Neutrinoless double beta decays of hyperons in covariant chiral perturbation theory

This paper investigates neutrinoless double beta decays of spin-1/2 hyperons using covariant baryon chiral perturbation theory, finding that while long-range one-loop amplitudes exist, the leading contributions arise from short-range counterterm operators and result in branching ratios far below current experimental limits.

The Gist

The Mystery of the "Ghostly Twins": A Simple Guide to Hyperon Decay

Imagine you are watching a high-stakes magic trick. A magician takes a single playing card, snaps his fingers, and suddenly, two identical cards appear out of thin air. In the world of particle physics, scientists are looking for a similar "magic trick" in nature. They call it Neutrinoless Double Beta Decay.

This paper explores a specific, rare version of this trick involving "Hyperons"—heavy, exotic cousins of the protons and neutrons that make up your body.

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1. The Main Character: The Majorana Neutrino

To understand this paper, you first have to meet the Neutrino. Neutrinos are "ghost particles." They are so small and slippery that trillions of them are passing through your thumb right now, and you can’t feel a thing.

Most scientists think neutrinos are their own "anti-particles" (the mirror image of themselves). If this is true, they are called Majorana neutrinos.

The Analogy: Imagine a person who is both a "hero" and a "villain" at the same time. If you look at them in a mirror, they don't change. If neutrinos are Majorana particles, they can perform a "forbidden" trick: two of them can collide and cancel each other out, leaving behind only energy and other particles, without leaving any "anti-matter" footprints behind. This "missing footprint" is what scientists are hunting for.

2. The Setting: Hyperon Decays

While most scientists look for this trick in heavy atoms (like Uranium), this paper looks at Hyperons.

The Analogy: If searching for neutrino decay in an atom is like trying to find a tiny leak in a massive, complex dam, searching in Hyperons is like looking for a leak in a single, high-pressure water pipe. The "pipe" (the hyperon) is much simpler to study mathematically, even if the "leak" (the decay) is incredibly rare.

3. The Problem: The Math is a Mess

The researchers used a complex mathematical framework called Chiral Perturbation Theory.

The Analogy: Imagine you are trying to predict the path of a leaf falling in a storm. You can't track every single molecule of air (that's too hard), so you use "rules of thumb" to approximate the wind. Chiral Perturbation Theory is a set of highly sophisticated "rules of thumb" that allow physicists to calculate how these particles behave without needing to know the impossible complexity of every subatomic interaction.

However, when they did the math, they ran into a problem called "Power Counting Breaking." It’s like trying to use a ruler to measure a mountain, but every time you move the ruler, the scale changes. The math kept "breaking" the rules of how small things should behave.

4. The Solution: The "EOMS" Cleanup

The authors used a specialized mathematical "cleaning service" called the EOMS scheme.

The Analogy: Imagine you are building a Lego castle, but every time you add a brick, the foundation shifts and the whole thing wobbles. The EOMS scheme is like a specialized stabilizer that keeps the foundation perfectly still, allowing you to build the castle (the calculation) accurately without the whole structure collapsing under its own weight.

5. The Big Discovery: "The Short-Range Secret"

The most interesting part of the paper is what they found when they finished the math. They realized that the "long-range" trick (the one involving the ghostly neutrino traveling between particles) is actually much weaker than they thought.

Instead, the "leading" part of the decay likely comes from "Short-Range" interactions.

The Analogy: Imagine you see a light turn on in a room. You might assume someone flipped a switch far away (long-range). But after doing the math, the researchers realized it’s much more likely that a tiny, invisible spark happened right at the bulb itself (short-range).

6. Why does this matter?

The researchers calculated that these decays are incredibly rare—so rare that they are 20 orders of magnitude (that's a 1 followed by 20 zeros!) smaller than what our current machines can even detect.

The Takeaway:
If a scientist ever actually sees one of these hyperon decays in an experiment, it won't be the "ghostly neutrino" trick they expected. It will be something much more exciting: New Physics. It would be a signal that there are forces and particles in the universe that we haven't even dreamed of yet.

They have essentially provided the "map" for future scientists, telling them: "If you see this specific signal, you haven't just found a neutrino; you've found a whole new door to the universe."

Technical Summary

This paper, titled "Neutrinoless double beta decays of hyperons in covariant chiral perturbation theory," presents a systematic theoretical investigation into lepton number violation (LNV) within the hyperon sector.

1. The Problem

The search for neutrinoless double beta ($0\nu\beta\beta$) decay is the primary method for testing the Majorana nature of neutrinos and probing lepton number violation. While nuclear $0\nu\beta\beta$ decay is the most studied, it suffers from significant theoretical uncertainties due to the difficulty of calculating nuclear matrix elements.

Hyperon $0\nu\beta\beta$ decays (e.g., $\Sigma^- \to p e^- e^-$) offer a complementary probe. They involve flavor-changing weak processes (strangeness changes $\Delta S = 0, 1, 2$) and are theoretically cleaner because they can be described using Effective Field Theory (EFT) at the hadronic level. However, previous studies were limited by model dependence or lacked a systematic treatment of the chiral expansion and renormalization.

2. Methodology

The authors employ SU(3) Covariant Baryon Chiral Perturbation Theory (BChPT), the low-energy EFT of QCD, to calculate the decay amplitudes. Their approach includes:

• Mechanism: They focus on the "mass mechanism," where LNV is driven by the exchange of light Majorana neutrinos (long-range contribution), which is proportional to the effective Majorana neutrino mass $m_{\ell\ell}$.
• Lagrangian Construction: The standard chiral Lagrangian is extended by a $\Delta L = 2$ operator derived from the dimension-5 Weinberg operator.
• Renormalization: To handle ultraviolet (UV) divergences and the Power Counting Breaking (PCB) problem (a common issue in baryon ChPT where loop contributions violate the expected chiral order), they utilize:
  • Dimensional Regularization (DR) with the $\overline{\text{MS}}$ subtraction scheme.
  • The Extended-On-Mass-Shell (EOMS) scheme to restore consistent chiral power counting.
• Amplitude Decomposition: The hadronic tensor is decomposed into 34 parity-even and 34 parity-odd Lorentz operators.

3. Key Contributions

• Systematic One-Loop Calculation: They provide the first systematic calculation of the long-range $0\nu\beta\beta$ decay amplitudes for six kinematically allowed hyperon channels at the one-loop level ($O(p^3)$).
• Identification of the Leading Order (LO): A crucial theoretical finding is that the short-range counterterm operators (representing contact interactions) actually provide the leading contribution to the decay amplitude at $O(p^2)$, which is lower than the $O(p^3)$ one-loop long-range contribution.
• Neutrinoless Transition Form Factors (TFFs): Because the short-range contribution depends on unknown Low-Energy Constants (LECs), the authors propose the definition of "neutrinoless TFFs." These TFFs encapsulate the strong dynamics and are designed to be targets for future Lattice QCD simulations.

4. Results

• Branching Ratio Predictions: For the electronic modes ($e^-e^-$), using a benchmark Majorana mass $m_{ee} = 100$ meV (consistent with current nuclear limits), the predicted branching ratios are extremely small, on the order of $10^{-31}$ to $10^{-38}$. For muonic modes ($\mu^-\mu^-$), using $m_{\mu\mu} = 10$ eV, they are $\sim 10^{-28}$.
• Comparison with Experiment: The predicted branching ratios are more than 20 orders of magnitude smaller than current experimental upper bounds (from BESIII and HyperCP).
• Kinematic Behavior: The differential decay rates are dominated by the proximity to the decay threshold. The effect of the electron mass is found to be negligible in most channels.
• TFF Analysis: They show that the TFFs possess imaginary parts in certain kinematic regimes due to intermediate states going on-shell, and they analyze how these TFFs scale with the pion mass and momentum transfer.

5. Significance

The paper concludes that if a neutrinoless hyperon decay were ever observed at current or near-future experimental sensitivities, it cannot be explained by the standard light-neutrino exchange mechanism. Such an observation would be definitive evidence for new physics beyond the Standard Model, such as heavy Majorana neutrinos or new short-range LNV operators.

By providing the mathematical framework and the proposed TFFs, this work bridges the gap between high-energy LNV theory and low-energy hadronic physics, offering a roadmap for Lattice QCD to eventually provide the precision needed to test these models.