# SBND Comprehensive Notes

[TOC]

---

* For physics behind SBND: https://hackmd.io/@castalyfan1012/S1hNe3s5R
* For generating samples: https://hackmd.io/xjAl8h0vQiCk2QOJFqPZgQ
* For ML analysis: https://hackmd.io/@castalyfan1012/SkNBTv8p6

# Neutrino Experiments

## Worldwide projects
| **Project** | **Full Name** | **Purpose/Goal** | **Location** | **Key Features** | **Timeline** |
|----------------|-------------------------------------------------------|----------------------------------------------------------------------------------------------------|----------------------------------|---------------------------------------------------------------------------------------------------------------------------------------------------------------------|---------------------------------|
| **SBND** | Short-Baseline Near Detector | Study neutrino oscillations and sterile neutrinos. | Fermilab, USA | Part of the Short-Baseline Neutrino program, uses LArTPC technology. | Built: 2018, Data: 2020-present |
| **MicroBooNE** | Micro Booster Neutrino Experiment | Investigate the low-energy excess of neutrinos observed by the MiniBooNE experiment. | Fermilab, USA | Uses LArTPC technology, focused on neutrino interactions and sterile neutrino searches. | Built: 2015, Data: 2015-present |
| **ICARUS** | Imaging Cosmic And Rare Underground Signals | Search for sterile neutrinos and study neutrino oscillations. | Fermilab, USA (previously CERN) | Large-scale LArTPC, originally operated in Gran Sasso, Italy, now part of the SBN program at Fermilab. | Built: 1985, Moved: 2017 |
| **MINERvA** | Main Injector Neutrino Experiment for v-A | Study neutrino interactions with different nuclei. | Fermilab, USA | Uses a fine-grained detector, provides data on neutrino-nucleus interactions important for other neutrino experiments. | Built: 2010, Data: 2010-present |
| **NoVA** | NuMI Off-Axis νe Appearance | Study neutrino oscillations, specifically the appearance of electron neutrinos from a muon neutrino beam. | Fermilab, USA to Ash River, Minnesota, USA | Long-baseline experiment, uses a highly segmented liquid scintillator detector. | Built: 2010, Data: 2014-present |
| **MINOS** | Main Injector Neutrino Oscillation Search | Study neutrino oscillations using muon neutrino disappearance. | Fermilab, USA to Soudan Mine, Minnesota, USA | Long-baseline experiment, uses magnetized iron detectors. | Built: 2003, Data: 2005-2016 |
| **DUNE** | Deep Underground Neutrino Experiment | Study neutrino oscillations, supernova neutrinos, and proton decay. | Sanford Lab, South Dakota, USA | Long-baseline experiment, uses large-scale LArTPC detectors, international collaboration. | Built: 2015, Data: 2026 (exp.) |
| **Hyper-K** | Hyper-Kamiokande | Study neutrino oscillations, proton decay, and supernova neutrinos. | Kamioka, Japan | Water Cherenkov detector, successor to Super-Kamiokande, larger volume for increased sensitivity. | Built: 2020, Data: 2027 (exp.) |
| **JUNO** | Jiangmen Underground Neutrino Observatory | Determine the neutrino mass hierarchy and study oscillations. | Jiangmen, China | Large liquid scintillator detector, high energy resolution. | Built: 2015, Data: 2023 (exp.) |
| **IceCube** | IceCube Neutrino Observatory | Detect high-energy neutrinos from astrophysical sources. | South Pole, Antarctica | Uses a cubic kilometer of ice instrumented with photodetectors, detects Cherenkov radiation from neutrino interactions. | Built: 2010, Data: 2010-present |

## Types of neutrino experiments

| Feature | Solar Neutrino | Atmospheric Neutrino | Reactor-Based Neutrino | Accelerator-Based Neutrino |
|----------------------------|----------------------|----------------------|------------------------|---------------------------|
| **Source of Neutrinos** | Nuclear fusion in the Sun (\( pp \), CNO cycle) | Cosmic rays hitting Earth's atmosphere | Nuclear reactors (beta decay of fission products) | Neutrino beams from accelerators (pion decay) |
| **Energy Range** | ~0.1–10 MeV | ~100 MeV – 100 GeV | ~1–10 MeV | ~100 MeV – TeV |
| **Main Goals** | Study solar fusion, neutrino oscillations, solar neutrino problem | Neutrino oscillations, mass hierarchy, matter effects | Measure $\theta_{13}$, sterile neutrino searches, reactor anomaly | Neutrino oscillations, CP violation, mass hierarchy |
| **Key Experiments** | Homestake, SNO, Super-Kamiokande, Borexino | Super-Kamiokande, IceCube, Hyper-K, DeepCore | KamLAND, Daya Bay, Double Chooz, JUNO | MINOS, NOvA, T2K, DUNE, MicroBooNE |

Note that among several types of neutrino experiments, the SBN program belongs to the **accelerator-based experiment** because we employ the beam source which produces pions / kaons to be detected. The primary source is the pion decay, which produces muons, and muons will decay into electrons, muon neutrinos, and electron neutrinos.

## More on accelerator-based neutrino experiment:
| Feature | Short-Baseline (SBL) | Long-Baseline (LBL) |
|--------------------------|---------------------------------|--------------------------------|
| **L/E Ratio** | Small (minimal oscillations) | Tuned to maximize oscillations |
| **Main Goals** | Cross-section measurements, searches for sterile neutrinos, non-standard interactions | Study neutrino oscillations, measure mixing angles and mass splittings |
| **Oscillation Effects** | Negligible under standard 3-neutrino framework | Strong oscillation probability |
| **Detector Configuration** | Typically multiple detectors to reduce systematic uncertainties | Typically multiple detectors for precise appearance/disappearance measurements |
| **Example Experiments** | MicroBooNE, SBND, ICARUS | T2K, NOvA, DUNE |

## Neutrino beam sources at Fermilab

| **Aspect** | **BNB** | **NuMI** |
|------------------------|--------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------|
| **Full Name** | Booster Neutrino Beam | Neutrinos at the Main Injector |
| **Purpose** | Provide a source of neutrinos for short-baseline neutrino experiments, such as MicroBooNE, SBND. | Provide high-intensity neutrino beams for long-baseline neutrino experiments like MINOS, NOvA, and DUNE.|
| **Location** | Fermilab, USA | Fermilab, USA |
| **Established Year** | 2002 | 2005 |
| **Key Features** | Produces a lower energy neutrino beam using Fermilab's Booster accelerator. | Produces a high-intensity, high-energy neutrino beam using Fermilab's Main Injector accelerator. |
| **Primary Experiments**| MicroBooNE, SBND, ICARUS | MINOS, NOvA, DUNE |

## Detector Technologies
### Comparison by medium

| Feature | Super-Kamiokande (Pure Water) | SNO (Heavy Water) | DUNE / SBN (Liquid Argon) |
|----------------------|----------------------------|--------------------------|------------------------------|
| **Detection Medium** | Ultra-pure water ($H_2O$) | Heavy water ($D_2O$) | Liquid argon ($^{40}Ar$) |
| **Primary Detection** | Cherenkov radiation | Cherenkov radiation | Ionization charge + Scintillation |
| **Sensitivity to Neutrino Flavors** | Mostly $\nu_e$ (ES favors $\nu_e$) | Detects all flavors (NC), distinguishes $\nu_e$ (CC) | Detects all flavors, precise electron-neutrino tracking |
| **Event Reconstruction** | Cherenkov light rings | Cherenkov light rings + neutron detection | High-resolution 3D tracking |
| **Photodetectors** | PMTs (~13,000 large-diameter) | PMTs (~9,000) | Wire planes + PMTs/SiPMs for scintillation |
| **Best For** | Neutrino oscillations, supernova neutrinos, proton decay searches | Measuring total solar neutrino flux, confirming neutrino oscillations | Precision neutrino physics, CP violation, detailed event reconstruction |
| **Advantages** | Cost-effective, large volume, long-term stability | Distinguishes all neutrino flavors, unique NC measurement | Excellent spatial resolution, electron/photon separation |
| **Main Experiments** | Super-Kamiokande, Hyper-Kamiokande | SNO, SNO+ | ICARUS, MicroBooNE, DUNE |

### Comparison by detector types
| Feature | Cherenkov Detector | Time Projection Chamber (TPC) |
|-------------------------|--------------------------------|------------------------------------|
| **Detection Principle** | Detects **Cherenkov light** from fast charged particles | Detects **ionization tracks** from charged particles |
| **Medium** | Water, heavy water, ice, aerogel | Liquid Argon (LArTPC), gas |
| **Signal Type** | Light (Cherenkov radiation) | Ionization electrons + electric drift |
| **Best For** | Fast detection, neutrino oscillations, supernova neutrinos | Precise tracking, neutrino interactions, CP violation studies |
| **Event Reconstruction** | Ring-shaped Cherenkov patterns | Full 3D particle tracking |
| **Electron vs. Photon Separation** | Limited (based on ring shape) | Excellent (ionization pattern analysis) |
| **Energy Sensitivity** | Less effective for low-energy events | Good for both high- and low-energy events |
| **Speed of Signal Collection** | Fast (light-speed signal) | Slower (drift time needed for ionization electrons) |
| **Examples** | Super-Kamiokande, SNO, IceCube | ICARUS, DUNE, ALICE TPC, MicroBooNE |

---

# SBN Program
## Motivation
In 1990s, the short-baseline neutrino experiment **Liquid Scintillator Neutrino Detector (LSND)** observed an unexpected surplus of electron-like events observed at low energies (**LSND anomaly**). One possible explanation was a new oscillation channel involving **sterile neutrinos**, a type of neutrinos that even not involved in weak interaction.

To confirm or dispute the anomaly, the **Mini Booster Neutrino Experiment (MiniBooNE)** has taken data from 2002 to 2019, while it found an even bigger discrepancy (~$4.8 \sigma$) i.e. the **Low Energy Excess (LEE) anomaly** or the **short-baseline anomaly**. The anomaly suggested too many electron-like events at low energy, which didn’t match standard neutrino oscillation models. However, MiniBooNE’s weird signal was even bigger than what the sterile neutrino model predicted. Nonetheless, both LSND and MiniBooNE's combined statistical significance was $6 \sigma$, which is still very strong evidence that something unusual is happening, and this motivates the proposal of the SBN program. (Anything above 5σ is usually considered a discovery in physics.)

The LEE anomaly:

# Detectors

## TPC (time projection chamber)

### Purpose:
Reconstruct 3D particle trajectories or interactions using E-field, B-field, and a volume of gas or liquid

### LArTPC (Liquid Argon Time Projection Chamber):
#### Why argon (Ar)?
1. Electronegativity = 0 → electrons produced by ionizing radiation will not be absorbed as they drift toward the detector readout.
2. Scintillation → When a charged particle passes by, Ar releases photons that is proportional to the energy deposited in the Ar by the passing particle.
3. High density → Increase likelihood of particle interaction therein.

#### Function:
1. Cathode: Establishes a 500 V/cm drift field across opposite the anode.
2. Anode: Comprises multiple wire planes, including induction planes and a collection plane, for signal readout and 2D event reconstruction.
3. Field Cage: Maintains a uniform electric field to minimize drift electron trajectory distortion during event reconstruction.

#### Signal (light) collection:
- **Photomultipliers (PDS)**

#### Signal readout:
- RC circuit → amplify & digitize signals from event construction
- 3 wire planes → signals created:
1. 1D standard deconvolution on wire signals
2. 2D deconvolution using wirecell
3. CNNs

#### Goals:
1. Get the number of electrons reaching a specific wireplane crossing
2. Use the interaction time from the PDS to resolve the drift coordinate

https://lar.bnl.gov/wire-cell/

## PDS (Photon Detection System)
* Components:
- **Photomultiplier tubes (PMTs)**:
- Purpose: convert photons to electric signals.
- Measurement: signal waveforms on the anode
1. Calibration source → determine single photoelectrons (SPE) strength in ADC
2. Waveforms are calibrated by setting the gains of all the PMTs to match using this SPE calibration (typical gain: $5\times10^6$)
3. Each of the 120 PMTs are calibrated to have the same gain.


- Silicone based photomultipliers (**X-ARAPUCAs**): Similar to PMTs but use optical electronics with a light trapping surface instead of dynodes (lower voltage than PMTs) → lower detection efficiency

* Passive component: Tetra-Phenyl-Butadiene (TPB) coating
- Role: wavelength shifter (128 nm vacuum UV from de-exciting argon → 430 nm blue light)
- Convert VUV photons released from argon scintillation light to the wavelength where the active PDS components peak in detection efficiency.
- 96/120 PMTs & 92/196 X-ARAPUCAs are coated.

* Purpose: Reject cosmic rays as neutrino events & determine interaction time
- PDS has to be very fast to resolve short time scale events
- The whole PDS is attached to digitizer modules that are able to resolve waveforms with 2 ns resolution.

* Cosmic ray taggers (CRTs):
- Purposes: reject cosmic rays & beyond SM searches
- Components: panels filled with liquid scintillator strips that surround SBND’s cryostat.
- Principles: Similar to PDS but the incoming particle is a cosmic particle → waveform’s ADC corresponds to its energy (timing can be synced with PDS)

### Calibration system

* 5 diffuser sets installed on each side of the CPA (cathode plane assembly).
* Optical fibers connect diffusers to a laser system - 213 nm (VUV) & 532 nm (visible).
* Diffusers:
* UV fused silica offers high transmission deep into the ultraviolet and good homogeneity
* It exhibits virtually no laser-induced fluorescence

---

# ML Reconstruction

## ML reco chain for LArTPC


* Key components:
1. **Input**: The reconstruction chain takes 3D particle interaction images as input.
2. **Semantic Segmentation and Point Proposal**: The first module in the reconstruction chain is designed to identify the abstract particle type of each voxel and the location of important points. This module uses a backbone architecture called "Sparse U-ResNet" for voxel-level feature extraction and point identification.
3. **UResNet**: The Sparse U-ResNet is a U-Net architecture composed of a down-sampling encoder and an up-sampling decoder for feature extraction at various scales.
4. **PPN** (Point Proposal Network): This network is used for reconstructing 3D particle positions with sub-pixel precision in LArTPCs.
5. **GNN** (Graph Neural Network): Graph networks are used to assemble shower objects, identify primary fragments, aggregate particles into interactions, and identify their species.
6. **Primaries**: The network identifies primary fragments before aggregating particles into interactions.
7. **Particles GNN**: Graph networks are used to identify individual particle types and trajectories.
8. **Interactions/Identification**: The network aggregates particles into interactions and identifies their species.

* Recap:
1. #### Space points:
- Tomographic construction: By cluster 3D
- Ghosts: artifact spacepoints by false three-fold wire coincidence
2. #### Semantic segmentation:
- Semantic labeling by sparse UResNet
- Five classes: **shower, track, delta, Michel, low energy**
- Michel electrons = electron produced in the decay of a muon
3. #### PPN (Point Proposal Network):
- CNN with encoder-decoder architecture
- Labels start/end points of tracks, deltas, and shower start points
4. #### Clustering:
- Coordinates → embedded space (where tracks spatially isolated)
- Cluster IDs: learned by graphSPICE
5. #### Aggregator:
- Particle level:
- Graph particle aggregator (GrapPA) → Identify shower primaries & cluster individual particles
- Aggregating clusters into particles for showers
- 92% shower primary ID accuracy
- Interaction level:
- Determine interaction primaries, interaction clusters and PID
- 91% primary identification accuracy; overall primary accuracy = 86.3%

---

# Data analysis techniques
## $\chi^2$ Analysis

### Definition

- **Purpose**: Compare observed data with expected data to evaluate model fit.
- **Formula**:
$$
\chi^2 = \sum_{i=1}^{N} \frac{(O_i - E_i)^2}{E_i}
$$
- $O_i$: Observed data
- $E_i$: Expected data
- $N$: Number of observations
### **Interpretation of Values**
#### **$\chi^2$ Fit Evaluation**
- **Lower $\chi^2$** → **Better fit** (observed data matches expected well)
- **Higher $\chi^2$** → **Worse fit** (large deviations from expected)
- **Critical threshold:** Depends on degrees of freedom (df) and significance level ($\alpha$), often compared to a Chi-square distribution table.

#### **$R^2$ Fit Evaluation**
- **$R^2 = 1$** → **Perfect fit** (all points lie on the regression line)
- **$R^2 > 0.8$** → **Strong fit**
- **$R^2 \approx 0.5$** → **Moderate fit**
- **$R^2 < 0.2$** → **Poor fit**
- **$R^2 = 0$** → **No explanatory power**

### Comparison of $\chi^2$ and $R^2$ analysis
| Feature | $\chi^2$ (Chi-Square) | $R^2$ (Coefficient of Determination) |
|--------------|----------------------|--------------------------------|
| **Definition** | Measures how well observed data match expected values. Used for hypothesis testing. | Measures how well a regression model explains the variance in the dependent variable. |
| **Formula** | $\chi^2 = \sum \frac{(O_i - E_i)^2}{E_i}$, where $O_i$ = observed values, $E_i$ = expected values. | $R^2 = 1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2}$, where $y_i$ = actual values, $\hat{y}_i$ = predicted values, $\bar{y}$ = mean of $y_i$. |
| **Purpose** | Measures the goodness of fit for categorical/discrete data. | Measures how well regression explains variance in continuous data. |
| **Common Applications** | Hypothesis testing, physics experiments, contingency tables. | Linear regression, predictive modeling. |
| **Example** | Comparing die roll frequencies to expected values | Predicting test scores based on study hours |
| **Image** |  | 

## Principal Component Analysis (PCA)

Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify datasets with many correlated variables into a smaller set of uncorrelated variables, called principal components (PCs), while retaining most of the original information.

### Objective
PCA aims to find new directions (principal components) where the variance of the data is maximized.

### Steps
1. **Mean Centering**: Subtract the mean from each feature.
- $X_{\text{centered}} = X - \text{mean}(X)$

2. **Covariance Matrix ($\Sigma$)**: Compute the covariance matrix of the centered data.
- $\Sigma = \frac{1}{n} X_{\text{centered}}^T X_{\text{centered}}$

3. **Eigenvalues and Eigenvectors**: Calculate the eigenvectors $v$ and eigenvalues ($\lambda$) of the covariance matrix.
- $\Sigma v = \lambda v$

4. **Select Principal Components**: Choose the top ($k$) eigenvectors with the highest eigenvalues.

5. **Transform Data**: Project the original data onto the selected principal components.
- $X_{\text{new}} = X_{\text{centered}} \cdot \text{eigenvectors}$

### Example
Suppose we have a 2D dataset $X$ with two features (columns) $x_1$ and $x_2$:

$$
X = \begin{bmatrix}
1 & 2 \\
2 & 3 \\
3 & 4 \\
4 & 5 \\
\end{bmatrix}
$$

1. **Mean Centering**: Subtract the mean of each column.
$$X_{\text{centered}} =
\begin{bmatrix}
-1.5 & -1.5 \\
-0.5 & -0.5 \\
0.5 & 0.5 \\
1.5 & 1.5 \\
\end{bmatrix}$$

2. **Covariance Matrix $\Sigma$**:
$$\Sigma = \frac{1}{4} X_{\text{centered}}^T X_{\text{centered}} =
\begin{bmatrix}
1.6667 & 1.6667 \\
1.6667 & 1.6667 \\
\end{bmatrix}
$$

3. **Eigenvalues and Eigenvectors**:
- Solve $\Sigma v = \lambda v$ to get eigenvectors $v$ and eigenvalues $\lambda$:
- Eigenvectors: $v_1 = [0.7071, 0.7071]$, $v_2 = [-0.7071, 0.7071]$
- Eigenvalues: $\lambda_1 = 3.3333$, $\lambda_2 = 0$

4. **Select Principal Components**: Choose $v_1$ (highest $\lambda$).

5. **Transform Data**:
- $X_{\text{new}} = X_{\text{centered}} \cdot \text{eigenvector}$
- $X_{\text{new}} = \begin{bmatrix}
-2.1213 \\
-0.7071 \\
0.7071 \\
2.1213 \\
\end{bmatrix}$

This result represents the original data $X$ projected onto the first principal component $v_1$. The data is now in a new coordinate system where the variance is maximized along $v_1$, reducing the dimensionality from 2D to 1D.

# Other Links

* Getting started with particle gun simulator: https://sbnsoftware.github.io/SBNYoung/particle_gun_tut.html
* Techical note: https://hackmd.io/@castalyfan1012/rJytx3tOp