The meV frontier of neutrinoless double beta decay in the JUNO era

This paper utilizes anticipated JUNO results on solar neutrino oscillation parameters to establish updated conditions under which the effective Majorana mass in the normal ordering scenario is guaranteed to exceed specific meV thresholds, considering both generic and symmetry-constrained Majorana phase scenarios.

The Gist

Imagine the universe is a giant, complex orchestra. For decades, we've been listening to the music of neutrinos—tiny, ghost-like particles that pass through everything, including you, without you ever noticing. We know they have mass, and we know they can change their "flavor" (like switching from a violin to a flute) as they travel. This is called neutrino oscillation.

But there's a big mystery we haven't solved yet: Are neutrinos their own antiparticles?

In the world of physics, most particles have a "twin" called an antiparticle (like matter and antimatter). If you meet your twin, you might annihilate each other. But if a particle is its own twin, it's called a Majorana particle. Proving neutrinos are Majorana particles would be a massive discovery, rewriting the rules of how the universe works.

The Great Detective Hunt: Neutrinoless Double Beta Decay

To catch this ghost, scientists are looking for a very rare event called neutrinoless double beta decay.

Think of a normal radioactive atom as a shy person who, when they change, whispers a secret to two invisible neighbors (neutrinos) before disappearing.

• Normal Decay: The atom changes, and two electrons and two neutrinos fly out.
• The "Ghost" Decay (Neutrinoless): The atom changes, and two electrons fly out, but no neutrinos are seen.

If we see this happen, it means the two neutrinos that should have been there canceled each other out because they are the same particle (Majorana). It's like two people shaking hands and vanishing into thin air because they are actually the same person.

The Problem: The "Silent Zone"

The difficulty is that this event is incredibly rare. Whether we can see it depends on something called the Effective Majorana Mass (let's call it $| \langle m \rangle |$). Think of this mass as the "volume knob" for the ghost signal.

• Inverted Ordering (IO): Imagine the neutrinos are arranged like a pyramid where the bottom two are heavy and the top one is light. In this case, the volume knob is always turned up loud enough that we should be able to hear the signal soon.
• Normal Ordering (NO): Imagine the neutrinos are arranged like a staircase where the steps get smaller and smaller. In this scenario, the volume knob can be turned down so low that the signal becomes a whisper, or even silence. If the neutrinos are arranged this way, and the "ghosts" (CP phases) align just right, the signal might disappear completely. This is the "Well of Unobservability."

The New Tool: JUNO

Enter JUNO (Jiangmen Underground Neutrino Observatory). Think of JUNO as a brand-new, ultra-sensitive microphone that just started listening to the neutrino orchestra.

Before JUNO, we had a rough idea of the music's rhythm (oscillation parameters), but the timing was fuzzy. JUNO has now measured the rhythm with incredible precision. The authors of this paper used JUNO's new, sharp data to redraw the map of where the "Silent Zone" is.

The Findings: When Can We Hear the Ghost?

The paper asks: "How heavy do the lightest neutrino need to be for us to guarantee we can hear the signal, even if the universe tries to hide it?"

They looked at two "volume thresholds" (1 meV and 5 meV) that future giant experiments hope to reach.

1. The "Goldilocks" Zone is Gone:
   Previously, we weren't sure if the neutrino mass was in a "safe zone" where the signal is loud, or a "danger zone" where it's silent.

   • The Good News: If the lightest neutrino is very heavy (heavier than 10 meV for the 1 meV threshold, or 20 meV for the 5 meV threshold), the signal is guaranteed to be loud enough to hear, no matter how the "ghosts" align.
   • The Bad News: If the lightest neutrino is very light (lighter than 0.2 meV), the signal is also guaranteed to be loud enough.
   • The Danger Zone: If the lightest neutrino is in the middle (between 0.2 and 10 meV), the universe might have set the volume knob to zero. In this middle range, the signal could vanish completely, making it impossible to detect even with the best future machines.

2. The "Symmetry" Shortcut:
   The paper also looked at scenarios where the universe follows strict rules of symmetry (like a perfectly choreographed dance). If the neutrinos follow these specific "dance moves" (Generalized CP symmetry), even if they are in the "danger zone," the signal cannot vanish. It guarantees a minimum volume. This gives scientists hope that if we look hard enough, we might find the signal even in tricky situations.

The Big Picture: Why This Matters

This paper is essentially a roadmap for the next generation of experiments.

• If we find nothing: It doesn't mean neutrinos aren't Majorana particles. It might just mean they are in that "Silent Zone" (the middle weight range) and our current machines aren't sensitive enough yet.
• The Goal: We need to build detectors that can hear whispers down to the millielectronvolt (meV) level.
• The Verdict: Even if the "Normal Ordering" scenario tries to hide the signal, JUNO's new data tells us exactly where to look. If the lightest neutrino is heavy enough, we will find it. If it's light enough, we will find it. If it's in the middle, we need to keep building bigger, better microphones to ensure we don't miss the most important secret in particle physics.

In short: We have a better map now. We know exactly how heavy the neutrino needs to be for the "ghost" to show up, and we know that if we build sensitive enough detectors, we can't help but find it.

Technical Summary

Here is a detailed technical summary of the paper "The meV frontier of neutrinoless double beta decay in the JUNO era" by J. T. Penedo and S. T. Petcov.

1. Problem Statement

The primary goal of neutrinoless double beta decay ($(\beta\beta)_{0\nu}$) experiments is to establish lepton number violation and confirm the Majorana nature of neutrinos. The decay rate is proportional to the square of the effective Majorana mass, $|\langle m \rangle|$.

• The Challenge: In the standard three-neutrino paradigm, $|\langle m \rangle|$ depends on the absolute neutrino mass scale ($m_{\min}$), the neutrino mass ordering (Normal Ordering [NO] vs. Inverted Ordering [IO]), and two unknown Majorana CP-violating (CPV) phases ($\alpha_{21}$ and $\alpha'_{31}$).
• The Specific Issue: While $|\langle m \rangle|$ has a guaranteed lower bound in the IO scenario, it can be vanishingly small (approaching zero) in the NO scenario due to destructive interference between the mass eigenstates. This creates a "well of unobservability" where current and near-future experiments might fail to detect the decay even if neutrinos are Majorana particles.
• The Context: Recent data from the JUNO (Jiangmen Underground Neutrino Observatory) experiment has significantly reduced uncertainties on solar neutrino oscillation parameters. The authors aim to update the conditions under which $|\langle m \rangle|$ in the NO scenario is guaranteed to exceed specific experimental thresholds (1 meV and 5 meV) given this new precision.

2. Methodology

The authors perform a phenomenological analysis updating their previous 2018 work [12] with the latest global fit data, specifically incorporating the first JUNO results [14].

• Input Parameters: They utilize oscillation parameters ($\Delta m^2_{21}, \Delta m^2_{31}, \sin^2\theta_{12}, \sin^2\theta_{13}$) at $1\sigma, 2\sigma,$and$3\sigma$ confidence levels (CL) from Refs. [2, 15], which include JUNO data.
• Theoretical Framework:
  • The effective mass is calculated as $|\langle m \rangle| = |\sum U_{ei}^2 m_i|$.
  • They analyze the vector sum in the complex plane, where the relative orientations are determined by the CPV phases.
• Scenarios Analyzed:
  1. Unconstrained Phases: The CPV phases are allowed to vary freely in $[0, 2\pi]$.
  2. Constrained Phases: The phases are restricted to specific values motivated by:
     • CP Conservation: Phases take values $\{0, \pi\}$.
     • Generalized CP (gCP) + Flavour Symmetries: Phases take discrete values $\{0, \pi/2, \pi, 3\pi/2\}$.
• Thresholds: The analysis focuses on two reference thresholds for $|\langle m \rangle|$:
  • $10^{-3}$ eV (1 meV): The goal of next-generation ton-scale experiments.
  • $5 \times 10^{-3}$ eV (5 meV): A higher sensitivity target.

3. Key Contributions

• Integration of JUNO Data: The paper provides the first updated constraints on the "meV frontier" specifically utilizing the reduced uncertainties on solar parameters ($\theta_{12}$ and $\Delta m^2_{21}$) from the initial JUNO data release.
• Refined Exclusion Zones: The authors precisely map the regions of the lightest neutrino mass ($m_{\min}$) where $|\langle m \rangle|$ is guaranteed to be above the detection thresholds, regardless of the unknown CP phases.
• gCP Symmetry Analysis: They systematically evaluate 10 inequivalent pairs of gCP-compatible phases, demonstrating that specific CP-violating values (compatible with gCP symmetries) can strictly enforce a lower bound on $|\langle m \rangle|$ even in the NO scenario.

4. Key Results

A. Unconstrained CP Phases (General Case)

Using $3\sigma$ variations of oscillation parameters:

• Threshold of 1 meV ($10^{-3}$ eV):
  • $|\langle m \rangle|_{NO} > 1$ meV is guaranteed if $m_{\min} < 0.2$ meV or $m_{\min} > 10.0$ meV.
  • Conversely, if $m_{\min} \in [1.3, 7.5]$ meV, there exist phase combinations where $|\langle m \rangle|_{NO} < 1$ meV (the "well of unobservability").
  • In terms of the sum of neutrino masses ($\Sigma$): Guarantee holds if $\Sigma < 0.060$ eV or $\Sigma > 0.074$ eV.
• Threshold of 5 meV ($5 \times 10^{-3}$ eV):
  • $|\langle m \rangle|_{NO} > 5$ meV is guaranteed only if $m_{\min} > 20.8$ meV (corresponding to $\Sigma > 0.097$ eV).
  • If $m_{\min} < 16.0$ meV, there always exist phase choices that suppress $|\langle m \rangle|$ below 5 meV.

B. Constrained Phases (Symmetry Schemes)

• CP Conserving ($\alpha \in \{0, \pi\}$): The results largely follow the standard bounds, with specific "islands" of allowed mass values.
• Generalized CP (gCP) Compatible:
  • The authors identify 10 inequivalent pairs of phases from the set $\{0, \pi/2, \pi, 3\pi/2\}$.
  • Crucial Finding: In cases where the phases are gCP-compatible but not CP-conserving (i.e., at least one phase is $\pi/2$ or $3\pi/2$), the effective mass$|\langle m \rangle|_{NO}$is **strictly bounded from below** at the$3\sigma$ level.
  • Specifically, for these gCP-violating (but symmetry-preserving) cases, $|\langle m \rangle|_{NO} \geq 1$ meV is guaranteed, provided $m_{\min}$ is not in a very narrow excluded range (e.g., $m_{\min} \notin [0.3, 4.9]$ meV for certain phase pairs). This eliminates the "zero" possibility for these specific symmetry-motivated scenarios.

C. Inverted Ordering (IO)

• Confirmed that $|\langle m \rangle|_{IO}$ has a robust lower bound of $\approx 15.8$ meV (at $3\sigma$), well within the reach of current and next-generation experiments, regardless of the mass ordering preference in global fits.

5. Significance

• Experimental Motivation: The results reinforce the necessity of pushing $(\beta\beta)_{0\nu}$ experiments beyond the Inverted Ordering frontier (sensitivity $< 10$ meV). Even if the neutrino mass ordering is Normal, a discovery is possible if $m_{\min}$ is sufficiently large ($> 20$ meV) or if the underlying physics follows specific gCP symmetry patterns.
• Theoretical Implications: The study highlights that if future experiments rule out the IO region and find no signal in the NO region up to 1 meV, it would strongly constrain the Majorana phases. Specifically, it would disfavor scenarios where the phases take gCP-compatible values that enforce a non-zero lower bound.
• JUNO Impact: The inclusion of JUNO data tightens the constraints on the "unobservable" mass window, making the conditions for guaranteed detection more precise.

In conclusion, the paper argues that the search for neutrinoless double beta decay must extend to the meV scale (specifically 1–5 meV). While the NO scenario allows for suppression, specific theoretical frameworks (gCP) and mass ranges ($m_{\min} > 20$ meV) guarantee observability, making the continued exploration of this frontier essential for testing physics beyond the Standard Model.