Position Reconstruction in LUX

TL;DR

This paper presents a new position reconstruction method for the LUX experiment that uses a statistical, iterative approach with calibration data to improve spatial resolution of detected events.

Contribution

The method introduces a statistical test with an iterative algorithm utilizing calibration data and a two-dimensional functional form for photon response, enhancing position accuracy in LUX.

Findings

Achieved 0.82 cm position uncertainty for small signals of 200 photons.

Achieved 0.17 cm position uncertainty for larger signals of 4,000 photons.

Reconstructed positions of single-electron events with 2.13 cm uncertainty.

Abstract

The $(x, y)$ position reconstruction method used in the analysis of the complete exposure of the Large Underground Xenon (LUX) experiment is presented. The algorithm is based on a statistical test that makes use of an iterative method to recover the photomultiplier tube (PMT) light response directly from the calibration data. The light response functions make use of a two dimensional functional form to account for the photons reflected on the inner walls of the detector. To increase the resolution for small pulses, a photon counting technique was employed to describe the response of the PMTs. The reconstruction was assessed with calibration data including ${}^{\mathrm{83m}}$Kr (releasing a total energy of 41.5 keV) and ${}^{3}$H ($\beta^-$ with Q = 18.6 keV) decays, and a deuterium-deuterium (D-D) neutron beam (2.45 MeV). In the horizontal plane, the reconstruction has achieved an $(x, y)$ position uncertainty of $\sigma$= 0.82 cm for events of only 200 electroluminescence photons and $\sigma$ = 0.17 cm for 4,000 electroluminescence photons. Such signals are associated with electron recoils of energies $\sim$0.25 keV and $\sim$10 keV, respectively. The reconstructed position of the smallest events with a single electron emitted from the liquid surface has a horizontal $(x, y)$ uncertainty of 2.13 cm.