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The measurement of the mass of the $W$ boson is currently one of the most promising precision analyses of the Standard Model, that could ultimately reveal a hint for new physics.
The mass of the $W$ boson is determined by comparing the $W$ boson, which cannot be reconstructed directly, to the $Z$ boson, where the full decay signature is available. With the help of Monte Carlo simulations one can extrapolate from the $Z$ boson to the $W$ boson.
Technically speaking, the measurement of the $W$ boson mass is performed by comparing data taken by the ATLAS experiment to a set of calibrated Monte Carlo simulations, which reflect different mass hypotheses.\
A dedicated calibration of the reconstructed objects in the simulations is crucial for a high precision of the measured value.
The comparison of simulated $Z$ boson events to reconstructed $Z$ boson candidates in data allows to derive event weights and scale factors for the calibration.
This thesis presents a new approach to reweight the hadronic recoil in the simulations. The focus of the calibration is on the average hadronic activity visible in the mean of the scalar sum of the hadronic recoil $\Sigma E_T$ as a function of pileup. In contrast to the standard method, which directly reweights the scalar sum, the dependency to the transverse boson momentum is less strongly affected here.
The $\Sigma E_T$ distribution is modeled first by means of its pileup dependency. Then, the remaining differences in the resolution of the vector sum of the hadronic recoil are scaled. This is done separately for the parallel and the pterpendicular component of the hadronic recoil with respect to the reconstructed boson.
This calibration was developed for the dataset taken by the ATLAS experiment at a center of mass energy of $8\,\textrm{TeV}$ in 2012. In addition, the same reweighting procedure is applied to the recent dataset with a low pileup contribution, the \textit{lowMu} runs at $5\,\textrm{TeV}$ and at $13\,\textrm{TeV}$, taken by ATLAS in November 2017. The dedicated aspects of the reweighting procedure are presented in this thesis. It can be shown that this reweighting approach improves the agreement between data and the simulations effectively for all datasets.
The uncertainties of this reweighting approach as well as the statistical errors are evaluated for a $W$ mass measurement by a template fit to pseudodata for the \textit{lowMu} dataset. A first estimate of these uncertainties is given here. For the pfoEM algorithm a statistical uncertainty of $17\,\text{MeV}$ for the $5\,\textrm{TeV}$ dataset and of $18\,\text{MeV}$ for the $13\,\textrm{TeV}$ are found for the $W \rightarrow \mu \nu$ analysis. The systematic uncertainty introduced by the resolution scaling has the largest effect, a value of $15\,\text{MeV}$ is estimated for the $13\,\textrm{TeV}$ dataset in the muon channel.
The quest for finding a unifying theory for both quantum theory and gravity lies at the heart of much of the research in high energy physics. Although recent years have witnessed spectacular experimental confirmation of our expectations from Quantum Field Theory and General Relativity, the question of unification remains as a major open problem. In this context, the perturbative aspects of quantum black holes represent arguably the best of our knowledge of how to proceed in this pursue.
In this thesis we investigate certain aspects of quantum gravity in 2 + 1 dimensional anti-de Sitter space (AdS3), and its connection to Conformal field theories in 1 + 1 dimensions (CFT2), via the AdS/CFT correspondence.
We study the thermodynamics properties of higher spin black holes. By focusing on the spin-4 case, we show that black holes carrying higher spin charges display a rich phase diagram in the grand canonical ensemble, including phase transitions of the Hawking-Page type, first order inter-black hole transitions, and a second order critical point.
We investigate recent proposals on the connection between bulk codimension-1 volumes and computational complexity in the CFT. Using Tensor Networks we provide concrete evidence of why these bulk volumes are related to the number of gates in a quantum circuit, and exhibit their topological properties. We provide a novel formula to compute this complexity directly in terms of entanglement entropies, using techniques from Kinematic space.
We then move in a slightly different direction, and study the quantum properties of black holes via de Functional Renormalisation Group prescription coming from Asymptotic safety. We avoid the arbitrary scale setting by restricting to a narrower window in parameter space, where only Newton’s coupling and the cosmological constant are allowed to vary. By one assumption on the properties of Newton’s coupling, we find black hole solutions explicitly. We explore their thermodynamical properties, and discover that very large black holes exhibit very unusual features.