> # SBND Comprehensive Notes

[TOC]

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# Neutrino Physics

## Outlines
- Profile:
- Mass: < 0.120 eV (< $2.14 × 10^{−37}$ kg, ~500,000 times smaller than electron)
- Speed: $\lesssim$ Speed of light
- Properties:
- Leptons
- Neutral
- Interact with weak, gravity only
- Oscillation: change flavor periodically with time
- Flavor problem: the origin of the fermion families and of the masses and mixing of quarks and leptons.
- Types (flavour):
- Muon, electron, tau
- Interactions:
- Couple with $Z^0$ boson
- Couple with $W^{+/-}$ boson
- $W^+$ → lepton(+) + neutrino
- $W^-$ → lepton(-) + anti-neutrino
- Productions:
- Electron neutrino (**beta decay**): $$n \rightarrow p + e^- + \bar{\nu}_e$$
- Muon neutrino:
$$\pi^+ \rightarrow \mu^+ + \bar{\nu}_{\mu}$$ $$\mu^+ \rightarrow e^+ + \nu_e + \bar{\nu}_{\mu}$$
- Tau neutrino:
$$\begin{split}
\tau^- &\rightarrow \nu_{\tau} + W^{-} \\
&\rightarrow \nu_{\tau} + e^{-} + \bar{\nu}_e \\
&\rightarrow \nu_{\tau} + \mu^- + \bar{\nu}_{\mu}
\end{split}$$

## Neutrino-Nucleus Scattering
- Types:
- Energy: Elastic vs. Inelastic
- Phase/fluctuation: Coherent vs. Incoherent
- Charged current (CC) cross sections:
- CC exclusive: Specific hadronic final states, i.e. CC $\nu_{\mu}$ with a single proton ($p$), with a single pion ($\pi^+$), etc.
- CC inclusive: Sum the contributions from all exclusive channels.

### Particles in Matter
- Bethe-Bloch formula (how much energy lost of a charged particle when traveling through matter):
$$-\frac{dE}{dx} = K z^2 \frac{Z}{A} \frac{1}{\beta^2} \left[\frac{1}{2} \ln\frac{2 m_e c^2 \beta^2 \gamma^2}{I^2} - \beta^2 - \frac{\delta(\beta \gamma)}{2} \right]
$$
- $\frac{dE}{dx}$: Energy loss per unit path length
- $K$: A constant
- $z$: Charge of the particle
- $Z$: Atomic number of the medium
- $A$: Atomic mass of the medium
- $\beta$: Velocity of the particle in units of the speed of light
- $\gamma$: Lorentz factor ($\gamma = 1/\sqrt{1 - \beta^2}$)
- $m_e$: Electron mass
- $c$: Speed of light
- $I$: Mean excitation energy of the medium
- $\delta(\beta \gamma)$: Density effect correction
- For small velocities ($\beta \ll 1$):
$$-\frac{dE}{dx} = K z^2 \frac{Z}{A} \frac{4 \pi}{m_e c^2} \frac{n Z}{v^2} \left[ \ln\frac{2 m_e v^2}{I} - \beta^2 \right]
$$

---

# 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. Electronegravity = 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

## 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)

---

# 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: leared 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%

## 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/edit