Studies of mass constraints in the treatment of background subtraction in Dalitz plots

Dalitz plots are an important analytical tool in particle physics. Their analysis often employs mass constraints to improve mass resolution and generate more accurate kinematics. However, the impact of these mass constraints on Dalitz plots, particularly with regard to background subtraction, has not yet been studied in detail. This thesis addresses this issue. Using a mass constraint results in clear, measurable and visible shifts in the Dalitz plot. The shifts depend on the measured decay, the position of the events in the mass distribution and on the distance to the mass constraint and are therefore unique to each Dalitz plot analysis. For a symmetric mass distribution around the mass constraint, these shifts, on average, nearly cancel each other out. However, the shifts that can be seen in the sideband of the mass distributions of the parent particle are clearly significant and substantially distort the distribution within the Dalitz plots. The degree of distortion is primarily determined by the difference between the mass of the parent particle of the data points and the mass constraint that is used. For this reason, the application of background subtraction, when using mass constraints, is not a scientifically viable method in its current form. The outlook discusses ways to mitigate this effect, which could, with further research, possibly be excluded from future analyses. Further research is also advised into the exact effects on subsequent evaluation methods that analyse distributions within Dalitz plot bins and use mass constraints, since these methods could also be affected.