Prospect of the NUCLEUS Experiment at Chooz for Coherent Elastic Neutrino-Nucleus Scattering and New Physics Searches

This paper presents sensitivity projections for the NUCLEUS experiment at Chooz, demonstrating its potential to achieve a 4.7$\sigma$ observation of coherent elastic neutrino-nucleus scattering and provide leading constraints on new physics by utilizing gram-scale cryogenic calorimeters to access unprecedentedly low nuclear recoil energies.

The Gist

Imagine you are trying to hear a single, tiny whisper in the middle of a roaring stadium. That is essentially what the NUCLEUS experiment is trying to do.

Here is the story of how they plan to do it, broken down into simple concepts.

1. The Mission: Catching a Ghost

Neutrinos are like ghosts. They are tiny particles that zip through the entire Earth without bumping into anything. Because they are so shy, catching them is incredibly hard. Usually, when a neutrino hits something, it bounces off with a tiny "kick" (recoil).

For decades, scientists could only catch these kicks if they were loud enough (high energy). But the NUCLEUS team wants to hear the quietest whispers possible. They want to detect the tiniest, gentlest tap a neutrino can give to an atom. This is called Coherent Elastic Neutrino-Nucleus Scattering (CEνNS).

2. The Tool: A Super-Sensitive Microphone

To hear such a faint sound, you need a microphone that is incredibly sensitive.

• The Detector: They are using crystals made of Calcium Tungstate (CaWO4). Think of these as tiny, super-cold bells.
• The Temperature: These bells are cooled down to near absolute zero (colder than outer space). At this temperature, even the tiniest tap from a neutrino makes the crystal vibrate just enough to be felt.
• The Size: The target is surprisingly small—only about 7 grams (roughly the weight of a large paperclip). Most other experiments use targets the size of a bathtub or a swimming pool. NUCLEUS proves you don't need a big net if your net is made of the finest silk.

3. The Location: The Nuclear Power Plant

They are setting up their experiment inside the Chooz nuclear power plant in France.

• Why there? Nuclear reactors are like giant factories that spit out a massive, continuous stream of neutrinos. It's the best place to find them.
• The Problem: The plant is on the surface (or just underground), meaning the experiment is exposed to a lot of "noise" from cosmic rays (particles raining down from space) and other radiation. It's like trying to listen to a whisper while standing next to a jet engine.

4. The Big Hurdle: The "Low-Energy Excess" (The Static)

During their test runs, the scientists found a problem. Their detectors were picking up a lot of "static noise" at very low energies. They call this the Low-Energy Excess (LEE).

• The Analogy: Imagine you are trying to hear a whisper, but your microphone is picking up a weird, constant crackling sound that looks like a whisper but isn't.
• The Cause: They suspect this noise comes from the detector itself—maybe tiny stresses in the crystal or the metal holding it, like a guitar string settling down.
• The Fix: They are building a special "inner shield" (an instrumented holder) for the next phase of the experiment. Think of it as putting the microphone inside a soundproof box to stop the static.

5. The Secret Weapon: The Reactor's "Heartbeat"

Here is the clever trick the scientists are using to separate the real signal from the noise.

• The Scenario: The nuclear reactor doesn't run at 100% power all the time. It has scheduled maintenance breaks where it shuts down or slows down.
• The Strategy:
  • The Neutrinos (The Signal): When the reactor slows down, the neutrino stream gets weaker. When it speeds up, the stream gets stronger. The signal breathes with the reactor.
  • The Noise (The Background): The background noise (cosmic rays, static) doesn't care about the reactor. It stays constant.
• The Result: By watching how the number of "hits" changes as the reactor power goes up and down, they can mathematically filter out the constant noise and isolate the neutrino signal. It's like listening for a song that gets louder and softer in time with a specific drumbeat, while ignoring the constant traffic noise outside.

6. What Will They Find? (The Physics)

If they succeed, this experiment will be a game-changer for two reasons:

A. Testing the Standard Model (The Rulebook)
They will measure a fundamental property of the universe called the Weak Mixing Angle.

• Analogy: Imagine the Standard Model is a rulebook for how particles interact. NUCLEUS is checking if the rules are written correctly at a scale no one has ever looked at before. If the measurement is slightly off, it means the rulebook is missing a page, and we might have discovered New Physics.

B. Hunting for New Particles
They are also looking for "invisible" particles that might be messing with the neutrinos.

• Light Mediators: They are looking for a new, super-light force carrier (like a tiny messenger particle) that might be interacting with neutrinos.
• Neutrino Magnetic Moment: Neutrinos are supposed to be electrically neutral, but if they have a tiny magnetic "spark," NUCLEUS might catch it. Finding this would be a massive discovery, proving neutrinos are more complex than we thought.

Summary

The NUCLEUS experiment is like a team of detectives trying to solve a mystery in a noisy room.

1. They have a super-sensitive ear (the cryogenic crystal).
2. They are standing next to a loud factory (the nuclear reactor).
3. They are dealing with static noise (the Low-Energy Excess).
4. But they have a secret code: they know the factory's schedule. By watching how the "hits" change when the factory changes its rhythm, they can tune out the static and finally hear the ghostly whisper of the neutrino.

If they succeed, they will not only confirm our current understanding of the universe but might also open a door to a whole new world of physics that we haven't seen yet.

Technical Summary

1. Problem Statement

The NUCLEUS experiment aims to measure Coherent Elastic Neutrino-Nucleus Scattering (CE$\nu$NS) with unprecedented precision at extremely low nuclear recoil energies ($\mathcal{O}(10 \text{ eV})$). While CE$\nu$NS was first observed by the COHERENT collaboration using a Spallation Neutron Source, reactor-based measurements offer a continuous, high-flux source of low-energy antineutrinos.

The primary challenges addressed in this paper are:

• Background Dominance: The experiment operates in a low-overburden environment (3 m water-equivalent) at the Chooz nuclear power plant, leading to significant cosmic-ray-induced backgrounds.
• Low-Energy Excess (LEE): During commissioning, a dominant background of sub-keV events (the LEE) was observed, which exceeds the expected CE$\nu$NS signal by orders of magnitude. The origin is suspected to be stress-induced relaxation in the detector crystals or mechanical structures.
• Low Signal-to-Background Ratio (S/B): In the region of interest, the S/B ratio is much less than 1, making standard spectral analysis insufficient for signal extraction.
• Small Target Mass: The experiment uses gram-scale targets (7 g of CaWO$_4$), which is orders of magnitude smaller than other CE$\nu$NS experiments (kg-scale), necessitating ultra-low energy thresholds to compensate for the low event rate.

2. Methodology

Experimental Setup

• Location: Chooz Nuclear Power Plant (France), Very Near Site (VNS), located ~72 m and ~102 m from two reactor cores.
• Detectors: Gram-scale cryogenic calorimeters using CaWO$_4$ crystals instrumented with Tungsten Transition-Edge Sensors (W-TES).
• Operating Conditions: Cryogenic operation at 10 mK with an energy resolution of $\sigma_0 \approx 4$ eV.
• Phases:
  1. Technical Run: 7 g total target mass (4 detectors). Dominated by LEE.
  2. Physics Run: Same target mass but integrated into an instrumented inner veto (holder) designed to reject stress-induced LEE events. Assumes LEE suppression to negligible levels.

Analysis Framework

• Likelihood Approach: The authors developed an unbinned log-likelihood function that exploits two distinct dimensions:
  1. Energy Information: The spectral shape of the signal vs. background.
  2. Time Information: The variation in reactor power.
• Reactor Power Modulation: The two-reactor configuration at Chooz allows for scheduled shutdowns and power variations. The antineutrino flux scales with reactor power, while the background (LEE and particle-induced) is largely time-independent (or follows a known decay law for LEE).
• Statistical Model:
  • The likelihood function $L$ combines the time-dependent signal rate (proportional to reactor power $P(t)$) and the time-dependent background rate $\beta(t)$.
  • For the Technical Run, the LEE rate is modeled as a power-law decay $R(t) \propto (t-t_0)^{-k}$.
  • For the Physics Run, the background is assumed constant (particle-induced only).
• Systematics: The study incorporates systematic uncertainties regarding energy scale calibration (conservatively 25%), reactor flux (2%), and thermal power (5% for public data).

3. Key Contributions

1. Novel Analysis Strategy: The paper introduces a robust likelihood framework that disentangles signal and background in a regime where $S/B \ll 1$ by combining spectral shape with reactor-power modulation. This is a significant improvement over analyses relying solely on energy spectra or total event rates.
2. Comprehensive Sensitivity Projections: It provides the first detailed sensitivity projections for both the upcoming Technical Run (LEE-dominated) and the Physics Run (LEE-suppressed).
3. BSM Physics Reach: The study quantifies the experiment's ability to probe Beyond the Standard Model (BSM) physics even without a direct observation of the Standard Model (SM) CE$\nu$NS signal, leveraging the ultra-low threshold.
4. Validation: The statistical framework is validated using $\sim 5,000$ to $10,000$ Monte Carlo pseudo-experiments, confirming the unbiased reconstruction of parameters and the validity of asymptotic $\chi^2$ approximations for the test statistics.

4. Results

Standard Model (SM) CE$\nu$NS

• Technical Run: Due to the dominant LEE, a direct SM observation is not expected. However, the experiment can set competitive upper limits, constraining the signal to be $\approx 35$ times the SM prediction (90% CL).
• Physics Run: Assuming successful LEE suppression, the experiment projects a 4.7$\sigma$ discovery of SM CE$\nu$NS in 1 year of data.
  • Precision: Statistical uncertainty on the cross-section is projected at ~20%.
  • Weak Mixing Angle: This precision allows for a determination of the weak mixing angle $\sin^2 \theta_W$ at the lowest momentum transfer probed to date ($|q| \approx 5$ MeV), with an expected 1$\sigma$ interval of $0.187 < \sin^2 \theta_W < 0.286$.

Beyond the Standard Model (BSM)

The ultra-low threshold provides enhanced sensitivity to new physics that modifies the spectrum at low energies:

• Neutrino Charge Radius (NCR): The Physics Run is expected to constrain the diagonal electronic neutrino charge radius to $(-8.3 < \langle r^2_{\nu_e} \rangle < 5.6) \times 10^{-32} \text{ cm}^2$ (90% CL), one of the tightest constraints to date.
• Light Vector Mediators: The experiment can probe light mediator masses ($m_{Z'}$) between 0.1 and 10 MeV with coupling strengths ($g_{Z'}$) competitive with or better than existing experiments (CONUS+, COHERENT), even during the LEE-dominated Technical Run.
• Neutrino Magnetic Moment ($\mu_\nu$):
  • Technical Run: Projected limit $\mu_{\nu_e} < 22.3 \times 10^{-10} \mu_B$ (90% CL).
  • Physics Run: Projected limit $\mu_{\nu_e} < 2.0 \times 10^{-10} \mu_B$ (90% CL).
  • This sensitivity is driven by the $1/T_{nr}$ enhancement of the magnetic moment contribution at low recoil energies.

Mass Scaling

The study demonstrates that the 7 g target mass is sufficient for a 20% precision measurement. To reach the precision of current COHERENT measurements (~5-10%), the target mass would need to increase to ~40 g. A transition to systematic-limited precision would occur at ~340 g.

5. Significance

• Unique Physics Reach: NUCLEUS occupies a unique niche by accessing the lowest nuclear recoil energies ($\sim 10$ eV) ever attempted. This allows it to probe momentum transfers where nuclear form factors are unity, minimizing nuclear structure uncertainties and providing a "clean" probe of electroweak parameters.
• Complementarity: While large-mass experiments (like CONUS+ or COHERENT) rely on higher statistics, NUCLEUS compensates for its small mass with extreme energy resolution and low thresholds, offering complementary sensitivity to BSM scenarios that manifest at low energies.
• Dark Matter Connection: The detector technology and analysis techniques developed for NUCLEUS are directly applicable to low-mass dark matter searches. Furthermore, precise CE$\nu$NS measurements are crucial for defining the "neutrino fog" (irreducible background) for future dark matter experiments.
• Methodological Benchmark: The successful application of reactor-power modulation to extract a signal in a background-dominated regime sets a precedent for future reactor-based neutrino experiments operating in challenging environments.

In conclusion, the NUCLEUS experiment is poised to deliver the first reactor-based observation of CE$\nu$NS with gram-scale detectors, enabling precision tests of the Standard Model and stringent constraints on new physics, provided the Low-Energy Excess background can be effectively mitigated in the Physics Run.