PandaX-4T S2-Only Search

• The paper presents the S2-only analysis method that pushes energy thresholds as low as 0.04 keV, enabling the exploration of sub-GeV dark matter interactions.
• It details the advanced dual-phase liquid xenon TPC design with a 3.7-tonne LXe target and high-efficiency readout systems that capture low-energy ionization signals.
• The results set world-leading exclusion limits on dark matter–electron and dark matter–nucleon interactions, establishing new benchmarks for low-energy direct detection.

The PandaX-4T Ionization S2-only search is a central analysis strategy within the PandaX experimental program for direct dark matter and rare event searches at the China Jinping Underground Laboratory. This approach exploits the dual-phase liquid xenon time projection chamber’s (TPC) optimized sensitivity to ionization (S2) signals, enabling detection of extremely low-energy depositions from weakly interacting massive particles (WIMPs), sub-GeV dark matter candidates, solar neutrinos, axions, and other exotic phenomena. The S2-only methodology has facilitated world-leading exclusion limits on dark matter–nucleus and dark matter–electron interactions, advanced novel searches for new physics at low thresholds, and introduced methods critical for operation at formidable exposures.

1. Principle of S2-Only Analysis in Dual-Phase Liquid Xenon TPCs

PandaX-4T employs a dual-phase (liquid–gas) xenon TPC, wherein a particle interaction produces both prompt scintillation (S1) and ionization electrons, the latter being drifted upward by an electric field and extracted into the gas phase to generate secondary proportional scintillation (S2) (Cao et al., 2014, Meng et al., 2021). S1 and S2 signals enable three-dimensional event reconstruction and background discrimination; however, for energy depositions below the S1 detection threshold—characteristic of low-mass dark matter or solar neutrino coherent nuclear recoils—only the S2 signal may be reliably observed. S2-only (unpaired S2 or "US2", Editor's term) analyses thus prioritize ionization charge collection and low-electron-count event identification.

The S2 signal amplitude is modeled as

$\mathrm{S2} = g_2 \times n_e$

where $n_e$ is the number of ionization electrons extracted from the liquid, and $g_2$ captures the combined electron extraction efficiency and gas-phase electroluminescence gain.

This approach allows the experiment to push its energy threshold to $\lesssim 0.04$–$0.07$ keV (for ER) and $0.33$–$0.77$ keV (for NR), facilitating searches for lighter dark matter and rare low-energy processes inaccessible to S1-based analyses (Collaboration, 2022, Zhang et al., 16 Jul 2025).

2. Detector Design and Readout Systems for S2-Only Sensitivity

The PandaX-4T TPC consists of a 3.7 tonne ultra-pure LXe target, bounded by PTFE reflectors, equipped with 369 (top) and 199 (bottom) 3" Hamamatsu R11410-23 PMTs, and a fine-tuned field cage with an optimized extraction field ($E_\text{extraction} \sim 8.3$ kV/cm in earlier stages) for $\sim$90% electron extraction efficiency (Cao et al., 2014). Stable high-voltage operation, minimized micro-discharge, and precise cryogenic controls are essential to sustain low-threshold operation required for S2-only searches.

A crucial enabling feature is the upgraded readout electronics and DAQ: the triggerless, self-triggered CAEN V1725 digitizer-based system records all PMT data with single photoelectron (SPE) sensitivity ($\sim$96% efficiency), high bandwidth ($>450$ MB/s), and robust synchronization across all channels (Yang et al., 2021). This architecture ensures no low-energy S2 events are lost due to inefficiency or threshold effects, setting the foundation for threshold-limited analyses required for low-mass dark matter and CE$\nu$NS searches (Collaboration, 2022, Collaboration et al., 15 Jul 2024).

3. S2 Signal Modeling, Event Reconstruction, and Selection

Comprehensive modeling of S2 signal response is performed to accurately quantify the relationship between deposited energy and measured charge. Principally, the process is described by

$N_q = \frac{\xi}{W}$

where $N_q$ is the total quanta for a deposited energy $\xi$ ($W=13.7$ eV) (Luo et al., 7 Mar 2024). The fraction of quanta yielding free electrons versus excitons is modeled with energy- and field-dependent recombination parameterizations, incorporating binomial and Gaussian fluctuations.

The reconstruction chain includes baseline subtraction, hit finding, clustering, pulse classification, and spatial reconstruction. S2-dominated events are recognized via pulse width, spatial (x–y) pattern, and bottom/top charge asymmetry (TBA). Corrections incorporate drift-time-based $z$-attenuation (accounting for electron lifetime), spatial charge maps (from $^{83\text{m}}$Kr calibration), and potential field non-uniformities (Luo et al., 7 Mar 2024, Qian et al., 11 Feb 2025). Horizontal positions are determined with high precision using the photon acceptance function (PAF) method, providing $\sigma_x,\,\sigma_y\approx$1.0 mm (bulk) and 4.4 mm (surface) for typical S2 charges (Qian et al., 11 Feb 2025). Partial waveform reconstruction (PWR) and geometric position correction (GPC) further refine edge-reconstruction artifacts.

Selection of S2-only events employs stringent data quality cuts: pulse width and shape, TBA, S2 isolation, rejection of pileup, and radial fiducialization to suppress surface and electrode-related backgrounds. Surface background modeling is data-driven, exploiting $^{210}$Po alpha events for probability density function construction, resulting in robust estimates such as $0.09\pm0.06$ (Run0) and $0.17\pm0.11$ (Run1) surface events in typical search exposures (Qian et al., 11 Feb 2025).

4. Backgrounds, Thresholds, and Sensitivity

S2-only analyses lack the powerful electron/nuclear recoil discrimination from S2/S1 ratios, making background rejection more challenging. Major backgrounds include:

• ER background: intrinsic radioactivity ($^{85}$Kr, $^{222}$Rn, $^{136}$Xe), external gammas, solar neutrino electron recoils.
• NR background: neutrons (spontaneous fission, $(\alpha,n)$), solar $^8$B CE$\nu$NS.
• Surface/cathode backgrounds: largely from $^{210}$Pb daughters and microdischarges, characterized via spatial and waveform features (Collaboration, 2022, Luo et al., 7 Mar 2024, Qian et al., 11 Feb 2025).

The S2-only search typically imposes thresholds in S2 of $\sim$60–200 PE (US2 channel), corresponding, under calibration models (NEST/constant-$W$), to $0.07$–$0.23$ keV for ER and $0.77$–$2.54$ keV for NR (Collaboration, 2022). Above-threshold efficiencies are carefully calibrated with double-scatter events and waveform simulations, and systematic uncertainties incorporate discrepancies between calibration and data models—reaching $\sim$31% at low energies (Collaboration, 2022).

Statistical interpretations adopt binned likelihood or profile likelihood ratio (PLR) methods with explicitly treated nuisance parameters for background rates, signal efficiency, and signal model uncertainties (Collaboration, 2022, Collaboration et al., 15 Jul 2024). For example, the likelihood function is constructed as

$$\mathcal{L} = G(\delta_\epsilon)G(\delta_s)G(\delta_\text{cat})G(\delta_\text{MD}) \prod_i \frac{\lambda_i^{N_i}e^{-\lambda_i}}{N_i!}$$

with background and efficiency constraints, where $\lambda_i$ incorporates signal and background components in each S2 bin.

5. Results: Constraints from S2-Only Searches

PandaX-4T’s S2-only and “US2” analyses have yielded significant results across a range of channels:

• Light dark matter–electron: Exclusion limits on DM–electron scattering cross-section set world-best constraints in the $40$ MeV–10 GeV mass range, reaching $2.1\times10^{-41}$ cm$^2$ at $200$ MeV/c$^2$ for the point-like interaction scenario (Collaboration, 2022, Zhang et al., 16 Jul 2025).
• Light dark matter–nucleus: Spin-independent DM–nucleon limits reach $1.3\times10^{-43}$ cm$^2$ near 3.5 GeV/c$^2$, with strengthened constraints in the 2.5–5.0 GeV/c$^2$ (SI), 1.0–5.6 GeV/c$^2$ (SD-neutron), and 1.0–4.1 GeV/c$^2$ (SD-proton) mass ranges (Zhang et al., 16 Jul 2025).
• Dark photon/dark mediator scenarios: S2-only data leveraging the Migdal effect provide leading constraints in $30$ MeV–$2$ GeV mass intervals, excluding significant parameter space for thermal relic DM models mediated by dark photons (Huang et al., 2023).
• Solar boosted DM: PandaX-4T S2-only limit of $3.51 \times 10^{-39}$ cm$^2$ at $0.08\,\mathrm{MeV}/c^2$ marks a 23-fold improvement over previous experiments (Shen et al., 28 Dec 2024).
• Axions and exotic ER signals: S2-only approaches set competitive limits on axion-electron, axion-photon, and axion-nucleon couplings (e.g., $g_{ae} < 2.9\times10^{-12}$ for $m_a < 1$ keV/$c^2$), as well as neutrino magnetic moments ($\mu_\nu < 2.3\times10^{-11} \mu_B$) (Collaboration et al., 14 Aug 2024).
• CE$\nu$NS and $^8$B solar neutrinos: First indication of solar $^8$B CE$\nu$NS “fog” in a DM detector using US2 (S2-only) data, with a measured flux consistent with solar model predictions (Collaboration et al., 15 Jul 2024).

The S2-only approach enables energy thresholds as low as $0.04$ keV, positioning PandaX-4T to probe DM and solar neutrino parameter space previously inaccessible to TPCs with higher S1 thresholds.

6. Impact of S2-Only Search on Future Experimentation

The S2-only technique fundamentally enhances detector reach across several axes:

• Low-mass reach: Sensitivity to sub-GeV/c$^2$ dark matter is governed by threshold, for which S2-only methods are essential (Collaboration, 2022, Zhang et al., 16 Jul 2025).
• Multi-purpose observatory: The S2-only mode enables measurements of CE$\nu$NS, axion searches, and exotic ER signatures in a single apparatus (Collaboration et al., 14 Aug 2024, Collaboration et al., 15 Jul 2024).
• Detector upgrades and future observatories: The next-generation PandaX-xT will scale to 43 tonnes, and adopt enhanced photosensor arrays (Hamamatsu R12699), increased drift fields, higher electron extraction, and advanced digitizer bandwidth. S2-only analyses are central to operating near or at the “neutrino floor” and will be decisive in further testing the WIMP paradigm (Collaboration et al., 6 Feb 2024).
• Background modeling and position reconstruction: Developments in S2-based horizontal position reconstruction (PAF, TM) and sophisticated surface background modeling yield exceptional performance in background rejection and fiducial volume definition (Qian et al., 11 Feb 2025).

A plausible implication is that as exposures and target masses increase, the S2-only methodology will phase into an essential role for both dark matter discovery and precision measurements of rare neutrino processes, with the ultimate sensitivity limit set by the irreducible solar neutrino background.

7. Challenges and Ongoing Developments

Key technical challenges in S2-only analyses include:

• Background discrimination: Loss of S1 precludes S2/S1 ratio cuts; thus, discrimination of ER, NR, and surface backgrounds must rely on spatial, temporal, and pulse-shape analysis.
• Detector systematics: Non-uniform drift fields, localized PMT failures, and electron lifetime fluctuations require continuous recalibration (e.g., rolling gain, geometric corrections) and advanced data-driven modeling (Luo et al., 7 Mar 2024, Qian et al., 11 Feb 2025).
• Statistical uncertainties: Low-energy thresholds increase relative systematic uncertainties in efficiency, background modeling, and signal response calibration (31% at low-S2), impacting exclusion sensitivity (Collaboration, 2022).
• Event reconstruction: Accurate $x$–$y$ (PAF, $\sim$1mm), $z$ (drift time for S1–S2, otherwise inferred from S2 width), and pileup/event merging remain focus areas.

Continued hardware and software innovations—including calibration campaigns, DAQ upgrades, and improved signal model parameterizations—are anticipated for future iterations and upgrades (e.g., PandaX-xT) (Collaboration et al., 6 Feb 2024, Luo et al., 7 Mar 2024). The eventual convergence of S2-only search capability with large target mass, high extraction efficiency, and sub-keV thresholds defines the leading frontier for direct detection experiments searching for low-mass dark matter and associated low-energy phenomena.