The reconstruction of charged particle trajectories ("tracking") in particle physics detectors is one of the computationally most challenging tasks of the field, limiting the amount of high-quality data that can even be recorded. Applied to particle collider experiments such as the CMS experiment, this task is different from many other problems that involve trajectories: There are millions of particle collisions per second, each with thousands of individual particles that need to be tracked, there is no time information (the particles travel too fast), and we do not observe a continuous trajectory but instead only 5-15 points ("hits") along the way in different detector layers. The task can be described as a combinatorically very challenging "connect-the-dots" problem, essentially turning a cloud of points (hits) in 3D space into a set of O(1000) trajectories.

While traditional methods scale disfavorably with the number of particles in each collisions, there is hope that machine learning techniques can analyze the data more efficiently. In this project, we use Graph Neural Networks for this purpose.

While the Standard Model of particle physics describes particles and their interactions to astonishing accuracy, there are a range of shortcomings. One of the avenues to probe and test the Standard Model further is to investigate differences between similar particles of different "flavor". Studies of B mesons are particularly sensitive to this.

In this project, data from the Belle experiment is analyzed with the software of its successor, the Belle II experiment. One of the key ingredients is the Full Event Interpretation, a machine learning algorithm that reconstructs \(B\) mesons from their decay products as recorded by the detector. To apply it with confidence, careful calibration and validation of its behavior needs to be performed.

Most of our current understanding of elementary particle physics is encoded in the "Standard Model", a mathematically consistent description of all known particles and their interactions (except gravitation). There are a number of shortcomings of the Standard Model and most notably, astrophysical observations suggest that the currently known particle content accounts for but 5% of the total mass content of the universe (the rest being called dark matter). However, at the same time, accelerator experiments have confirmed the predictions of the Standard Model with astonishing accuracy.

One of the few exceptions are the so called "anomalies in semileptonic B decays", anomalies found in decays of B mesons into other mesons (particles made up of two quarks) and leptons (e.g. electrons, neutrinos). Deviations have been seen by three independent experiments (Belle, BaBar and LHCb) and taken together, the measurements challenge the Standard Model like few before.

In my Master thesis project, I give an overview over possible models of physics beyond the Standard Model, develop new observables that could help to distinguish between them and finally present continuing work on an analysis of one kind of semileptonic B decays that plays an important role in the anomalies.

The spectroscopic study of interstellar and circumstellar molecules has been long ongoing, with researchers concluding already in the 1970s that interstellar dust contains large numbers of complex organic molecules (COMs). Since then, ever improving searches have found about 50 such COMs. Besides being of great interest for astrochemistry and some researchers even pointing out their potential role regarding the origin of life, COMs also serve as valuable probes for the physical conditions of the surrounding medium.

The build-up of molecular complexity in a given system can be studied with chemical reaction networks (CRNs), mathematical models of the concentrations of various molecules based on a fixed set of reactions and an initial set of reactant concentrations. By expanding the previously studied CRNs with additional dust grain-surface reactions, we tried to improve the description of COM formation in protoplanetary disks. Trying to automize some time-consuming manual tasks necessary for studies of the influence of physical and chemical parameters, I wrote an analysis framework that will enable future students to conduct similar studies much more efficiently, thereby opening new research possibilities.

The LHCb experiment is one of the particle physics detector experiments located at the LHC at CERN. At the collision points at the LHC, millions of particle collisions happen every second. Due to limitations in computing power and storage capacity, so far not every one of these events could be recorded and processed. Rather, only a fraction of the events were picked out to be processed by so called triggers. From 2020, the LHCb experiment plans to proceed to a trigger-free readout, where all of the events can be processed, thereby increasing the amount of data available to physicists. This requires an update of the LHCb Data Acquisition (DAQ) systems, which are responsible for the recording and processing of the events. DAQPIPE (Data Acquisition Protocol Independent Performance Evaluator) is a tool to simulate and evaluate the performance of such a DAQ system.

The aim of this 10-week summer student project was to implement network monitoring for a more detailed performance evaluation of different transport protocols and to spot potential bottlenecks. First, several existing performance monitors were tested. To that end DAQPIPE was run together with Tau and the obtained performance data was plotted with ParaProf, JumpShot and Vampir. In the second stage of the project, a light-weight performance analysis tool was written from scratch in C++.

Most of our current understanding of elementary particle physics is encoded in the "Standard Model", a mathematically consistent description of all known particles and their interactions (except gravitation). However there are a number of shortcomings of the Standard Model and most notably, astrophysical observations suggest that the currently known particle content can account for but 5% of the total mass content of the universe (the rest being called dark matter). One of the most popular theoretical concept that introduces additional particles is the concept of supersymmetry (SUSY).

Current searches for SUSY particles are for example conducted with the ATLAS detector at the LHC at CERN. However, as SUSY theories depend on many unknown parameters, computation power becomes a limiting resource for the study (and exclusion) of possible concrete SUSY scenarios. To address this, two types of analysis methods are used: Truth level analysis (fast but unreliable) and reco level analysis (slow but reliable). Because truth level analysis is a shortcut, it has to be validated by comparing it with the reliable reco level analysis results.

For my thesis I performed such a comparison for a specific setup. Unfortunately I found but low levels of agreement between the results of both analysis strategies. I ruled out several sources of error and showed the necessity of a more detailed study of the underlying assumptions.

Central subject of this thesis are so called elliptic functions. Elliptic functions are a special type of meromorphic functions (complex-valued functions in one complex variable, which are holomorphic apart from a discrete set of poles) that are periodic in two directions on the complex plane, i.e. \( f(x) = f(x+a) \) and \( f(x) = f(x+b) \) for any \( x \) out of the domain with two complex numbers \( a \) and \( b \) (which are required to be non-collinear on the complex plane).

Among others, elliptic functions are of great use in number theory, in particular there are interesting connections to sums of divisors of natural numbers. Furthermore they are used in the theory of elliptic curves and elliptic integrals.