Sensitivity to low-mass WIMPs with an improved liquid argon ionization response model within the DarkSide programme

By integrating new ReD calibration data with existing DarkSide-50, ARIS, and SCENE results to refine the liquid argon ionization response model for nuclear recoils, this study establishes new world-leading exclusion limits on low-mass WIMPs in the 1–3 GeV/c² range and demonstrates significantly enhanced discovery potential for the upcoming DarkSide-20k detector.

The Gist

The Big Picture: Hunting for Ghosts in a Jar of Argon

Imagine scientists are trying to catch "ghosts." In the world of physics, these ghosts are called WIMPs (Weakly Interacting Massive Particles), a leading candidate for Dark Matter. Dark matter makes up most of the universe, but it doesn't shine, reflect light, or interact with normal matter easily. It's like trying to find a specific, invisible ghost in a dark room by only feeling the air move when it walks past.

The DarkSide experiment uses a giant, ultra-pure jar of liquid argon (frozen argon gas) to act as this "dark room." When a WIMP ghost bumps into an argon atom, it creates a tiny "kick" (a nuclear recoil). This kick should produce two things: a flash of light and a few free electrons (electricity).

The Problem: The "Fuzzy" Ruler

For years, the DarkSide team has been very good at detecting these kicks. However, they faced a tricky problem: How do you measure the size of the kick?

When an argon atom gets kicked, it doesn't just turn all that energy into electrons. Some energy gets lost to heat or light, and some electrons get "stuck" to the atoms they bumped into (a process called recombination). To figure out how big the original kick was, scientists had to use a mathematical "ruler" to estimate how many electrons would escape.

The problem was that they had three different rulers (called Screening Functions):

1. The ZBL Ruler: The one they used before. It was a bit conservative, assuming fewer electrons would escape.
2. The Molière Ruler: A slightly different guess.
3. The Lenz-Jensen Ruler: Another theoretical guess.

These rulers disagreed on how the electrons behave, especially for tiny kicks (low-energy recoils). Since the lightest WIMPs create the tiniest kicks, this disagreement meant the scientists couldn't be sure if they were missing a ghost or if their ruler was just wrong. It was like trying to weigh a feather on a scale that might be off by a few grams; you can't tell if the feather is there or if the scale is broken.

The Solution: A New, Sharper Camera (The ReD Experiment)

To fix this, the team built a new, smaller, super-sensitive detector called ReD. Think of ReD as a high-definition camera placed right next to the main jar.

• The Setup: They shot neutrons (tiny particles) at the liquid argon in ReD. These neutrons acted like a known "hammer" to hit the argon atoms.
• The Measurement: Because they knew exactly how hard the hammer hit, they could count exactly how many electrons came out.
• The Result: They measured the "electron yield" (how many electrons escape per unit of energy) with incredible precision in the low-energy range where the WIMP ghosts hide.

The Verdict: Picking the Right Ruler

The team took the new, sharp data from ReD and combined it with older data from their main detector (DarkSide-50) and two other smaller experiments (ARIS and SCENE). They fed all this data into a giant computer model to see which "ruler" (Screening Function) fit the facts best.

The Winner: The Lenz-Jensen ruler.

The data showed that the old ruler (ZBL) was underestimating the number of electrons. The new Lenz-Jensen model showed that more electrons escape than previously thought when an atom gets a tiny kick.

• Analogy: Imagine you thought a leaky bucket only let 1 drop of water out for every 100 you poured in. But your new, precise measurement shows it actually lets out 2 drops. Suddenly, you realize you can catch twice as much water as you thought you could.

The Impact: Stronger Limits on Ghosts

Because the new model says more electrons escape, the scientists can now detect smaller kicks with more confidence. This changes the rules of the hunt:

1. Better Sensitivity: They can now rule out the existence of WIMPs in a specific mass range (1 to 3 GeV) much more strictly than before.
2. New World Records: The paper claims they have set the world's most stringent limits on low-mass WIMPs. In plain English: They have proven that if these light ghosts exist, they are even rarer or harder to find than we thought, effectively narrowing the search area significantly.
3. Future Hope: They also looked ahead to a future, much larger detector called DarkSide-20k. With this new, better ruler, the future detector will be much more likely to find a ghost if one is hiding in that low-mass range.

Summary

The DarkSide team realized their math for counting electrons in liquid argon was a bit fuzzy. By building a new, precise experiment (ReD) to measure exactly how electrons behave during tiny collisions, they proved that their old math was too pessimistic. By switching to a better math model (Lenz-Jensen), they sharpened their "ghost hunting" tools, allowing them to set much stricter rules on where light Dark Matter could be hiding.

Technical Summary

Technical Summary: Sensitivity to Low-Mass WIMPs with an Improved Liquid Argon Ionization Response Model within the DarkSide Programme

Problem Statement
The detection of low-mass Weakly Interacting Massive Particles (WIMPs) using liquid argon (LAr) dual-phase time projection chambers (TPCs) relies critically on the precise characterization of the ionization response to nuclear recoils in the keV energy range. The ionization yield ($Q_y$) is governed by atomic collision processes between the recoiling nucleus and surrounding argon atoms, which are modified by electron screening. Theoretical descriptions of these screening effects utilize screening functions (SFs), specifically those proposed by Ziegler et al. (ZBL), Molière, and Lenz-Jensen. Previous analyses by the DarkSide collaboration, utilizing data from DarkSide-50, ARIS, and SCENE, were unable to definitively discriminate between these models due to insufficient experimental sensitivity at sub-keV energies. This ambiguity led to significant variations in predicted $Q_y$ values below 5 keV, directly impacting the interpretation of experimental data and the sensitivity limits for light dark matter searches.

Methodology
This work presents a unified analysis combining new measurements from the ReD experiment with existing calibration data from DarkSide-50, ARIS, and SCENE. The methodology involves:

1. Data Integration: The analysis incorporates ReD data, which provides direct sensitivity in the 2–10 keV nuclear recoil energy range, alongside DarkSide-50's continuous spectrum (0.4–200 keV) and mono-energetic lines from ARIS (7–120 keV) and SCENE (17–60 keV).
2. Model Framework: The ionization yield is modeled using the Thomas–Imel box recombination formalism. The number of initial electron-ion pairs ($N_i$) is calculated based on the ratio of electronic to nuclear stopping powers, which depends on the chosen screening function.
3. Correction of Previous Implementations: The authors address a known discrepancy in the implementation of the Molière potential in prior works, adopting an improved parametrization by Wilson et al. that aligns with the original Molière function.
4. Statistical Analysis: A global $\chi^2$ minimization is performed across all datasets to constrain the model parameters: the recombination constant ($C_{box}$) and the normalization constant ($\beta$). Nuisance parameters, including the gas gain ($g_2$) and the vertical offset ($\Delta z$) of the ReD TPC, are marginalized.
5. Model Selection: Bayesian analysis is employed to compute Bayes factors (BF) to quantify the preference among the ZBL, Molière, and Lenz-Jensen screening models.

Key Contributions

• ReD Experimental Data: The paper utilizes new ReD measurements obtained using a $^{252}\text{Cf}$ fission source and a small-scale dual-phase LAr TPC equipped with silicon photomultipliers. These data provide high-precision constraints on $Q_y$ in the 2–8 keV range, a region previously unconstrained by DarkSide-50 alone.
• Refined Screening Function Selection: The analysis demonstrates that the Lenz-Jensen screening function provides a significantly better fit to the combined dataset than the ZBL or Molière functions. The study reports a decisive preference for Lenz-Jensen over ZBL ($\log_{10} \text{BF} = 3.8$) and an even stronger preference over Molière ($\log_{10} \text{BF} = 7.2$).
• Improved Ionization Model: By fixing the screening function to Lenz-Jensen, the authors derive updated values for $C_{box}$ and $\beta$, resulting in a model that predicts a higher ionization yield at low energies compared to the previous ZBL-based model.

Results

• Global Fit: The simultaneous fit of ReD, ARIS, SCENE, and DarkSide-50 data using the Lenz-Jensen SF shows excellent agreement across all datasets, with overlapping confidence regions in the $(C_{box}, \beta)$ parameter space. In contrast, the ZBL and Molière models exhibit tension, particularly between the ReD and DarkSide-50 datasets below 5 keV.
• WIMP Sensitivity: The updated ionization model is applied to re-evaluate the exclusion limits for DarkSide-50 and the projected sensitivity for the upcoming DarkSide-20k detector.
  • DarkSide-50: The 90% Confidence Level (C.L.) exclusion limit improves by a factor of 5 (assuming binomial quenching fluctuations) or 2.5 (assuming no fluctuations) at a WIMP mass of 1.2 GeV/$c^2$. This sets world-leading constraints in the 0.8–3.5 GeV/$c^2$ mass range.
  • DarkSide-20k: The projected sensitivity for DarkSide-20k improves by a factor of 3 (binomial fluctuations) or 10 (no fluctuations) at 1.2 GeV/$c^2$, significantly enhancing the discovery potential for low-mass dark matter candidates.

Significance
The paper claims that the combination of ReD data with existing DarkSide calibrations allows for a data-driven selection of the atomic screening function, resolving previous ambiguities in the modeling of LAr ionization. By adopting the Lenz-Jensen screening function, the DarkSide programme achieves stronger exclusion limits for low-mass WIMPs. The authors emphasize that this improved modeling is essential for maximizing the physics reach of current and future liquid argon detectors, particularly in the GeV/$c^2$ mass regime where nuclear recoil energies are close to detector thresholds. The work establishes a more robust foundation for interpreting low-energy signals in liquid argon dark matter searches.