudo-Dirac" Gauginos

The authors propose a new model involving two special particles from a theory called Supersymmetry: the Bino and the Wino.

Think of these particles as twin siblings who are almost identical but have a tiny secret difference. In physics, we call them "Pseudo-Dirac."

• The Wino: This sibling is the "heavy lifter." Its main job is to explain why neutrinos have mass. It does this by acting like a bridge, connecting the known world to a hidden, heavy world (a mechanism called the "Inverse Seesaw").
• The Bino: This sibling is the "trickster." It is the one responsible for creating the matter-antimatter imbalance.

3. The Dance of the Twins (Oscillations)

Here is the magic trick. Because the Bino and its "antiparticle" twin are so similar, they can oscillate.

Imagine a dancer who can instantly switch between being a "Boy" and a "Girl" while spinning on stage.

• At first, you have a room full of "Boy" dancers (Binos).
• As they spin, some turn into "Girls" (Anti-Binos) and some turn back.
• Because of a tiny flaw in their dance steps (CP violation), they don't switch back and forth perfectly. They get slightly "stuck" as Girls more often than Boys, or vice versa.

The paper argues that this switching dance creates a bias. If the Bino decays (stops dancing and disappears) while it is still switching back and forth, it leaves behind a pile of "Girls" (leptons) and very few "Boys."

4. The Domino Effect

Once the Binos have created an excess of "Girls" (leptons), the universe's natural laws (specifically, something called Sphalerons) act like a translator. They take that lepton imbalance and convert it into a Baryon imbalance (an excess of protons and neutrons).

• Result: We end up with a universe full of matter (us) and almost no antimatter.

5. The Catch: The "Heavy" Kitchen

For this story to work, the universe needs to be very specific about the "weights" of the ingredients:

• The Bino needs to be heavy (around the size of a TeV, or a thousand billion electron volts) but not too heavy.
• The "Sfermions" (other particles in this theory) need to be incredibly heavy—so heavy they are like invisible giants weighing 50 to 100 TeV. Because they are so heavy, they don't interfere with the Bino's dance, allowing the Bino to live long enough to do its job.
• The Messenger Scale: The "messenger" that tells these particles how to behave needs to be at a scale of about 10 million TeV. This is a very high energy level, far beyond what our current particle colliders can reach directly.

6. What This Means for the LHC (The Particle Zoo)

Since we can't build a machine big enough to create those heavy "giants" (Sfermions), how do we test this?

The paper suggests looking for displaced vertices.

• Imagine a firework that is supposed to explode immediately when lit.
• In this model, the Bino is a "slow-burn" firework. It gets created, travels a short distance away from the explosion point, and then explodes.
• If the Large Hadron Collider (LHC) sees particles appearing in a spot where they shouldn't be (a "displaced" spot), it could be the signature of this long-lived Bino.

Summary

The paper proposes a two-part solution to two of physics' biggest mysteries:

1. Neutrino Mass: The Wino acts as a heavy anchor to give neutrinos their tiny weight.
2. Matter vs. Antimatter: The Bino acts as a dancing trickster, oscillating between matter and antimatter states before decaying, creating the slight bias that allowed our universe to exist.

It's a story of twins, a cosmic dance, and a very specific set of heavy ingredients that, if they exist, might leave a "slow-burn" trail for us to find in our particle accelerators.

Technical Summary

Technical Summary: Leptogenesis and Neutrino Masses Via Pseudo-Dirac Gauginos

Problem Statement
The Standard Model (SM) fails to explain two fundamental observational facts: the origin of neutrino masses and the baryon asymmetry of the universe (BAU). While the SM satisfies the Sakharov conditions for baryogenesis only partially (lacking sufficient CP violation and out-of-equilibrium dynamics), and neutrino oscillations imply non-zero masses requiring new physics (NP), a unified framework is desirable. Traditional leptogenesis models often rely on heavy right-handed (RH) Majorana neutrinos at scales ($M \sim 10^{10-14}$ GeV) inaccessible to current or near-future experiments. Conversely, low-scale leptogenesis (e.g., resonant or ARS) requires nearly degenerate RH neutrinos. This paper investigates a scenario within a $U(1)_{R-L}$ symmetric supersymmetric model where pseudo-Dirac bino and wino fields act as the RH neutrinos, aiming to simultaneously generate light neutrino masses and the BAU at the TeV scale.

Methodology
The authors analyze a specific extension of the Minimal Supersymmetric Standard Model (MSSM) possessing a global $U(1)_{R-L}$ symmetry. In this framework, gauginos cannot possess Majorana masses; instead, they acquire Dirac masses through interactions with adjoint chiral superfields (singlino $S$ and tripletino $T$). The global symmetry is broken by gravity, inducing small Majorana mass terms, resulting in pseudo-Dirac gaugino states.

The methodology involves:

1. Model Construction: The authors utilize a hybrid Type I + III Inverse Seesaw (ISS) mechanism. The Lagrangian includes effective operators coupling the bino ($\tilde{B}$), wino ($\tilde{W}$), and their Dirac partners ($S, T$) to lepton doublets and Higgs fields.
2. Mass Matrix Analysis: A $5 \times 5$ mass matrix is constructed in the basis $(\nu_i, \tilde{B}, \tilde{W}, S, T)$. The authors propose a hierarchy where the wino sector (involving $m_T$ and $G_T$) primarily generates neutrino masses, while the bino sector (involving $m_{\tilde{B}}$ and $G_{\tilde{B}}$) is responsible for leptogenesis.
3. Dynamics of Oscillations: The paper employs the density matrix formalism to describe bino-antibino oscillations in the early universe. Unlike generic RH neutrinos, the bino interacts copiously with the SM plasma via sfermion exchange. The authors derive Boltzmann equations governing the evolution of the bino density matrix, accounting for vacuum oscillations, decays, and thermal scatterings (both flavor-blind and flavor-sensitive).
4. Parameter Space Scan: The study focuses on a bino mass range of $500 \text{ GeV} - 5 \text{ TeV}$ and sfermion masses $M_{sf} \gtrsim 50 \text{ TeV}$. The messenger scale $\Lambda_M$ is a critical parameter, constrained by the requirement that the bino decays out-of-equilibrium but before electroweak sphalerons freeze out ($T_{sph} \approx 130 \text{ GeV}$).

Key Contributions

• Hybrid Leptogenesis Mechanism: The paper demonstrates that a pseudo-Dirac bino can generate the BAU through particle-antiparticle oscillations and CP-violating decays, while a pseudo-Dirac wino simultaneously generates neutrino masses. This "sequestering" of roles allows for a long-lived bino (necessary for leptogenesis) without suppressing neutrino masses, a limitation found in pure-bino scenarios.
• Thermal Effects on Oscillations: The authors explicitly calculate the impact of sfermion-mediated scatterings on bino oscillations. They show that these interactions can delay the onset of oscillations (quantum Zeno effect) and wash out asymmetries, necessitating a decoupled spectrum with heavy sfermions ($M_{sf} \gtrsim 50 \text{ TeV}$) to ensure successful leptogenesis.
• Messenger Scale Constraints: The analysis establishes that for a TeV-scale bino to decay out-of-equilibrium before sphaleron freeze-out, the messenger scale must be high, $\Lambda_M \sim \mathcal{O}(10^7 - 10^8) \text{ TeV}$. This scale is significantly higher than in previous $U(1)_{R-L}$ models but remains consistent with the generation of correct neutrino masses via the wino sector.

Results

• Baryon Asymmetry: Numerical solutions of the Boltzmann equations show that the model can successfully reproduce the observed baryon asymmetry ($\eta \approx 6 \times 10^{-10}$). The asymmetry is maximized when the ratio of the mass splitting to the decay width ($x = \Delta m / \Gamma_{\tilde{B}}$) is of order unity to hundreds.
• Parameter Dependencies:
  • Sfermion Mass: Smaller sfermion masses ($M_{sf} \lesssim 50 \text{ TeV}$) lead to stronger washout effects, reducing the final asymmetry. Successful leptogenesis requires $M_{sf} \gtrsim 100 \text{ TeV}$ in the benchmark scenarios.
  • Majorana Mass: The Majorana mass splitting ($m \sim 10^{-4} - 10 \text{ eV}$) must be large enough to initiate oscillations before the bino decays but small enough to maintain the pseudo-Dirac nature.
  • Messenger Scale: A messenger scale of $\Lambda_M \sim 10^7 \text{ TeV}$ is required to satisfy the out-of-equilibrium condition for TeV-scale binos.
• Collider Phenomenology: The required high messenger scale and heavy sfermions imply that sfermions are inaccessible at the LHC. However, the wino (and potentially the bino, depending on mass ordering) can be produced. The wino, mixing with neutrinos, would decay into final states with leptons, quarks, and missing energy. Due to the large $\Lambda_M$, these decays are suppressed, leading to displaced vertices. The paper suggests that if the wino is the lightest accessible SUSY particle, it could manifest as a long-lived particle with displaced vertices, detectable by current LHC detectors or proposed facilities like MATHUSLA and CODEX-b.

Significance
The paper claims that this hybrid scenario offers a viable, testable alternative to high-scale leptogenesis. By utilizing the unique properties of pseudo-Dirac gauginos in a $U(1)_{R-L}$ symmetric MSSM, the model addresses both the neutrino mass problem and the BAU within a TeV-scale framework. The separation of duties between the wino (neutrino masses) and bino (BAU) resolves the tension between the need for a long-lived bino for leptogenesis and the need for sufficient neutrino mass generation. The requirement of a decoupled sfermion spectrum and a high messenger scale provides specific, albeit challenging, signatures for future collider searches, particularly in the realm of long-lived particles and displaced vertices.