Global decay chain vertex fitting at Belle II

In this paper we report the implementation of a global vertex fitting algorithm within the Belle II analysis software environment, which was originally developed for BaBar (Hulsbergen, 2005). We explore the impact of global vertex fitting algorithms for flavour physics analyses with the Belle II detector at the SuperKEKB e(+)e(-) collider, such as in the reconstruction of final states with neutral particles, and in fits with geometrical constraints from SuperKEKB's nano-beam interaction region. The algorithm is compared to the standard vertex fitting algorithm employed by the Belle experiment. We have developed the fitting framework to utilise the EIGEN library for linear algebra operations, reducing the computation time for vertex fitting operations by an order of magnitude over previous methods. This has a significant impact on physics analysis computing efficiency, where vertex fitting over large combinations of final state particles is one of the most CPU intensive operations at Belle II.