Transverse Position Reconstruction in a Liquid Argon Time Projection Chamber using Principal Component Analysis and Multi-Dimensional Fitting

Abstract

One of the most enduring questions in modern physics is the dark matter problem. Measurements of galactic rotation curves taken in the middle of the twentieth century suggest that there are large spherical halos of unseen matter permeating and surrounding most galaxies, stretching far beyond their visible extents. Although some of this mass discrepancy can be attributed to sources like primordial black holes or Massive Astrophysical Compact Halo Objects (MACHOs), these theories can only explain a small percentage of this "missing matter". One approach which could account for the entirety of this missing mass is the theory of Weakly Interacting Massive Particles, or "WIMPs". As their name suggests, WIMPs interact only through the weak nuclear force and gravity and are quite massive (100 GeV/c2 to 1 TeV/c2). These particles have very small cross sections (≈ 10−39 cm2) with nucleons and therefore interact only very rarely with "normal" baryonic matter. To directly detect a dark matter particle, one needs to overcome this small cross-section barrier. In many experiments, this is achieved by utilizing detectors filled with liquid noble elements, which have excellent particle identification capabilities and are very low-background, allowing potential WIMP signals to be more easily distinguished from detector noise. These experiments also often apply uniform electric fields across their liquid volumes, turning the apparatus into Time Projection Chambers or "TPCs". TPCs can accurately determine the location of an interaction in the liquid volume (often simply called an "event") along the direction of the electric field. In DarkSide-50 ("DS-50" for short), the electric field is aligned antiparallel to the z-axis of the detector, and so the depth of an event can be determined to a considerable degree of accuracy by measuring the time between the first and second scintillation signals ("S1" and "S2"), which are generated at the interaction point itself and in a small gas pocket above the liquid region, respectively. One of the lingering challenges in this experiment, however, is the determination of an event’s position along the other two spatial dimensions, that is, its transverse or "xy" position. Some liquid noble element TPCs have achieved remarkably accurate event position reconstructions, typically using the relative amounts of S2 light collected by Photo-Multiplier Tubes ("PMTs") as the input data to their reconstruction algorithms. This approach has been particularly challenging in DarkSide-50, partly due to unexpected asymmetries in the detector, and partly due to the design of the detector itself. A variety of xy-Reconstruction methods ("xy methods" for short) have come and gone in DS- 50, with only a few of them providing useful results. The xy method described in this dissertation is a two-step Principal Component Analysis / Multi-Dimensional Fit (PCAMDF) reconstruction. In a nutshell, this method develops a functional mapping from the 19-dimensional space of the signal received by the PMTs at the "top" (or the "anode" end) of the DarkSide-50 TPC to each of the transverse coordinates, x and y. PCAMDF is a low-level "machine learning" algorithm, and as such, needs to be "trained" with a sample of representative events; in this case, these are provided by the DarkSide geant4-based Monte Carlo, g4ds. In this work, a thorough description of the PCAMDF xy-Reconstruction method is provided along with an analysis of its performance on MC events and data. The method is applied to several classes of data events, including coincident decays, external gamma rays from calibration sources, and both atmospheric argon "AAr" and underground argon "UAr". Discrepancies between the MC and data are explored, and fiducial volume cuts are calculated. Finally, a novel method is proposed for finding the accuracy of the PCAMDF reconstruction on data by using the asymmetry of the S2 light collected on the anode and cathode PMT arrays as a function of xy.