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

## TL;DR

This paper introduces an extension to the GooFit framework enabling efficient time-dependent amplitude analysis of four-body decays on GPUs, demonstrating significant performance gains and sensitivity to D0-D0bar mixing parameters.

## Contribution

The paper presents a novel GPU-accelerated extension to GooFit for four-body decay amplitude analysis, improving computational speed and sensitivity in mixing parameter measurements.

## Key findings

- GPU implementation significantly outperforms CPU in analysis speed
- Sensitivity to D0-D0bar mixing parameters achieved at 0.019%
- Extension enables detailed studies of four-body decay dynamics

## Abstract

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 $x = (0.49 \pm0.15) \%$ and $y = (0.61 \pm0.08) \%$, the statistical sensitivities of $x$ and $y$ are determined to be $\sigma(x) = 0.019 \%$ and $\sigma(y) = 0.019 \%$.