Improved liquid argon ionization model and its impact on the DarkSide low-mass WIMP search programme

This paper presents a new global fit for the liquid argon nuclear-recoil ionization yield using data from multiple experiments, which refines the Thomas-Imel box model by favoring the Lenz-Jensen screening potential and significantly improves the sensitivity of the DarkSide low-mass WIMP search program.

The Gist

Imagine you are trying to find a tiny, invisible ghost (a dark matter particle) by listening for the faintest "thump" it makes when it bumps into a heavy object (an atomic nucleus) inside a giant tank of liquid argon.

This paper is about improving the microphone we use to hear those thumps. Specifically, it fixes how we calculate the "echo" (ionization) left behind when a ghost hits a nucleus.

Here is the breakdown of what the authors did, using simple analogies:

1. The Problem: A Noisy, Confusing Echo

The DarkSide-50 experiment is like a very sensitive listening room filled with liquid argon. When a dark matter particle hits an argon atom, it creates a tiny spark of electricity (ionization). Scientists need to know exactly how big that spark should be for a given "thump" energy.

However, for a long time, the scientists were using a slightly outdated map to predict the size of that spark. They were using a model based on the ZBL function (a mathematical rule for how atoms interact). It was like trying to navigate a city using a map from 1990 that had a few streets drawn in the wrong place. This made it hard to confidently say, "Yes, we heard a ghost," especially for the lightest, fastest ghosts (low-mass WIMPs).

2. The New Map: Gathering Better Data

To fix the map, the authors didn't just guess; they went on a data scavenger hunt. They combined measurements from four different experiments:

• DarkSide-50: Their own listening room.
• ARIS & SCENE: Other specialized listening rooms.
• ReD: A new, very precise experiment that acts like a high-speed camera, capturing the exact speed of the "thump" before it happens.

By mixing all these data points together, they created a "Global Fit." Think of this as taking thousands of photos of the same object from different angles to build a perfect 3D model.

3. The Big Discovery: Choosing the Right Rulebook

The scientists tested three different mathematical "rulebooks" (screening potentials) to see which one best explained the data:

• ZBL: The old, widely used rulebook.
• Molière: A complex rulebook based on older physics theories.
• Lenz–Jensen: A simpler, cleaner rulebook.

The Result: The data overwhelmingly voted for Lenz–Jensen.
The authors used a statistical method (Bayesian model comparison) to decide. The result was decisive:

• The data was 10,000 times more likely to be explained by Lenz–Jensen than by ZBL.
• The data was 10 million times more likely to be explained by Lenz–Jensen than by Molière.

It's as if they were trying to identify a suspect in a lineup, and the new evidence made the old suspect (ZBL) look completely innocent, while the new suspect (Lenz–Jensen) was an obvious match.

4. The Impact: Hearing the Ghosts Better

Why does this matter? Because the new model changes how we interpret the "thumps" from light dark matter particles.

• For DarkSide-50 (The Past): With the new model, the scientists realized that for very light particles (around 1.2 GeV), the "echo" (ionization) is actually stronger than they previously thought. This means their old limits were too conservative. By updating the math, they can now rule out dark matter candidates in the 1–3 GeV range much more strictly. They have effectively tightened the net, catching more potential "ghosts" or proving they aren't there with much higher confidence.
• For DarkSide-20k (The Future): This is a massive upgrade to the listening room (20 tons of argon). The new model suggests that this future detector will be 10 times more sensitive to the lightest dark matter particles than previously projected. It's like upgrading from a standard microphone to a super-sensitive parabolic dish; the chance of hearing that faint, low-mass thump just got much, much higher.

Summary

The paper says: "We found a better way to calculate how liquid argon reacts to particle collisions. By combining data from four experiments, we proved that an old mathematical model (ZBL) was wrong and a simpler one (Lenz–Jensen) is correct. This correction makes our current experiment (DarkSide-50) much better at ruling out light dark matter, and it promises that our future giant experiment (DarkSide-20k) will be incredibly powerful at finding it."

Technical Summary

Technical Summary: Improved Liquid Argon Ionization Model and its Impact on the DarkSide Low-Mass WIMP Search Programme

Problem Statement
The DarkSide programme utilizes dual-phase liquid-argon time projection chambers (LAr TPCs) to search for dark matter via elastic scattering off atomic nuclei. While the DarkSide-50 experiment achieved world-leading limits on WIMP–nucleon interactions in the 1.2–3.5 GeV/$c^2$ mass range using an ionization-only analysis, the interpretation of data in this low-mass regime is critically dependent on the accurate modeling of the nuclear-recoil ionization yield ($Q_y$). Previous analyses relied on the Thomas–Imel box model constrained by neutron calibrations and external datasets (ARIS, SCENE). However, the model predictions at sub-keV energies remained sensitive to the assumed nuclear stopping power ($s_n$), which is determined by screening functions (SFs). Earlier studies combining DarkSide-50, ARIS, and SCENE data lacked the sensitivity to distinguish between the commonly used ZBL, Molière, and Lenz–Jensen screening potentials. Furthermore, previous implementations of the Molière model utilized approximations (Winterbon) that deviate from the true Molière stopping power.

Methodology
To address these uncertainties, the authors performed a new global fit combining nuclear-recoil response measurements from four sources:

1. DarkSide-50: In-situ AmC neutron calibration data (down to $\sim$0.4 keV).
2. ARIS and SCENE: Monoenergetic recoil measurements (down to 7 keV).
3. ReD: New measurements from the ReD experiment, a small dual-phase LAr TPC providing event-by-event nuclear recoil energies via neutron time-of-flight from a $^{252}$Cf source (2–10 keV range).

The analysis employs the Thomas–Imel box framework (Eq. 1.1), varying the model parameters $C_{box}$ and $\beta$ while fixing the drift field. A key methodological improvement involves the adoption of the Wilson et al. parametrization for the Molière model to ensure percent-level accuracy, replacing the previously used Winterbon approximation.

The study utilizes a Bayesian model comparison to evaluate three non-nested models based on different screening functions: ZBL, Molière (Wilson parametrization), and Lenz–Jensen. Nuisance parameters, such as ionization-electron amplification gain and TPC vertical offsets for the ReD data, are assigned Gaussian priors and marginalized over during the construction of the global $\chi^2$.

Key Contributions

• Integration of ReD Data: The inclusion of high-precision ReD data (2–10 keV) significantly enhances the sensitivity of the global fit to the choice of screening potential, specifically in the recoil-energy region most relevant for light WIMPs.
• Refined Molière Implementation: The use of the Wilson et al. parametrization corrects previous deviations in the Molière model implementation, enabling a fair comparison with other screening functions.
• Bayesian Model Selection: The application of Bayes factors (BFs) to the combined dataset provides a quantitative basis for selecting the most appropriate screening function.

Results
The combined dataset strongly favors the Lenz–Jensen screening function over both ZBL and Molière:

• Bayes Factors: The data prefer Lenz–Jensen over ZBL with $\log_{10} \text{BF} = 3.8$ (odds $\approx 10^4:1$) and over Molière with $\log_{10} \text{BF} = 7.2$ (odds $> 10^7:1$). These values constitute decisive evidence according to standard model-selection criteria.
• Ionization Yield: The resulting model establishes Lenz–Jensen as the only screening model capable of consistently reproducing the full ensemble of ReD, ARIS, SCENE, and DarkSide-50 measurements.

Impact on Sensitivity and Limits
The adoption of the Lenz–Jensen-based ionization model directly impacts the interpretation of low-energy nuclear recoils:

• DarkSide-50: Re-evaluating the exclusion limits with the new model yields a significantly larger predicted signal rate below 5 keV. Consequently, the 90% C.L. exclusion limit improves by a factor of up to 5 at a WIMP mass of 1.2 GeV/$c^2$ under the quenching-fluctuation (QF) hypothesis, and by a factor of 2–3 under the no-fluctuation (NQ) assumption. DarkSide-50 now sets the strongest published constraints in the 1–3 GeV/$c^2$ mass range.
• DarkSide-20k: Sensitivity projections for the upcoming DarkSide-20k experiment (assuming a 2 $e^-$ threshold and 342 ton$\times$year exposure) show substantial gains. For a 1.2 GeV/$c^2$ WIMP, the improvement in detection probability reaches nearly one order of magnitude in the NQ scenario and a factor of 3 in the QF case.

Significance
The paper asserts that the revised liquid argon response model strengthens both the reinterpretation of existing DarkSide-50 data and the discovery potential of the future DarkSide-20k experiment. The work highlights that a precise understanding of nuclear-recoil ionization at the few-keV scale is essential for advancing the search for low-mass dark matter.