Neutrino Mass Induced $n$-$\overline{n}$ Oscillation

This paper investigates the intrinsic connection between Majorana neutrino mass generation and neutron-antineutron oscillation within various extensions of the Georgi-Glashow grand unification model that break lepton number, demonstrating how the dynamics responsible for neutrino masses inevitably induce baryon-number-violating transitions.

The Gist

The Big Picture: A Cosmic "Double-Edged Sword"

Imagine the universe is built on a set of strict accounting rules. One rule says "Baryon number" (the count of protons and neutrons) must always stay the same. Another says "Lepton number" (the count of electrons and neutrinos) must also stay the same.

For a long time, physicists thought these were two separate, unbreakable ledgers. However, this paper argues that if the Georgi-Glashow model (a specific, elegant theory about how all forces unite) is true, these two ledgers are actually tied together by a single string.

The authors' main discovery is a "cosmic double-edged sword": If you break the rule to give neutrinos mass, you automatically break the rule that keeps neutrons stable.

The Analogy: The "Locked Door" and the "Leaky Faucet"

Think of the universe's symmetry (specifically a rule called $B-L$) as a locked door that keeps protons and neutrons from turning into each other or disappearing.

1. The Problem with Neutrinos: In the simplest version of this theory, the door is locked so tight that neutrinos have no mass (they are like ghosts that can't weigh anything). But we know from real experiments that neutrinos do have a tiny bit of mass.
2. The Fix: To give neutrinos mass, physicists have to install a "leaky faucet" in the system. This faucet allows the universe to violate the "Lepton number" rule by 2 units.
3. The Unintended Consequence: Because the door is a single unit, you can't just leak the "Lepton" side without the "Baryon" side leaking too. When you open the faucet to give neutrinos mass, you accidentally create a hole in the "Baryon" side of the door.
4. The Result: This hole allows a neutron to spontaneously turn into an anti-neutron. This is called neutron-antineutron ($n-\bar{n}$) oscillation.

The Bottom Line: You cannot have massive neutrinos in this specific universe without also having the possibility of neutrons turning into anti-neutrons.

The "Menu" of Models

The authors looked at a "menu" of different ways to fix the neutrino mass problem (called Seesaw mechanisms, radiative models, etc.). They checked each one to see what kind of "leak" it creates.

• The "Simple" Fixes (Type I, II, III Seesaws): These are the most straightforward ways to give neutrinos mass. The paper finds that while they work for neutrinos, they usually create a leak so big that it causes protons to decay instantly. Since we haven't seen protons decay, these simple versions are likely ruled out (unless the leak is incredibly tiny, which makes the neutron oscillation impossible to detect).
• The "Tricky" Fixes (Zee, Zee-Babu, and Variants): These models use more complex machinery (like extra particles that act as "scissors" or "glue").
  • Some of these models manage to give neutrinos mass without causing immediate proton decay.
  • However, they often require new particles (like "color sextet" scalars) to be very light.
  • The Catch: If these particles are light enough to let neutrons oscillate, the Large Hadron Collider (LHC) should have already seen them. Since the LHC hasn't seen them yet, many of these specific models are also in trouble.

The "Detective Work"

The paper acts like a detective narrowing down suspects. They are looking for a scenario where:

1. Neutrinos have mass.
2. Protons don't decay (because we haven't seen it).
3. Neutrons can oscillate (which is what we hope to find in future experiments like DUNE or NNBAR).

Who is the suspect?
The paper concludes that the only models that might survive all these constraints are specific, slightly more complex versions of the "Type II" and "Type III" seesaws, and the "Zee" model. These models use special particles (like color-sextet scalars) that allow the neutron to oscillate without triggering the proton decay alarm.

Why Should You Care?

The authors are saying: "If you ever catch a neutron turning into an anti-neutron, you have proven two things at once."

1. You have proven that neutrinos get their mass from a specific type of "Majorana" mechanism (where a particle is its own antiparticle).
2. You have proven that the universe is built on the specific unification theory (SU(5)) that ties quarks and leptons together.

It's like finding a single fingerprint at a crime scene that proves both who did it and how they did it. If we see this neutron oscillation, it confirms a deep, intrinsic connection between the smallest particles (neutrinos) and the stability of matter itself.

Summary in One Sentence

If the universe follows the rules of the Georgi-Glashow model, the very act of giving neutrinos their weight inevitably causes neutrons to wobble and turn into anti-neutrons, offering a potential new way to prove how the universe is built.

Technical Summary

Technical Summary: Neutrino Mass Induced n–n Oscillation

Problem Statement
The Georgi-Glashow (GG) $SU(5)$ grand unification model, while the simplest realization of quark-lepton unification, fails to account for neutrino masses as it preserves a global $U(1)_{B-L}$ symmetry, rendering neutrinos massless. To address the origin of neutrino masses, extensions of the GG model must introduce mechanisms that break lepton number ($L$) by two units ($|\Delta L| = 2$). The central problem addressed in this work is the intrinsic connection between such $|\Delta L| = 2$ interactions (required for Majorana neutrino mass generation) and baryon number ($B$) violation. Specifically, the authors investigate whether the dynamics generating neutrino masses in $SU(5)$ unavoidably induce $|\Delta B| = 2$ transitions, leading to neutron-antineutron ($n$–$\bar{n}$) oscillation.

Methodology
The authors employ an effective field theory (EFT) approach within the framework of renormalizable $SU(5)$ extensions. They analyze the breaking of the accidental $U(1)_{B-L}$ symmetry, demonstrating that any mechanism generating Majorana neutrino masses (requiring $|\Delta L| = 2$) simultaneously breaks $B-L$ by two units, thereby inducing $|\Delta B| = 2$ processes.

The study systematically examines minimal renormalizable extensions of the GG model that yield realistic neutrino masses. These extensions include:

• Tree-level Seesaw Mechanisms: Type I, Type II, and Type III, along with specific variants.
• Radiative Models: One-loop (Zee model) and two-loop (Zee-Babu model) mechanisms, including their variants.

For each model, the authors:

1. Identify the particle content (scalars and fermions) required to generate neutrino masses.
2. Construct the corresponding Feynman diagrams for neutrino mass generation.
3. Derive the associated $n$–$\bar{n}$ oscillation topologies (Class I, II, or III) and the specific $d=9$ operators responsible for the transition.
4. Calculate the relevant mass scales and coupling constraints required to satisfy current neutrino mass data, Super-Kamiokande ($SK$) bounds on $n$–$\bar{n}$ oscillation, and Large Hadron Collider (LHC) limits on dijet resonances and proton decay.

Key Contributions and Results
The paper establishes a direct correlation between the specific mechanism of neutrino mass generation and the observability of $n$–$\bar{n}$ oscillation. The key findings are categorized by model viability:

• Intrinsic Link: The analysis confirms that in $SU(5)$, quark-lepton unification combined with Majorana mass generation automatically yields baryon-number-violating interactions with $|\Delta B| = 2$.
• Model Exclusions:
  • Minimal Type I, II, and III Seesaws: These models typically require scalar color-triplet mediators (e.g., $(3,1,-1/3)$) that induce proton decay. To satisfy stringent proton decay limits, the couplings of these triplets must be extremely suppressed ($\lesssim 10^{-24}$), rendering the associated $n$–$\bar{n}$ oscillation unobservable.
  • Minimal Zee-Babu Model: This model requires scalar diquarks (a color triplet and a sextet) in a mass range already excluded by LHC searches for dijet resonances. Furthermore, the antisymmetric nature of the Yukawa couplings necessitates two mediators, pushing the required mass scale beyond experimental reach.
  • BNT Model: Similar to the minimal seesaws, the presence of color-triplet mediators leads to proton decay constraints that suppress the $n$–$\bar{n}$ signal.
• Viable Models: The study identifies specific model variants where $n$–$\bar{n}$ oscillation remains observable and consistent with current bounds:
  • Extended Type II and Type III Seesaws: These utilize scalar color-sextet mediators (and in the Type III case, a color-octet fermion) that do not induce proton decay.
  • Zee Model: The minimal Zee extension ($GG + 10_S + 45_S$) involves a color-triplet scalar $(3,1,-2/3)$ that is free from proton decay constraints, allowing for observable oscillation.
  • Zee-Babu Variant: Replacing the $10_S$ with a $15_S$ introduces symmetric Yukawa couplings, allowing for tree-level contributions and avoiding the need for double $W$-boson exchanges, thus enhancing the oscillation rate.
• Experimental Reach: The authors map the viable parameter space against current LHC bounds and future sensitivities (NNBAR at ESS, DUNE). They find that while the Zee model is fully testable at the Future Circular Collider (FCC-hh) via low-mass diquark searches, the Type II/III variants and Zee-Babu variants retain viable parameter space even if no such collider signals are found.

Significance
The paper argues that the observation of $n$–$\bar{n}$ oscillation would provide independent evidence for Majorana neutrinos, complementing neutrinoless double beta decay ($0\nu\beta\beta$), provided that $SU(5)$ grand unification is realized in nature. The study provides a "roadmap" for model building: if $n$–$\bar{n}$ oscillation is observed, it would strongly disfavor minimal versions of the Type I, II, and III seesaw models and the BNT model, while favoring extended scenarios involving color-sextet scalars or specific radiative mechanisms. This work dovetails with studies enumerating $d=9$ operators and offers concrete guidance for upcoming experimental searches at DUNE, NNBAR, and high-energy colliders.