Track reconstruction for the Mu3e experiment based on a novel Multiple Scattering fit

The Mu3e experiment is designed to search for the lepton flavour violating decay mu(+)-> e(+) e(+) e(-). The aim of the experiment is to reach a branching ratio sensitivity of 10-16. In a first phase the experiment will be performed at an existing beam line at the Paul-Scherrer Institute (Switzerland) providing 108 muons per second, which will allow to reach a sensitivity of 2.10(-15). The muons with a momentum of about 28 MeV/c are stopped and decay at rest on a target. The decay products (positrons and electrons) with energies below 53 MeV are measured by a tracking detector consisting of two double layers of 50 mu m thin silicon pixel sensors. The high granularity of the pixel detector with a pixel size of 80 mu m x 80 mu m allows for a precise track reconstruction in the high multiplicity environment of the Mu3e experiment, reaching 100 tracks per reconstruction frame of 50 ns in the final phase of the experiment. To deal with such high rates and combinatorics, the Mu3e track reconstruction uses a novel fit algorithm that in the simplest case takes into account only the multiple scattering, which allows for a fast online tracking on a GPU based filter farm. An implementation of the 3-dimensional multiple scattering fit based on hit triplets is described. The extension of the fit that takes into account energy losses and pixel size is used for offline track reconstruction. The algorithm and performance of the offline track reconstruction based on a full Geant4 simulation of the Mu3e detector are presented.