Amplitude analysis of four-body decays using a massively-parallel fitting framework

The GooFit Framework is designed to perform maximum-likelihood fits for arbitrary functions on various parallel back ends, for example a GPU. We present an extension to GooFit which adds the functionality to perform time-dependent amplitude analyses of pseudoscalar mesons decaying into four pseudoscalar final states. Benchmarks of this functionality show a significant performance increase when utilizing a GPU compared to a CPU. Furthermore, this extension is employed to study the sensitivity on the $D^0-{\bar{D}}^0$ mixing parameters $x$ and $y$ in a time-dependent amplitude analysis of the decay $D^0 \rightarrow K^+\pi^-\pi^+\pi^-$. Studying a sample of 50 000 events and setting the central values to the world average of $x=(0.49\pm 0.15)\mathrm{\%}$ and $y = (0.61 \pm0.08) %$,thestatisticalsensitivitiesof$x$and$y$ are determined to be $\sigma (x)=0.019\mathrm{\%}$ and $\sigma (y)=0.019\mathrm{\%}$.