Event Reconstruction and Analysis

From the raw detector data, the SND and the HSDS pursue different reconstruction and analysis strategies. Both detectors address different physics questions. Therefore, the SND focuses on the reconstruction of neutrino interactions and the neutrino flux, while the HSDS focuses on the reconstruction of long-lived particle decays.

Event Reconstruction in the SND

The SND aims to reconstruct the charged particles, originating from neutrino interactions. The incoming signals are originating from an event of the following type:

\[ \nu + N \to l + X \]

where \(l\) is the charged lepton and \(X\) is the hadronic system. This process leaves traces in the Emulsion Target, hits in the Silicon Tracking layers, light in the Scintillator tiles and fibers of the Magnetic Tracking Calorimeter as well as energy deposits in the calorimeter. Furthermore, \(X\) might decay into a large number of secondary particles, which leave the same traces in the SND.

1: Hit Reconstruction:: At first, the hit positions in the ECC, the Silicon Target and the Magnetic Tracking Calorimeter are reconstructed.
2: Track-Finding:: From the reconstructed hits, different methods are used to combine them into tracks. The tracks yield information about the position, the momentum, the direction and the charge of the reconstructed particles.
3: Vertex Reconstruction:: Vertices are found by combining the tracks and extrapolating them to the interaction point. The vertex reconstruction allows for the identification of the primary neutrino interaction vertex and secondary decay vertices. It yields informations about the position of the vertex, the number of tracks originating from it and the topology of the interaction.
4: Particle Identification:: Combining the information from the track reconstruction, the calorimeter and the muon system, the particle types are identified. Muons leave only a small energy deposit in the calorimeter and are detected by the muon system. Electrons produce electromagnetic showers, while hadrons produce hadronic showers in the calorimeter.
5: Analysis:: From the event data, different physical properties are determined: The Neutrino Flavour and Energy, the interaction cross section and the \(\nu_tau\) production rate.

Event Reconstruction in the HSDS

Similar to the SND, the HSDS reconstructs the charged particles originating from long-lived particle decays. Within the targets, processes of the form

\[ p + A \to \text{HNL} + X \]

are expected, where \(A\) denotes the target nucleus. The "Heavy Neutral Leptons" (HNL) decay into charged particles in processes like:

\[ \begin{aligned} \text{HNL} &\to \mu^\pm + \pi^\mp \\ \text{HNL} &\to e^\pm + \pi^\mp \\ \text{HNL} &\to \mu^+ + \mu^- + \nu \\ \text{HNL} &\to e^+ + e^- + \nu \\ \end{aligned} \]

Vertices, resolved by the decay product tracks, should be reconstructed within the Decay Volume in events where no signal was detected by the Upstream Background Tagger and the Surround Background Tagger. The HNL decay products can produce secondary particles, leaving traces in the Tracker, the Calorimeter and the Muon System. The reconstruction of the decay products allows for the determination of the HNL mass, lifetime and production rate. Since SHiP is searching for unknown particles, the reconstruction and analysis requires the consideration of many different decay channels and topologies. The following steps summarize the reconstruction and analysis of the HSDS:

1: Hit Reconstruction:: At first, the hit positions in the four Tracker stations, the Calorimeter and the Muon System are found. Additionally, the timing information from the High-Precision Timing Detector is used to determine the arrival time of track hits with a lower spatial resolution than the Tracker.
2: Track Reconstruction:: From the reconstructed hits, different methods are used to combine them into tracks and extrapolate then back to the interaction point. The tracks yield information about the position, the momentum, the direction and the charge of the reconstructed particles. Good candidates have multiple tracks originating fro the same vertex and a large distance to the target. To separate vertices from different events, the timing information from the High-Precision Timing Detector is combined with the track information.
3: Vertex Reconstruction:: The reconstructed tracks are extrapolated to find common origins. Signal candidates are expected to contain multiple tracks originating from a common secondary vertex inside the decay volume. This process yields informations about the position of the vertex, the number of tracks originating from it and the topology of the interaction.
4: Vertex Selection & Particle Identification:: Only vertices within the Decay Volume with \(z_\text{min} \lt z_\text{vertex} \lt z_\text{max}\), are accepted for further analysis. The particle types are identified by combining the information from the track reconstruction, the calorimeter and the muon system. From the reconstruction, the invariant mass of the reconstructed final-state particles

\[ \begin{equation} m^2 = \left(\sum_i E_i\right)^2 - \left(\sum_i \vec{p}_i\right)^2 \end{equation} \]

is calculated and compared to the expected HNL mass. Furthermore, good candidates are expected to have impact parameters \(\lt 10\,\text{cm}\) (minimal distance between a reconstructed track and the primary interaction vertex) with respect to the proton beam. Since the HNL is expected to be long-lived, the decay products are expected to have a large distance to the target, thus resulting in a large impact parameter.
5: Background Rejection:: The most important part is the separation from background and signal. Typical sources of background are neutrino interactions, muon induced interactions and cosmic muons and interactions with the detector material. Therefore, different variables like the vertex position, the number of tracks, the invariant mass, the timing information, the topology of the event and the muon identification are combined to filter out background events. The goal is to achieve a "Zero Background" environment, where no background events are expected to mimic the accepted signal events.