Despite the many empirical hints for the existence of Dark Matter in the Universe,
Dark Matter has yet to be observed experimentally, be it directly through its scatterings
in detectors, indirectly through its annihilation in the galaxy, or implicitly through its
production and decay in particle colliders. Even though observations from astrophysics
and cosmology placed constraints on the Dark Matter energy density and selfinteraction
cross section and with Standard Model particles, much about the nature of
Dark Matter is still unknown, leaving much to the creativity of model builders.
Amongst the plethora of Dark Matter candidates, the Weakly Interactive Massive
Particle (WIMP) is especially attractive as its coupling automatically emerges at the
weak scale from purely cosmological arguments. Out of the various ways of searching
for the WIMP, direct detection experiments have been very successful in probing the
WIMP parameter space. These low background experiments employ different detector
technologies to search for WIMPs in different mass ranges, with the search of WIMPs
in the GeV-TeV mass range dominated by noble gas Time Projection Chambers
(TPCs). Due to the large atomic mass of xenon and the lack of abundant radioactive
xenon isotope, liquid xenon TPCs currently set the strongest limits in the spinindependent
WIMP-nucleon cross section and WIMP mass phase space.
The detector response of liquid xenon TPCs is defined using histograms in the
observable space constructed from Monte Carlo events generated from the detector
response model. Separate histograms, also known as ‘templates’, are constructed using
events generated at different discrete points in the model parameter space. During
statistical inference of the data, the detector response is interpolated between the
templates and this technique is known as ‘template morphing’. However, it presents
several challenges in terms of computation costs and modelling inflexibility, especially
when confronted with high-dimensional observable space and correlated model
parameters.
In this licentiate, we present an exploration of the usage of the likelihood methods as
an alternative to template morphing in fitting and performing statistical inference on
liquid xenon TPC data using the likelihood analysis framework provided by the
Python software package Flamedisx. We tested this new framework by fitting Monte
Carlo (MC) events generated from a model for electronic recoil (ER) events that was
employed in the analysis of XENON1T data.
We found that the estimators for some of the model parameters were biased but within
the uncertainties that one would obtain from fitting actual events. We developed
figures of merits to assess the goodness of fits and found that although the estimators
for some of the model parameters were biased, the fits from fitting the ER MC events
were good and consistent, with p-values > 0.29 in various observable spaces such as
energy, interaction depth, and scintillation against ionization signal space. We also
found some mismodelling in the corrected scintillation against ionization signal space,
and future work should include investigating if the reduction of the number of
nuisance parameters improves the fit in the corrected signal space.