DeeDeeExperiment: Multi-Domain Research

• DeeDeeExperiment is a designation covering multiple unrelated experimental projects in omics, high-energy physics, and nuclear physics that benchmark advanced methodologies.
• The omics implementation employs an S4 class in Bioconductor to rigorously store and integrate multi-contrast differential expression and functional enrichment analyses.
• High-energy physics and nuclear experiments use precise signal extraction and innovative clusterization techniques to validate theoretical models and enhance experimental reproducibility.

DeeDeeExperiment refers to several unrelated experimental projects across different scientific domains—most notably, (1) the DeeDeeExperiment S4 class in omics data analysis infrastructures within Bioconductor, (2) the “DeeDeeExperiment” at Belle for $D^0$–$\bar D^0$ mixing in high-energy physics, and (3) a dedicated experiment studying deuteron–deuteron breakup in nuclear physics. Each context employs the “DeeDeeExperiment” moniker for a distinct technical endeavor and dataset; the following account synthesizes the core methodologies, motivations, and results for each.

1. DeeDeeExperiment in Omics Data Analysis (Bioconductor)

1.1 Design and Class Architecture

DeeDeeExperiment is an S4 class designed for managing, contextualizing, and integrating multi-contrast omics analysis results within the R/Bioconductor ecosystem. It formally extends the SingleCellExperiment container, inheriting storage for assays (matrices of gene expression), rowData (feature-level annotations), colData (sample/cell-level annotations), reducedDims (dimensionality-reduction embeddings), and metadata (arbitrary list for experiment-level information) (Abassi et al., 5 Dec 2025).

The object introduces two core additional slots:

• dea: a named SimpleList of “contrast” entries, each storing summarized differential expression results and metadata (e.g., method, package version, analysis threshold).
• fea: a parallel SimpleList for functional enrichment results, indexed by contrast, capturing FEA method, parameters, and compacted enrichment outputs (e.g., GeneTonic objects).

A minimal R class definition is:

setClass( "DeeDeeExperiment", contains = "SingleCellExperiment", slots = c( dea = "SimpleList", fea = "SimpleList" ), prototype = prototype( dea = SimpleList(), fea = SimpleList() ), validity = function(object) { if (!all(vapply(object@dea, is.list, logical(1)))) { return("Each element of @dea must be a list with required fields") } TRUE } )

1.2 Data Integration and Analysis Workflows

The class schema supports formal addition and retrieval of both DEA and FEA results. Key workflow functions include addDEAResults, addDEAResultsFromLimma, addDEAResultsFromMuscat, and addFEAResults, with provenance-tracking for the source objects in the metadata slot. DEA entries typically include log₂FC, p-value, padj, method, and user-defined thresholds; FEA stores term-level statistics and enrichment object metadata.

Typical statistical model formulas follow the DESeq2/limma conventions: $$Y_{gi} = \beta_{0g} + \beta_{1g}\,T_i + \varepsilon_{gi}, \quad \varepsilon_{gi} \sim N(0,\sigma_g^2)$$

The structure supports complex experimental designs involving multiple conditions/batches and multi-group contrasts, with results and annotation columns organized in rowData and colData.

1.3 Metadata, Documentation, and Reproducibility

Global experiment parameters reside in the metadata slot; features and samples are annotated in rowData and colData, respectively. Scenario-level documentation (e.g., user-defined normalization, batch correction, session info) attaches via addScenarioInfo, securing robust reproducibility in downstream pipelines.

Original DEA and FEA analysis objects (e.g., DESeq2, DGEList) are preserved by pointer in the metadata, ensuring one-copy provenance and facilitating computational reproducibility.

1.4 Bioconductor Interoperability and Visualization

Inheriting from SingleCellExperiment affords seamless interaction with packages such as scater, slingshot, scran, and visualization via iSEE. Complex integration—including joint multi-omics, batch correction, downstream graph-based analyses, and “contrast-centric” reporting—is straightforward due to alignment with Bioconductor’s established data infrastructure and continuous integration (Abassi et al., 5 Dec 2025).

2. $D^0$–$\bar D^0$ Mixing at Belle (“DeeDeeExperiment” in High-Energy Physics)

2.1 Experimental Techniques and Signal Extraction

The Belle “DeeDeeExperiment” refers to the definitive observation of $D^0$–$\bar D^0$ mixing at the KEKB $e^+e^-$ collider using 976 fb$^{-1}$ of data (Ko et al., 2014). The analysis reconstructs the decay

$D^{*+}\to D^0 \pi_s^+ \quad (D^0\to K^+\pi^-)$

with the flavor of $D^0$ at production tagged by the charge of the “slow pion” $\pi_s$. Right-sign (RS: $D^0\to K^-\pi^+$) and wrong-sign (WS: $D^0\to K^+\pi^-$) samples are separated by particle identification based on likelihood ratios, with $K$ identification at 91% efficiency and $\pi$ at 94% (misID rates 12–18%).

Track and vertex requirements are enforced: $|d_z|<4$ cm, $|d_r|<2$ cm, $p_T>0.1$ GeV/$c$, and at least two hits in both $z$ and $\phi$ SVD layers per track.

2.2 Time-Dependent Analysis and Mixing Formalism

The time-dependent ratio of WS to RS yields probes the phenomenology of charm mixing. The key formula used is

$$R_{\text{theory}}(t/\tau) = R_D + \sqrt{R_D}\,y'\,(t/\tau) + \frac{x'^2 + y'^2}{4} (t/\tau)^2$$

where $$R_D = \Gamma(D^0\to K^+\pi^-)/\Gamma(D^0\to K^-\pi^+)$$ and $x',y'$ are rotated mixing parameters encoding the mass and width differences between mass eigenstates and the strong-phase $\delta$.

Proper-time resolution is modeled via a 4-Gaussian sum resolution function determined from RS decays, and finite-time resolution is fully accounted for in the fit. The WS/RS yield ratio is extracted in ten $t/\tau$ bins via $\Delta M$ fitting.

2.3 Results and Physics Impact

Fitting for the mixing hypothesis yields:

• $R_D=(3.53\pm0.13)\times 10^{-3}$
• $y'=(4.6\pm3.4)\times 10^{-3}$
• $x'^2=(0.09\pm0.22)\times 10^{-3}$

The no-mixing scenario is excluded at $5.1\,\sigma$ confidence ($p=4.3\times 10^{-7}$). This measurement constitutes the first observation of $D^0$–$\bar D^0$ mixing in $e^+e^-$ collisions using clean vertexing and kinematics, providing an independent determination in agreement with hadron-collider experiments.

3. Deuteron–Deuteron Collision (“DeeDeeExperiment” in Nuclear Physics)

3.1 Experimental Objectives and Apparatus

This DeeDeeExperiment refers to the measurement of deuteron–deuteron collision-induced breakup at $E_\text{lab}=160$ MeV, extending few-body nuclear dynamics to the four-nucleon regime (Khatri et al., 2016). The experiment focuses on precise differential cross-sections for the $dd\rightarrow dpn$ breakup in the deuteron-proton quasi-free scattering limit, aiming to test the single scattering approximation (SSA) and provide benchmark data for four-body calculations and the study of three-nucleon force (3NF) effects.

The experiment used the BINA detector: a nearly 4$\pi$ system with a "wall" multi-wire proportional chamber covering $13^\circ<\theta_{\rm lab}<40^\circ$ for angle and energy, and a backward "ball" of 149 phoswich detectors covering $40^\circ<\theta_{\rm lab}<165^\circ$.

3.2 Data Analysis Methodology

The "clusterization" approach was developed to address light-leakage between ball elements: a cluster's polar and azimuthal angles are energy-weighted averages over constituents, with energies corrected by an empirically determined attenuation factor ($\alpha\simeq 0.10$).

The fivefold differential cross-section is given by

$$\frac{d^5\sigma}{d\Omega_d d\Omega_p dE_p} = \frac{1}{\Phi t} N(\theta_d,\phi_d,\theta_p,\phi_p,E_p)$$

The dp quasi-free limit is characterized by the neutron acting as a near-spectator ($E_n\to 0$), and analyzed as a function of the arc-length $S$ along the breakup kinematic locus.

3.3 Results and Comparison to Theory

A total of 147 configurations ($\sim4500$ data points) were measured in the QFS region. The measured differential cross sections are consistently reproduced within $\lesssim15\%$ by both leading-order SSA (“1-term”) and a 4-term SSA extension near the QFS point; deviations increase at higher $E_n$, indicating the onset of multiple-scattering and four-nucleon dynamics not captured by SSA. The dataset is a critical benchmark for future high-precision four-body force and cluster calculations.

4. Methodological Features and Technical Innovation

4.1 Omics Infrastructure

DeeDeeExperiment’s design as a formal S4 subclass of SingleCellExperiment represents a convergence of formal object-oriented data storage, contrast-centric metadata archiving, and provenance tracking, enabling reproducibility and interoperability within Bioconductor workflows (Abassi et al., 5 Dec 2025). Dedicated storage for DEA and FEA results with full scenario annotation fills a recognized gap in high-throughput analysis infrastructure.

4.2 High-Energy Physics and Nuclear Methodology

In the $D^0$–$\bar D^0$ mixing measurement, innovations include precise flavor tagging strategies, rigorous finite-time resolution modeling via multi-Gaussian summations, and robust separation of RS/WS channels—ameliorating backgrounds systematic to hadron machines. The dd breakup experiment implemented a novel energy-weighted clusterization algorithm in a complex multi-module geometry, facilitating accurate angular/energy reconstruction across an unprecedented region of phase space (Khatri et al., 2016).

5. Scientific Significance and Legacy

The DeeDeeExperiment designation thus attaches to highly-cited work in both data infrastructure and experimental physics:

• In computational genomics, DeeDeeExperiment provides a standardized platform that integrates the results of multifactorial high-throughput studies, supporting multicontrast, multi-condition analyses, and facilitating reproducibility and data sharing across laboratories (Abassi et al., 5 Dec 2025).
• The high-energy physics implementation at Belle achieved the first $5.1\,\sigma$ observation of $D^0$–$\bar D^0$ mixing in $e^+e^-$ collisions, supplying essential parameters ($R_D$, $x'$, $y'$) for constraining Standard Model and new-physics scenarios (Ko et al., 2014).
• Nuclear physics advances include stringent new experimental benchmarks for four-nucleon breakup, direct validation of single-scattering mechanisms, and the demonstration of cluster-based angular reconstruction in large-acceptance systems (Khatri et al., 2016).

Each instantiation of the DeeDeeExperiment concept both addresses a unique technical challenge and expands the accessible analytic reach in its respective field.