Search for physics beyond the standard electroweak model with the WITCH experiment

A measurement of the $\beta$-neutrino angular correlation coefficient $a$ yields information on possible exotic couplings in the weak interaction. To this end the energy distribution of the recoiling daughter nucleus after $\beta$-decay, which depends on $a$, is measured precisely. Any deviation of the measured distribution with the one expected from the Standard Model can reveal new physics. If no deviation is found stringent limits can be set on the possible presence of different types of new physics beyond the Standard Model. The WITCH experiment, located at ISOLDE, CERN aims to determine $a$ with a final precision below 1%. $\\$ Ion bunches are created with REXTRAP and injected in the WITCH setup. The energy of these ion bunches is pulsed down in the Pulsed Drift Tube section, prior to the capture of the ions in the first of two Penning traps. The motion of the radioactive ions is cooled before the transfer to a second Penning trap, the decay trap, which acts as the scattering-free source of the experiment. The ions can decay in this trap while being stored for a couple of seconds. When an ion undergoes $\beta$-decay, it can escape the trap and the energy of the recoiling daughter nucleus is measured with a retardation spectrometer and an MCP detector. By varying the electric potential barrier in the retardation spectrometer, the recoil energy spectrum is obtained.$\newline\\$ The expected recoil energy spectrum is reconstructed with an ion tracking simulation program, called Sim WITCH, and a Penning trap simulation program, called Simbuca. This versatile simulation package was developed to investigate the behavior of multiple ions in a Penning trap. Due to its novel approach of using a graphics card (GPU) instead of a conventional CPU, the Coulomb interaction between the ions can be calculated much faster. Furthermore Simbuca incorporates three realistic buffer gas models, the possibility of importing realistic electric and magnetic field maps and different order integrators with adaptive step size and error control. $\\$The simulation package was used to analyze the first acquired retardation spectrum with WITCH, taken in an experiment in June 2011. Even though the statistics gathered is low, a first determination of $a$ with the WITCH experiment was possible. The analysis method for a typical WITCH experiment will be explained and it will be shown that a statistical precision below 1% can indeed be reached with the WITCH experiment. An outlook is given about the follow up experiments in October and November 2011, in which enough statistics were obtained to reach a statistical precision of around 4%. The WITCH experiment is now in a phase where systematic effects will have to be looked into and a preliminary result can be obtained even before a final dataset for a high precision result can be collected. $\\$ development of Simbuca made it possible to look at the behaviour of multiple ( 10$^6$ $\to$ 10$^7$ ) ions in a Penning trap, a regime that is currently being reached by the setup. Due to the mutual Coulomb interaction between the ions, they will cluster together to form an ion plasma which rotates around its own center of mass. The influence of this behaviour on the resonant quadrupole eigen-frequency will be discussed. An estimate for the range of the plasma parameters is extracted from simulations as well. Finally, an outlook is given on how to influence and/or determine these parameters. This will analyse the already available as well as future high statistics datasets of WITCH.