  The Mu3e experiment at the Paul Scherrer Institute searches for the charged
lepton flavor violating decay $\mu^+ \rightarrow e^+ e^+ e^-$. The experiment
aims for an ultimate sensitivity of one in $10^{16}$ $\mu$ decays. The first
phase of the experiment, currently under construction, will reach a branching
ratio sensitivity of $2.5\times10^{-15}$ by observing $10^{8}$ $\mu$ decays per
second over a year of data taking. The highly granular detector based on thin
high-voltage monolithic active pixel sensors (HV-MAPS) and scintillating timing
detectors will produce about 100 GB/s of data at these particle rates. The
Field Programmable Gate Array (FPGA) based Mu3e Data Acquisition System will
read out this data from the detector and reduce the event rate to 100 MB/s by
selecting interesting events using a filter farm of graphics processing units.
The paper presents the status of the data acquisition system (DAQ) and first
results from the 2021 integration run, which for the first time operated a
slice of the Mu3e detector at the $\pi$E5 muon beam line at the Paul Scherrer
Institute (PSI).
