Development of an APD amplifier for the runtime alignment of the ATLAS inner detector and SUSY studies

The search for the Higgs boson and supersymmetry (SUSY) are the current goals of particle physics which the advent of the Large Hadron Collider (LHC) aims to address. The ATLAS detector is one of two general purpose detectors to fully exploit the LHC's potential. However the high energy and large particle multiplicities put stringent demands on the performance of the detector; the tracker. In order to extract the optimal performance from the tracker, the detector elements will be required to be aligned to ${\cal{O}}(10\,\mu\text{m})$. The run-time alignment will be monitored by a combination of tracks and an alignment grid. The lengths of the alignment grid are measured by Frequency Scanning Interferometry (FSI). This is an interferometric technique capable of measuring distances to a precision of $1\,\mu \text{m}$ over 1\,m. A low mass FSI interferometer, known as a grid line interferometer (GLI), is placed at the nodes of the alignment grid. But this design returns little light,${\cal{O}}$(pW). Avalanche photodiodes (APD) were proposed as low cost photodetectors capable of resolving 1\,pW. This thesis follows the design of a low noise APD amplifier from initial conception to design and testing. Initial studies focused on measuring the signal-to-noise ratio (SNR) and factors affecting its performance. The final evaluation involved taking FSI data with APDs from a GLI. The results show APDs do not degrade the performance and a 1.5\,m GLI was measured to $1\,\mu\text{m}$ precision. The APD amplifier design was extended to a multichannel DAQ card and its integration to the complete FSI DAQ architecture. The final chapter of this thesis is a study of a heavy SUSY mass ($>1\,\text{TeV}$) model. The initial study showed discovery of this model would be achieved after 4 months of low luminosity running. The remainder of the study examined the measurement of the gluino mass via tagging of top pairs from the $\tilde{g} \rightarrow t \bar{t} \tilde{\chi}^0_1$ decay. The gluino mass was resolved to $1372.6\pm^{101.3}_{\,63.8}$\,GeV after the full LHC integrated luminosity of $300\, \text{fb}^{-1}$.