DarkSide-50 Analysis Framework

• DarkSide-50 Analysis Framework is a computational infrastructure that integrates simulation, signal modeling, and statistical methods to enable precise dark matter searches.
• It leverages detailed detector simulations and global fitting of calibration datasets (ReD, ARIS, SCENE) to optimize ionization and scintillation measurements.
• The framework rigorously propagates systematic uncertainties and supports both profile-likelihood and effective field theory approaches to enhance low-mass WIMP sensitivity.

The DarkSide-50 Analysis Framework is the computational and statistical infrastructure underlying the DarkSide-50 liquid argon time projection chamber (LAr-TPC) dark matter search program. It encompasses detector simulation, signal and background modeling, calibration fitting, systematics propagation, and statistical inference, enabling rigorous extraction of WIMP–nucleon interaction limits and exploration of effective field theory (EFT) parameter space.

1. Detector Signal Modeling and Response Functions

At the core of the DarkSide-50 analysis chain is a detailed physical model of scintillation and ionization response in liquid argon for both electronic and nuclear recoils. In dual-phase LAr-TPCs, a particle deposit yields both prompt scintillation (S1) and drifted ionization electrons (S2) which are proportional-scintillated in gas. The electron yield $Q_y(E_{nr})$ from a nuclear recoil of energy $E_{nr}$ is given by

$$Q_y(E_{nr}) \equiv f_q(E_{nr}) = \frac{(1 - r) N_i}{E_{nr}}$$

where $N_i$ is the number of initial electron–ion pairs and $r$ is the recombination probability. At few-keV energies, recombination is modeled by the Thomas–Imel box model,

$$r = 1 - \frac{1}{\gamma N_i} \ln(1 + \gamma N_i) \quad\text{with}\quad \gamma = \frac{C_{\rm box}}{F}$$

where $F$ is the drift field and $C_{\rm box}$ is a fitted "recombination constant".

The number of initial pairs incorporates electronic and nuclear stopping powers via the Lindhard function,

$$N_i(E_{nr}) = \beta \frac{\epsilon s_e(\epsilon)}{s_n(\epsilon) + s_e(\epsilon)}, \quad \epsilon \simeq 0.0135\, E_{nr}\, [\mathrm{keV}]$$

with $\beta$ a normalization parameter and $s_n$, $s_e$ determined by the choice of atomic-screening function (SF). Three SFs were tested: Ziegler–Biersack–Littmark (ZBL), Molière (corrected by Wilson parametrization), and Lenz–Jensen (single-term Thomas–Fermi). The model is fully specified by $(C_{\rm box},\, \beta)$ and the SF choice (Acerbi et al., 17 Nov 2025).

2. Calibration, Global Fits, and Model Selection

Global fits to the ionization model parameters employ four datasets:

• ReD: 5×5×6 cm$^3$ LAr TPC, $^{252}$Cf neutrons, event-by-event ToF, 2–8 keV
• ARIS: Monoenergetic neutron S1, 7–120 keV NR
• SCENE: Monoenergetic NR at 17–60 keV
• DarkSide-50 AmC: Continuous NR spectrum, threshold 0.4 keV$_{nr}$

For each, either likelihoods or $\chi^2$ statistics compare measured $Q_y$ values to model predictions. In ReD, $g_2$ (S2 gain) and $\Delta z$ (TPC offset) are profiled as Gaussian nuisances. ReD is split top/bottom and fitted in recoil-energy intervals by unbinned Gaussian+background likelihoods to extract means and uncertainties for $Q_y$ per bin. The global fit minimizes the sum of dataset $\chi^2$ values plus the ReD penalty terms, scanning $(C_{\rm box},\beta)$ for each SF and profiling over nuisances.

A decisive Bayes-factor comparison ($\log_{10} \mathrm{BF} = 3.8$ for Lenz–Jensen over ZBL, and $7.2$ over Molière) selects Lenz–Jensen SF as optimal. Best-fit values are (Acerbi et al., 17 Nov 2025):

Parameter	ZBL	Lenz–Jensen	Molière
$C_{\rm box}$ [V/cm]	$8.1^{+0.1}_{-0.2}$	$7.9^{+0.2}_{-0.2}$	$8.6^{+0.3}_{-0.2}$
$\beta$ ($10^3$)	$7.0^{+0.3}_{-0.2}$	$6.5^{+0.1}_{-0.3}$	$8.8^{+0.4}_{-0.5}$

3. Simulation, Data Reconstruction, and Energy Calibration

The G4DS Geant4-based Monte Carlo system simulates event generation, detector geometry and materials, full optical photon propagation, and electron drift (collaboration et al., 2017). All simulated p.e. times and PMT channel info are processed by the DarkArt framework, which executes waveform digitization, baseline subtraction, pulse finding, and calculation of observables (S1, S2, $f_{90}$, position). These outputs feed the event selection, background modeling, and WIMP search analyses.

Energy calibration proceeds by converting S2 pulse to extracted electrons $n_e$ with the latest $g_2$. Nuclear recoil energy $E_{nr}$ is inferred from $n_e$ using the updated $Q_y(E_{nr})$. Detector resolution from photon and electron counting statistics, together with single-electron response and electron lifetime, is folded into the reconstructed spectrum (Acerbi et al., 17 Nov 2025, collaboration et al., 2017).

4. Statistical Analysis and Likelihood Construction

For limit setting, data are binned in $n_e$ (analysis threshold: 4 e$^-$ for DarkSide-50). The WIMP-induced signal PDF is generated by normalizing the theoretical spectrum, applying $Q_y$ to obtain $n_e$, and folding over detector resolution and threshold acceptance.

Backgrounds consist of measured and simulated electromagnetic and nuclear sources, with "spurious-electron" events dominating at few-$e^-$, modeled empirically from dedicated runs. The composite likelihood function is

$$\mathcal{L}(\sigma,\{\theta\}) = \prod_{i} \mathrm{Poisson}[x_i \mid \lambda_i(\sigma,\{\theta\})]$$

where $x_i$ are observed event counts in $n_e$ bins, $\lambda_i$ is the total expectation from signal and background, and $\{\theta\}$ are nuisance parameters (background normalizations, calibration constants, systematics), constrained through Gaussian priors.

The 90% C.L. upper limit on $\sigma$ (WIMP–nucleon cross section) is extracted using a profile-likelihood ratio test statistic (Acerbi et al., 17 Nov 2025, Collaboration et al., 2023). For some analyses, Bayesian Network methods reframe all dependencies in terms of explicit probabilistic graphical models and employ MCMC for posterior sampling (Collaboration et al., 2023).

5. Systematics: Sources, Treatment, and Propagation

Systematic uncertainties are rigorously propagated at all stages:

• Ionization-yield model parameters: $(C_{\rm box},\beta)$ are floated within the $\pm1\sigma$ contours of the fit, generating an uncertainty band on the WIMP PDF.
• $g_2$ gain: Propagated as a Gaussian prior ($\pm3.8\%$), included as a nuisance in ReD calibration, fixed for DS50.
• TPC offset $\Delta z$: Affects energy assignment ($\pm2.4\%$ in ReD), profiled as a nuisance.
• Detector resolution: Uncertainties in single-electron response and lifetime folded into the resolution kernel.
• Background normalizations: Spurious electron rate (empirically $\pm30\%$), γ/neutron backgrounds (5–10% from Monte Carlo), all as Gaussian nuisance parameters.

All nuisance pulls are profiled in the likelihood, or marginalized over in Bayesian treatments, enabling full statistical propagation and robust coverage of confidence intervals (Acerbi et al., 17 Nov 2025, Collaboration et al., 2023).

6. Sensitivity Results and DarkSide-20k Projections

Adopting the Lenz–Jensen screening model led to substantial improvements in low-mass WIMP sensitivity. For example, assuming binomial quenching fluctuations (QF), the 90% C.L. cross-section limit at $m_\chi=1.2$ GeV/c$^2$ improved by a factor $\sim5$ relative to ZBL; with "no-quenching" (NQ) the gain is $\sim2.5$. World-leading exclusion limits are set in $[0.8,\,3.5]$ GeV/c$^2$ (QF) and $[1.0,\,3.3]$ GeV/c$^2$ (NQ), outperforming contemporary liquid xenon (XENONnT, PandaX-4T) and aligning with the LAr neutrino floor (Acerbi et al., 17 Nov 2025).

For the upcoming DarkSide-20k, with a projected exposure of 342 ton·yr and 2 e$^-$ threshold, this updated calibration predicts further sensitivity improvements: QF projection improves by a factor $\sim3$ (NQ: $\sim10$) at $1.2$ GeV/c$^2$, probing toward the irreducible background from solar neutrinos.

7. Effective Field Theory Interpretations and Model-Independent Searches

Beyond standard spin-independent interactions, the framework accommodates nonrelativistic EFT interpretations. Differential cross-sections for $^{40}$Ar are constructed as

$$\frac{d\sigma_N}{dE_R}(q,v) = \frac{2 m_T}{v^2} \sum_k R_k\left(v^{\perp2}, q^2 / m_N^2\right) W_k^{00}(q^2)$$

where $k \in \{M, \Phi'', M\Phi''\}$ enumerates nuclear response modes; $R_k$ are functions of coupling coefficients $c_i$ for each operator $\mathcal{O}_i$. Limits are set by a Poisson cut-and-count approach, with backgrounds subtracted and operator-by-operator cross-section bounds extracted. For $100$ GeV-scale WIMPs, 90% C.L. exclusion spans from $\sim 2.4 \times 10^{-45}$ to $2.3 \times 10^{-42}$ cm$^2$ depending on operator scaling (Collaboration et al., 2020).

This operator-by-operator paradigm provides target complementarity across argon, xenon, and germanium detectors, and allows model-independent exclusion of broad weakly-interacting mediator classes.

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The DarkSide-50 analysis framework is distinguished by its integration of a globally calibrated ionization response model, detailed simulation and reconstruction chain, comprehensive systematics handling, and both profile-likelihood and Bayesian inference approaches. These attributes yield leading constraints on low-mass dark matter and a platform for robust interpretations across multiple theoretical frameworks (Acerbi et al., 17 Nov 2025, collaboration et al., 2017, Collaboration et al., 2023, Collaboration et al., 2020).