Statistical sensitivity of neutrinoless double-beta decay exchange mechanism discrimination by tracking experiments

This paper demonstrates that tracking experiments can effectively discriminate between different neutrinoless double-beta decay exchange mechanisms with high statistical significance using only a few well-reconstructed events, even in the presence of realistic reconstruction uncertainties, thereby validating the continued pursuit of tracking detectors for discovery-class experiments.

The Gist

Imagine you are a detective trying to solve a mystery: Who committed the crime? In the world of particle physics, the "crime" is a rare event called neutrinoless double-beta decay. This is a process where an atom spontaneously changes its identity, emitting two electrons but no other particles.

For decades, scientists have been hunting for this event. If they find it, it proves that a fundamental rule of the universe (that matter and antimatter must be created in pairs) is broken. But finding the event is only step one. The real question is: What caused it?

The Three Suspects

The paper suggests there are three main "suspects" (theories) that could explain this decay:

1. The "Light Neutrino" (Suspect A): The decay is caused by a tiny, ghostly particle called a neutrino acting as a messenger.
2. The "Right-Handed Current" (Suspect B): The decay is caused by a new, exotic force where particles interact in a specific "right-handed" way.
3. The "Left-Handed Current" (Suspect C): The decay is caused by a different exotic force involving "left-handed" interactions.

Each suspect leaves a different fingerprint on the crime scene. Specifically, they leave different patterns regarding:

• How much energy each electron carries.
• The angle at which the two electrons fly apart (like two cars crashing and flying off in different directions).

The Old Belief vs. The New Discovery

The Old Belief:
Scientists previously thought that to tell these suspects apart, you needed to catch thousands of these events. They believed you needed a massive amount of data (high statistics) to see the subtle differences in the fingerprints. It was like trying to identify a suspect's handwriting by looking at just one letter; you'd need a whole novel to be sure.

The New Discovery:
This paper argues that the old belief is wrong. The fingerprints of these three suspects are so different that you don't need a novel. You only need a handful of pages.

• The "Aha!" Moment: If the "Light Neutrino" is the culprit, the electrons fly apart in a very specific way (mostly back-to-back). If "Suspect B" is the culprit, they fly off in the same direction.
• The Result: The authors show that if you catch just 3 to 4 events, you can already be reasonably sure (68% confidence) which suspect is guilty. If you catch about 10 events, you can be almost certain (99.7% confidence). Even with realistic "blurry" detectors, you only need about 25 events to be sure.

The Detective's Tools (Tracking Detectors)

To see these fingerprints, you need a special camera called a tracking detector. Think of it like a high-tech 3D motion-capture system.

• How it works: Instead of just seeing a flash of light, this camera tracks the exact path of every electron as it moves through a gas. It records the energy and the angle of their flight.
• The Challenge: Real cameras aren't perfect. They have "noise" and "blur" (like a foggy window). The authors simulated a real-world camera (a high-pressure gas chamber) and used a smart computer program (an AI called ParticleNet) to clean up the blurry images and reconstruct the paths.
• The Outcome: Even with the "foggy window" of a real detector, the AI could still clearly distinguish between the three suspects. The "blur" didn't ruin the case; it just required a few more witnesses (events) to be absolutely sure.

The Big Takeaway

The paper concludes that we don't need to wait for a massive, future experiment with millions of events to solve this mystery.

If a "discovery-class" experiment (one designed just to find the event) finds even a small handful of these decays, we can immediately use tracking technology to figure out which physics mechanism is responsible. We don't need to wait for the "perfect" future; the tools we have now (or are building now) are powerful enough to solve the case with just a few clues.

In short: You don't need a library of evidence to identify a criminal when the three suspects look completely different. A few snapshots are enough to catch the culprit.

Technical Summary

Technical Summary: Statistical Sensitivity of Neutrinoless Double-Beta Decay Exchange Mechanism Discrimination by Tracking Experiments

Problem Statement
The discovery of neutrinoless double-beta ($0\nu\beta\beta$) decay would confirm lepton number violation and potentially reveal the Majorana nature of neutrinos. However, an observation of the decay rate alone cannot distinguish between the standard light-neutrino exchange mechanism and alternative Beyond-the-Standard-Model (BSM) exchange mechanisms (e.g., short-range interactions or right-handed currents). While previous consensus suggested that discriminating between these mechanisms requires high-statistics experiments far into the future, this paper challenges that assumption. It investigates whether a small number of reconstructed events are sufficient to statistically distinguish between competing exchange mechanisms using tracking detectors capable of measuring individual electron energies ($E_1, E_2$) and their opening angle ($\theta$).

Methodology
The authors employ a statistical framework based on the Neyman construction for multiple simple hypotheses to evaluate discrimination power.

1. Hypothesis Definition: Three distinct kinematic hypotheses are defined based on effective field theory operators:

   • $H_\nu$: Dominated by light Majorana neutrino exchange (left-chiral currents). Predicts electron energy $E_1$ peaked near $Q_{\beta\beta}/2$ and back-to-back emission ($\cos\theta \approx -1$).
   • $H_\lambda$: Dominated by right-handed hadronic currents coupling to right-handed leptonic currents. Predicts a bi-modal $E_1$ distribution and collinear emission ($\cos\theta \approx 1$).
   • $H_\eta$: Dominated by left-handed hadronic currents coupling to right-handed leptonic currents. Predicts $E_1$ peaked near $Q_{\beta\beta}/2$ but with collinear emission.

2. Ideal Case Analysis: The study first models an ideal detector with perfect track reconstruction and zero background. Using the $\nu$DoBe tool, joint probability distributions for $E_1$ and $\cos\theta$ are generated. The discrimination power is quantified using likelihood ratios ($t_{jk} = -2 \ln(L_j/L_k)$) in a two-dimensional parameter space ($t_{\lambda\nu}$ vs. $t_{\eta\nu}$).

3. Realistic Detector Simulation: To account for experimental limitations, the authors simulate a high-pressure gaseous Time Projection Chamber (TPC) resembling the PandaX-III configuration (140 kg of $^{136}$Xe at 10 bar) using Geant4 and the REST framework.

   • Reconstruction: Electron tracks are reconstructed using a graph neural network (ParticleNet) operating on point-cloud data. The network predicts the maximum electron energy ($E_{\max}$) and the opening angle ($\cos\theta$), utilizing the known decay vertex (assumed available via auxiliary technologies like barium tagging).
   • Effects: The simulation incorporates electron diffusion, spatial resolution (1 mm pixels), and energy resolution (1% FWHM at $Q$-value).

Key Contributions and Results

• Low-Event Discrimination: Contrary to the prevailing view that high statistics are mandatory, the study demonstrates that significant discrimination power exists even with very few events.
  • Ideal Case: A $1\sigma$ level of discrimination is achievable with just a few well-reconstructed events. A $3\sigma$ discovery sensitivity (defined as a $>50\%$ probability of correctly identifying the single dominant mechanism) requires only $\sim 10$ events. In rare cases, a single event can suffice for a $3\sigma$ claim if its kinematics are highly distinct from alternative hypotheses.
  • Realistic Case: When including detector smearing and reconstruction uncertainties in a gaseous TPC, the requirement increases to approximately 25 events to reach $3\sigma$ sensitivity. Despite this increase, the discrimination power remains substantial.
• Hypothesis-Specific Sensitivity: The study finds that the $H_\lambda$ hypothesis (right-handed currents) is the easiest to distinguish, showing minimal degradation in discovery probability when detector effects are included. The $H_\nu$ and $H_\eta$ hypotheses are harder to distinguish from one another because they share similar energy distributions, differing primarily in the angular distribution, which is more susceptible to reconstruction smearing.
• Technological Validation: The use of ParticleNet for reconstructing kinematic observables from TPC point clouds successfully preserves the salient features of the differential phase space, validating the use of machine learning for topological reconstruction in this context.

Significance and Claims
The paper concludes that the pursuit of tracking detectors for exchange-mechanism discrimination is valuable even for "discovery-class" experiments where only a few signal counts are expected. The authors assert that mechanism identification is not a task reserved for future, massive high-statistics experiments but is potentially within reach of current or near-future tracking technologies (such as high-pressure gas TPCs or tracking calorimeters like SuperNEMO).

The authors emphasize that while nuclear matrix element uncertainties plague half-life comparisons across isotopes, decay kinematics are strongly determined by the chirality of the exchange currents. Therefore, even with a modest number of events, tracking experiments can provide a robust test of the underlying physics, distinguishing between standard light-neutrino exchange and exotic BSM mechanisms. The work suggests that the "pessimism" regarding the ability of tracking detectors to test mechanisms before high-statistics data is available is unfounded.