⚛️ phenomenology

New Avenues for $|\Delta B|$ = 2 Processes Beyond Neutron-Antineutron Oscillations

This paper investigates $|\Delta B|=2$ baryon-number-violating processes in the $\Lambda - \bar{\Lambda}$ system using Standard Model Effective Field Theory, demonstrating that while current experimental limits on neutron-antineutron oscillations and dinucleon decays constrain the parameter space, these transitions probe complementary energy scales up to $10^3$ TeV that are difficult to access via indirect bounds at BESIII.

Original authors: Arnau Bas i Beneito, Svjetlana Fajfer, Alexey A. Petrov

Published 2026-06-30

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Arnau Bas i Beneito, Svjetlana Fajfer, Alexey A. Petrov

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Picture: Looking for "Ghostly" Swaps

Imagine the universe is built out of tiny Lego blocks called quarks. These blocks snap together to form larger structures called baryons (like protons and neutrons). In our current understanding of physics (the Standard Model), there is a strict rule: you can't just make or destroy these Lego blocks out of thin air. The total number of "baryon blocks" must stay the same.

However, this paper asks a "what if" question: What if this rule is broken? specifically, what if two baryons could suddenly swap places with their "anti-baryon" twins? This is called Baryon Number Violation.

The paper focuses on a specific type of swap where the total change is 2 units (denoted as $|\Delta B| = 2$ ). Think of it like two people in a room suddenly swapping places with their evil twins, but doing it in a way that involves two people at once.

The Old Detective vs. The New Detective

For decades, scientists have been hunting for a specific "ghostly swap": the Neutron turning into an Anti-Neutron.

The Neutron ( $n$ ): A neutral particle made of three quarks (Up, Down, Down).
The Anti-Neutron ( $\bar{n}$ ): Its evil twin, made of anti-quarks.

Scientists have looked for this for years. If they find it, it proves new physics exists. But so far, they haven't seen it. The paper argues that we might be looking in the wrong place, or at least, we are ignoring a very promising new suspect.

The New Suspect: The Lambda ( $\Lambda$ ) Baryon
The paper introduces the Lambda baryon.

The Neutron is made of Up, Down, Down.
The Lambda is made of Up, Down, and Strange.

The "Strange" quark is like a special, heavier Lego block. Because the Lambda has this unique ingredient, it follows different rules than the neutron. The paper suggests that while the "Neutron Swap" might be impossible or extremely rare in certain new theories, the "Lambda Swap" could happen very easily.

The "Magic Recipe" (The Theory)

To explain how these swaps happen, the authors use a "recipe book" called Effective Field Theory.

Imagine you have a high-tech kitchen (the "UV" or high-energy world) where you have exotic ingredients (new particles like heavy scalars) that we can't see directly.
These ingredients mix together to create a "magic sauce" (a mathematical operator) that causes the swap.
The paper catalogs all the possible "magic recipes" (operators) that could turn a Lambda into an Anti-Lambda. They found 52 different recipes for the Lambda, compared to only 14 for the neutron. This means there are many more ways for the Lambda to cheat the rules than for the neutron.

The "Double-Edged Sword" of Constraints

The authors play a game of "connect the dots" using two different types of clues:

The Neutron Clue: We know the Neutron doesn't swap very often (or at all). This puts a strict limit on how "strong" the magic sauce can be.
The Proton Decay Clue: We also know that protons don't just fall apart into pions. This is another strict limit.

The paper shows that if you try to build a model where the Neutron swaps, you often accidentally make the Proton decay too fast (which we don't see). This forces the "magic ingredients" to be incredibly heavy and rare, making the Neutron swap impossible to detect.

However, there is a clever loophole. You can build a model where the "magic sauce" is designed specifically to work on the Lambda (because of its Strange quark) but doesn't work on the Neutron.

Analogy: Imagine a lockpick that fits the Lambda's lock perfectly but is too big to fit the Neutron's lock.
In these models, the Lambda could be swapping back and forth rapidly, while the Neutron sits still.

The "Dinucleon" Alarm

The paper also looks at a different alarm system: Dinucleon Decay.
Imagine two protons inside an atomic nucleus (like in a tank of water in the Super-Kamiokande experiment) suddenly turning into two Kaons (particles containing Strange quarks).

The paper calculates that if the Lambda is swapping, it would also cause these two protons to turn into Kaons.
The current experiments (Super-Kamiokande) have not seen this happening.
The Result: This "Dinucleon Alarm" is actually a much stricter police officer than the Neutron search. It puts a very tight leash on how fast the Lambda can swap.

The Conclusion: A Dead End for Now?

The authors run the numbers and find a somewhat disappointing but honest conclusion:

Because the "Dinucleon Alarm" is so sensitive, it already rules out most of the scenarios where the Lambda swap would be fast enough to be seen by current experiments (like the BESIII experiment in China).
Even though the Lambda is a theoretically interesting candidate, the current limits from other experiments make it very hard to find a "winning" signal for Lambda oscillations in the near future.

In short: The paper opens a new door to look for "ghostly swaps" using the Lambda particle instead of the neutron. They map out all the possible ways this could happen. But, after checking the security cameras (other experiments), they realize that the "Lambda Swap" is likely too quiet to be heard by our current detectors, because the "Dinucleon Alarm" has already told us the volume is turned down too low.

Summary of Key Takeaways

New Target: Instead of just looking for Neutron $\leftrightarrow$ Anti-Neutron swaps, we should look at Lambda $\leftrightarrow$ Anti-Lambda swaps.
Different Rules: The Lambda has a "Strange" quark, which allows for different types of "magic recipes" (operators) that don't affect the neutron.
The Loophole: We can build theories where the Lambda swaps easily, but the Neutron doesn't, avoiding the strict limits on Neutron decay.
The Catch: Even with this loophole, other experiments (looking for protons turning into Kaons) have set limits so strict that finding a Lambda swap with current technology is extremely difficult.

Technical Summary: New Avenues for $|\Delta B| = 2$ Processes Beyond Neutron–Antineutron Oscillations

Problem Statement
While baryon number ( $B$ ) conservation is an accidental symmetry of the Standard Model (SM), its violation is a necessary condition for explaining the baryon asymmetry of the Universe. Historically, research has focused on $|\Delta B| = 1$ processes (proton decay) and $|\Delta B| = 2$ neutron–antineutron ( $n-\bar{n}$ ) oscillations. However, $n-\bar{n}$ oscillations are constrained by extremely stringent experimental limits (Super-Kamiokande: $\tau_{n-\bar{n}} > 4.7 \times 10^8$ s), which often push the scale of new physics ( $\Lambda_{BNV}$ ) beyond the reach of current colliders.

This paper addresses the gap in understanding $|\Delta B| = 2$ processes involving strange quarks, specifically the $\Lambda-\bar{\Lambda}$ oscillation system. Unlike $n-\bar{n}$ , which involves $(udd)^2$ operators, $\Lambda-\bar{\Lambda}$ transitions involve $(uds)^2$ operators. The authors investigate whether $\Lambda-\bar{\Lambda}$ oscillations can probe a complementary parameter space, potentially offering sensitivity to baryon number violation at scales ( $10^2 - 10^3$ TeV) that are distinct from, or less constrained than, those governing $n-\bar{n}$ oscillations.

Methodology
The authors employ a multi-faceted theoretical framework:

Effective Field Theory (EFT): They utilize the Standard Model Effective Field Theory (SMEFT) to classify all dimension-9 operators responsible for $|\Delta B| = 2$ transitions. They distinguish between operators involving only first-generation quarks (relevant for $n-\bar{n}$ ) and those involving strange quarks (relevant for $\Lambda-\bar{\Lambda}$ ).
UV Completions: The study focuses on tree-level ultraviolet (UV) completions mediated by exotic scalar fields with trilinear interactions. They analyze specific scalar multiplets (diquarks and leptoquarks) and their couplings to determine which models generate $|\Delta B| = 2$ transitions.
Chiral Effective Theory: To connect quark-level operators to hadronic observables, the authors use Baryon Chiral Perturbation Theory (B $\chi$ PT). This allows them to derive indirect constraints on the $\Lambda-\bar{\Lambda}$ mass mixing parameter ( $\delta m_\Lambda$ ) using experimental limits on $n-\bar{n}$ oscillations and dinucleon decays.
Phenomenological Modeling: A simplified UV model is constructed to demonstrate a scenario where $\Lambda-\bar{\Lambda}$ oscillations occur at tree level while $n-\bar{n}$ oscillations are suppressed to the two-loop level.

Key Contributions and Results

Operator Classification: The authors extend the known basis of dimension-9 $|\Delta B| = 2$ operators. While $n-\bar{n}$ oscillations are described by 14 independent operators in the Low-Energy Effective Field Theory (LEFT) (reduced from 24 by symmetries), the inclusion of strange quarks for $\Lambda-\bar{\Lambda}$ increases the number of independent operators to 52. In SMEFT, the number of independent operators increases from 4 (for $n-\bar{n}$ ) to 20 (for $\Lambda-\bar{\Lambda}$ ).
Scalar Mediation and UV Constraints: The paper systematically reviews scalar-mediated UV completions. It identifies that models involving scalar leptoquarks $S_1$ and $S_3$ coupled to diquarks typically induce proton decay, forcing their masses to be $\gtrsim 10^{15}$ GeV. Consequently, these models render $n-\bar{n}$ oscillations phenomenologically negligible. The authors focus on models (specifically involving $\bar{S}_1$ and $\Omega_4$ ) that avoid tree-level proton decay, allowing for lower mass scales accessible to current experiments.
Indirect Constraints via Chiral Lagrangian:
- From $n-\bar{n}$ : Using B $\chi$ PT, the authors calculate tree-level and one-loop contributions to $n-\bar{n}$ oscillations mediated by $\Lambda-\bar{\Lambda}$ mixing (via pion and kaon loops). They derive an indirect bound: $\delta m_\Lambda \lesssim 10^{-18}$ GeV.
- From Dinucleon Decay: The study derives constraints from the dinucleon decay channel $pp \to K^+K^+$ , observed in Super-Kamiokande. This channel directly probes the $(uds)^2$ operator. The analysis yields a significantly stronger bound: $\delta m_\Lambda \lesssim 1.8 \times 10^{-32}$ GeV.
Comparative Sensitivity: The derived bounds indicate that indirect constraints from dinucleon decay are currently the most stringent, surpassing both the direct BESIII search for $\Lambda-\bar{\Lambda}$ oscillations ( $\delta m_\Lambda < 2.1 \times 10^{-18}$ GeV) and the indirect limits derived from $n-\bar{n}$ oscillations.
Simplified Model Analysis: In a specific UV model featuring scalars $\bar{S}_1$ and $\Omega_4$ , the authors demonstrate that $\Lambda-\bar{\Lambda}$ oscillations can be generated at tree level, while $n-\bar{n}$ oscillations are suppressed by a two-loop mechanism involving CKM factors and heavy quark masses. In this scenario, the current experimental limits on $\Lambda-\bar{\Lambda}$ (from BESIII) imply a lower bound on the new physics scale of $\Lambda_{BNV} \gtrsim 400$ GeV. However, this bound is roughly an order of magnitude weaker than the few-TeV limits from direct collider searches for these scalars.

Significance and Claims
The paper claims to establish a unified phenomenological framework for $|\Delta B| = 2$ processes, extending the analysis beyond the neutron sector to hyperons. The primary significance lies in demonstrating that $\Lambda-\bar{\Lambda}$ oscillations probe a distinct set of six-quark operators that are not necessarily correlated with $n-\bar{n}$ transitions.

However, the authors maintain a modest stance regarding the immediate experimental impact. They conclude that while $\Lambda-\bar{\Lambda}$ oscillations offer a theoretically complementary probe, the existing indirect bounds from dinucleon decays ( $pp \to K^+K^+$ ) are so stringent that they make it "challenging to provide a competitive bound on $\delta m_\Lambda$ at BESIII." The current experimental sensitivity at BESIII is insufficient to compete with the constraints derived from Super-Kamiokande data or direct collider searches for the relevant scalar mediators. Thus, while the theoretical framework is robust and identifies new avenues for baryon number violation, the paper suggests that $\Lambda-\bar{\Lambda}$ oscillations are not currently the leading probe for these specific UV scales compared to other existing constraints.