In this thesis we have presented the data taking campaign of the 7-GridPix 'Septemboard' detector used at CAST in 2017/18, its data analysis and limit calculations for different coupling constants.

In total about \(\SI{3150}{h}\) of active background and \(\SI{160}{h}\) of active solar tracking data were taken at CAST with this detector. Generally, detector performance was very stable, with a few issues likely relating to varying operating conditions. There were some other minor setbacks during CAST data taking, most notably a ruptured window, which delayed data taking by a short amount. Also the FADC setup was partially affected by significant noise, which was fixed by changing amplifier settings. In addition, the scintillator data was not recorded correctly in the Run-2 data taking period (Oct 2017 to Apr 2018) and temperature log files of the detector were mostly lost. In the grand scheme of things these issues are minor and do not affect the physics potential of the data much.

We have shown that the additional detector features are an extremely valuable addition. Most notably the Septemboard itself, in the form of the 'septem veto' and 'line veto', provide a large improvement to the backgrounds seen over the majority of the center GridPix. While the improvements to the center \goldArea region are not as large, over the entire chip background is suppressed by an order of magnitude.

In the course of the thesis, the data reconstruction and analysis code written TimepixAnalysis (Schmidt 2022c), was written with future Timepix3 based detectors in mind. It is ready for usage for such detectors.

Further, novel ideas were implemented to improve the reliability in the form of interpolating the reference datasets the likelihood cut classifier is based on. More interestingly though, a machine learning approach using a small multi-layer perceptron (MLP) was implemented, trained entirely on synthetic X-ray data and background data of the outer chips. This yields a classifier fully defined by data unrelated to its main application (background and tracking datasets) and verification (\cefe calibration and X-ray tube data). This MLP classifier achieves comparable performance to the likelihood cut at its default \(ε_{\ln\mathcal{L}} = \SI{80}{\%}\) using a software efficiency of \(\SI{95}{\%}\). Significant improvements to the limit calculation are possible as a result.

Following the 2017 CAST Nature paper (Collaboration and others 2017), an unbinned Bayesian likelihood method for limit calculation was implemented to compute limits on the axion-electron coupling \(g_{ae}\), the axion-photon coupling \(g_{aγ}\) and the chameleon coupling \(β\). This limit calculation requires a description of the irreducible background during data taking and several inputs to calculate the expected number of axion induced X-rays during the solar tracking time. The background is obtained from the application of the classifier (\lnL or MLP) to the background dataset.

To calculate the expected number of axion induced X-rays during the solar tracking dataset, the differential solar axion flux and the radial emission profile in the Sun is needed (in addition to the losses expected due to the detector window losses and gas transmission). To properly characterize the expected 'axion image' on the detector, a raytracing simulation taking these into account is required. Such a simulation was implemented in the context of this thesis and verified against PANTER measurements of the LLNL telescope.

Despite the additional detector features producing a more homogeneous background rate over the entire central chip, an interpolation of the background rate at each point is still required. Such an interpolation was developed based on a normal distribution weighted nearest neighbor approach, producing smooth results.

Further, the limit calculation method of (Collaboration and others 2017) was extended to allow the inclusion of systematic uncertainties into the likelihood function by usage of four nuisance parameters. As these need to be integrated out to obtain the posterior likelihood function from which a limit is computed, a Markov Chain Monte Carlo (MCMC) approach was developed to sample from the likelihood function efficiently. This is needed, because different choices of parameters (detector vetoes, software efficiencies and so on) are evaluated based on their resulting expected limit. Expected limits are computed by sampling toy candidate sets from the background distribution and computing their limits. The expected limit then is defined by the median of all such limits.

The expected limit for the best method based on \(\num{50 000}\) toy candidate sets came out to

\[ \left(g_{ae} · g_{aγ}\right)_{\text{expected}} = \SI{7.878225(6464)e-23}{GeV^{-1}}, \]

while the observed limit was computed to

\[ \left(g_{ae} · g_{aγ}\right)_{\text{observed}} \lesssim \SI{7.35e-23}{GeV⁻¹} \text{ at } \SI{95}{\%} \text{ CL}. \]

This is a good improvement over the current best limit obtained by CAST in 2013 (Barth et al. 2013) of

\[ \left(g_{ae} · g_{aγ}\right)_{\text{CAST2013}} \lesssim \SI{8.1e-23}{GeV⁻¹}. \]

For the axion-photon coupling our detector was not expected to improve on the current best limit (\(g_{aγ, \text{Nature}} < \SI{6.6e-11}{GeV⁻¹}\), (Collaboration and others 2017)), which is validated by an expected limit of

\[ g_{aγ, \text{expected}} = \SI{9.0650(75)e-11}{GeV⁻¹}, \] with an observed limit of \[ g_{aγ, \text{observed}} \lesssim \SI{9.0e-11}{GeV⁻¹} \text{ at } \SI{95}{\%} \text{ CL}. \]

However, for the chameleon limit this detector was expected to be highly competitive, due to a \(\SI{300}{nm}\) thin \ccsini window greatly increasing efficiency at the required low energies and additional detector vetoes improving background rates over the entire center GridPix. Indeed, these combined with an improved limit calculation method, allowing the inclusion of the entire center chip and thus full chameleon flux, and better classifier in the form of the MLP yields an expected limit of

\[ β_{γ, \text{expected}} = \num{3.6060(39)e+10}. \]

The observed limit was then computed to

\[ β_{γ, \text{observed}} \lesssim \num{3.1e+10} \text{ at } \SI{95}{\%} \text{ CL}. \]

which is a significant improvement over (Christoph Krieger 2018; Anastassopoulos et al. 2019)

\[ β_{γ, \text{Krieger}} < \num{5.74e10} \text{ at } \SI{95}{\%} \text{ CL}, \]

the current best bound on the chameleon-photon coupling.