# SBND Software

## Introduction

The data from a particle physics experiment are essentially electronic signals. The data required to conduct a physics analysis are physical variables such as particle four-vectors. There is a great deal of work involved in getting from the raw data to the physics variables, including (but not limited to!) detector calibration, data quality monitoring, track reconstruction and particle identification. The Sheffield group is heavily involved in developing many of these tools.

## Reconstructing particle properties

Liquid argon detectors provide highly detailed pictures of neutrino interactions, as in this example from ArgoNeuT. However, in order for the experiments to realise the full potential of such detailed event records, it is necessary to ensure that they are accurately reconstructed. Events may contain **tracks** created by individual charged particles, for example the red one moving upwards from the first vertex in the picture, and **showers** produced when photons or electrons create multiple lower-energy electrons and positrons by pair production and bremsstrahlung, as seen in the secondary vertices. The aim of the reconstruction is to measure the momentum or energy, the direction, and if possible identify the type of particle. This is not a trivial task, because these detectors, unlike most particle physics experiments, do not have a magnetic field to provide a momentum measurement from the resulting curvature of the tracks.

The MicroBooNE collaboration has demonstrated that the momenta of muons can be reconstructed using the properties of multiple Coulomb scattering, i.e. the deviation in the muon trajectory caused by scattering off atomic nuclei. The theoretical expectation is that this deviation should have a Gaussian distribution with a mean of zero and a width given by the Highland formula

where S_{2} and ε are parameters (given by MicroBooNE as 11 MeV (with some momentum dependence) and 0.038 respectively), z is the charge of the particle (1 for a muon), ℓ is the distance travelled, and X_{0} is the radiation length of the medium (i.e. liquid argon). For any reasonable energy, the muon's speed will be close to c, i.e. β ≈ 1, so this formula can be used to determine momentum by dividing a track into segments, so that a single track produces a distribution of multiple scattering angles whose width can be measured. Comparing momenta reconstructed using this technique with those derived from the standard method of using the range of the muon (for muon tracks which are "fully contained", i.e. they start and stop within the detector) shows good agreement, but the multiple-scattering method has the advantage that the track need not be fully contained within the detector.

Particle identification in liquid argon detectors is done through measuring the rate of energy deposition, dE/dx. The expected〈dE/dx〉is described by the Bethe formula, though the use of this formula in practice is complicated by the fact that the distribution of dE/dx is far from Gaussian, so there can be large fluctuations in the calculated mean. Various techniques are employed to deal with this, such as using truncated means or most probable values: these require appropriate modifications to the Bethe formula, but this is a known and well-studied problem. Some typical plots and numerical values for liquid argon can be found on the Brookhaven LAr site.

This work all refers to track reconstruction. Shower reconstruction is a more challenging problem, as showers involve a large number of short tracks that are very close together in three dimensions. It would be both difficult and time-consuming to reconstruct showers by attempting to reconstruct each individual contributing track, so it is probably necessary to develop a different algorithm which considers the shower as a single entity. This problem has not yet been tackled for SBND.

## Calibration and data quality

LAr TPCs such as SBND require the ionisation electrons to drift for quite large distances before they are collected on the anode plane wires. Therefore, the electron lifetime—that is, the time for which a free electron will remain free before recombining—is an important property. As argon is a noble liquid, argon atoms are very disinclined to capture electrons, so the electron lifetime in a real detector is dominated by impurities in the argon. Hence, electron lifetime measurements are a proxy for argon purity.

Sheffield PhD students are currently developing methods for measuring the electron lifetime using cosmic muon tracks. As SBND is not a deep underground detector like Super-Kamiokande or DUNE, the cosmic muon rate is high, so large samples of clean cosmic muon events will be available during SBND running. As muons are minimum-ionising particles, the number of ionisation electrons they produce per unit track length is expected to be approximately constant, whereas the number of electrons collected at the anode plane is expected to fall exponentially with drift distance (or, equivalently, drift time), because of the finite electron lifetime. If this exponential decay of the collected charge can be measured, the electron lifetime can be deduced.

The plot compares the performance of three different lifetime estimators for simulated data. Method 1 uses slices from an individual track which crosses both the cathode and the anode planes, and therefore provides data for a range of drift distances; method 2 uses the same type of muon tracks, but instead of taking them track by track it takes them time slice by time slice, and for each time slice fits a Landau-Gaussian convolution to the whole data sample. Method 3 uses a sample of tracks that are directed approximately parallel to the wire planes, so that the whole of each track falls in a single time slice. It can be seen that all three methods would be equally effective if the electron lifetime in SBND were rather short (< 4 ms or so), but method 1, and to a lesser extent method 3, tends to underestimate longer lifetimes. Method 3 has the advantage that the muons are selected by using the segmentation of SBND's cosmic ray tagger, a system of strips of plastic scintillator surrounding the TPC, and so minimal reconstruction is required—this technique could be implemented as a real-time (or nearly real-time) argon purity monitor.