Search for Annual Modulation in Combined ANAIS 112 and COSINE 100 Data using Bayesian Model Comparison

Using Bayesian model comparison on approximately three years of combined ANAIS-112 and COSINE-100 data, the study finds no evidence for a dark matter-induced annual modulation signal, as the Bayes factor strongly favors a constant background model over a sinusoidal one.

The Gist

The Big Mystery: What is Dark Matter?

Imagine our galaxy is a giant, invisible ocean. We know this ocean exists because the ships (stars) moving through it behave in a way that suggests they are being pushed by something we can't see. Scientists call this invisible stuff Dark Matter.

For decades, the leading theory is that this dark matter is made of tiny, ghostly particles called WIMPs (Weakly Interacting Massive Particles). These particles are so shy they rarely bump into normal matter, but if they do, they might leave a tiny "scratch" or signal.

The Dispute: The "Annual Modulation" Signal

In 1998, an experiment called DAMA/LIBRA claimed to have found these scratches. They said they saw a specific pattern: the number of "scratches" went up and down like a heartbeat once every year.

The Analogy: Imagine you are standing on a beach. You notice that every year, around June, the waves get slightly bigger, and around December, they get smaller. You conclude, "The ocean is breathing!" This is what DAMA claims: Earth moves through a "wind" of dark matter, and as we orbit the Sun, we hit more of it in June and less in December.

The Skeptics: COSINE-100 and ANAIS-112

Other scientists were skeptical. They built their own detectors, COSINE-100 (in Korea) and ANAIS-112 (in Spain), using the exact same materials as DAMA to see if they could hear the same "ocean breathing."

For a long time, these new experiments said, "We don't hear anything." They looked at the data and saw no clear up-and-down pattern.

The New Study: A Fresh Look with a New Tool

In this paper, two researchers (Om Godse and Shantanu Desai) decided to take a fresh look at the combined data from COSINE-100 and ANAIS-112 (about three years of data).

Instead of just looking at the numbers, they used a statistical tool called Bayesian Model Comparison.

The Analogy: Imagine you are a detective trying to solve a case. You have two theories:

1. Theory A (The Cosine Model): The waves are rhythmic. There is a real pattern (the "ocean breathing").
2. Theory B (The Constant Model): The waves are just random noise. There is no pattern; it's just a flat, boring line.

Usually, you might just look at the data and guess which theory fits better. But this paper uses a "Mathematical Scale" (called the Bayes Factor) to weigh the evidence. It asks: "How much more likely is it that the data comes from a rhythmic pattern compared to random noise?"

The Results: The Scale Didn't Tip

The researchers tested this scale using different "rules" (called priors) to see if the answer changed depending on how they set up the math. They looked at the data in two different energy ranges (like looking at the ocean with two different colored filters).

The Verdict:
The result was clear: The scale barely moved.

• The "Mathematical Scale" gave a score of less than 1.15.
• In the world of statistics, a score this low is like hearing a faint whisper in a noisy room. It is "barely worth mentioning."

What this means: The data from COSINE-100 and ANAIS-112 does not support the idea that there is a rhythmic "ocean breathing" (annual modulation). The data looks much more like random noise (a constant value) than a signal from dark matter.

The Conclusion

The paper concludes that when you combine the data from these two experiments and run it through this strict mathematical test, there is no evidence for the annual modulation signal that DAMA claims to see.

The researchers also shared their "recipe" (the computer code) with the public so anyone can check their work. This confirms the earlier findings that the "ocean breathing" might just be a trick of the light, not a real phenomenon.

Technical Summary

Technical Summary: Bayesian Model Comparison of Combined ANAIS-112 and COSINE-100 Data

Problem Statement
For over two decades, the DAMA/LIBRA experiment has reported a statistically significant annual modulation signal in the residual event rates of sodium iodide (NaI) detectors, a signature consistent with Weakly Interacting Massive Particle (WIMP) dark matter interactions. However, this claim remains unconfirmed by other direct detection experiments using the same target material, specifically COSINE-100 (Korea) and ANAIS-112 (Spain). While previous joint analyses of the first three years of combined data from COSINE-100 and ANAIS-112 (referred to as C25) utilized frequentist regression to find no evidence for modulation, this study seeks to complement those findings through a Bayesian framework. The core problem addressed is whether the combined residuals of these two experiments provide statistical evidence favoring a sinusoidal modulation model (expected from dark matter) over a constant background model, independent of the specific regression techniques used in prior work.

Methodology
The authors perform a Bayesian model comparison between two hypotheses:

• Model $M_2$ (Cosine Signal): The residual data follows a sinusoidal function $R(t) = S_m \cos(\omega(t - t_0))$, where $S_m$ is the amplitude, $\omega$ is the angular frequency, and $t_0$ is the phase.
• Model $M_1$ (Constant Background): The residual data is described by a constant value $A$.

The analysis utilizes approximately three years of combined data from COSINE-100 and ANAIS-112, covering a total exposure of 485 kg-year. The data is binned into 15-day intervals across two energy ranges: 1–6 keV and 2–6 keV.

Key methodological steps include:

1. Likelihood Construction: A Gaussian likelihood is assumed for the observed residuals, treating the errors as Gaussian.
2. Prior Selection: To ensure robustness, the authors test four distinct sets of priors for the free parameters ($S_m$, $\omega$, $t_0$):
   • Amplitude ($S_m$): Uniform priors ranging from the minimum to maximum observed residuals, and separately from zero to the maximum absolute residual.
   • Frequency ($\omega$) and Phase ($t_0$): Both uniform priors (covering the full dataset duration and 0–365 days, respectively) and normal priors centered on the best-fit values reported by DAMA/LIBRA ($T \approx 1$ year, $t_0 \approx 145$ days).
3. Evidence Calculation: The Bayesian evidence (marginal likelihood) for both models is computed using the nested sampling algorithm implemented in Dynesty. The comparison metric is the natural logarithm of the Bayes factor, $\ln(B_{21})$, where $B_{21}$ is the ratio of the evidence for the cosine model to the constant model.

Key Contributions

• Independent Verification: This work provides an independent validation of the C25 results using a Bayesian model comparison approach rather than the least-squares and Markov Chain Monte Carlo (MCMC) regression used in the original joint analysis.
• Prior Robustness: By testing multiple prior configurations—including those informed by DAMA/LIBRA best-fit values—the study demonstrates that the conclusion regarding the absence of a signal is robust against variations in prior assumptions.
• Open Science: The authors have made their analysis codes publicly available to ensure transparency and reproducibility of the Bayesian evidence calculation.

Results
The analysis yields the natural log of the Bayes factor ($\ln(B_{21})$) for all four prior sets across both energy intervals. The results are summarized as follows:

• For all tested prior combinations, the value of $\ln(B_{21})$ is less than 1.15.
• According to Jeffreys' scale for interpreting Bayes factors, a value of $\ln(B_{21}) < 1.15$ (corresponding to $B_{21} \leq \sqrt{10}$) indicates that the evidence for the cosine model over the constant model is "barely worth mentioning."
• Specifically, in the 1–6 keV and 2–6 keV intervals, the calculated values range from approximately -0.13 to 1.36, with the majority clustering near or below the 1.15 threshold.
• Marginalized posterior contours for the amplitude, frequency, and phase show no strong preference for the DAMA-favored parameters over the null hypothesis of a constant rate.

Significance and Claims
The paper concludes that the Bayesian model comparison provides no evidence to support the hypothesis that the combined ANAIS-112 and COSINE-100 data contains an annual modulation signal consistent with dark matter interactions. The results are consistent with the constant background hypothesis.

The authors modestly frame their contribution as a complement to the C25 analysis. They state that their findings reinforce the conclusion that the combined data from the first three years of these experiments does not support the DAMA annual modulation claim. The study does not claim to definitively rule out dark matter interactions in general but specifically finds no statistical preference for a sinusoidal signal over a constant background in this specific dataset, regardless of the prior assumptions regarding the signal's phase and frequency.