Results from the ATLAS Barrel Level-1 Muon Trigger Timing Studies Using Combined Trigger and Offline Tracking

The ATLAS Level-1 Muon Barrel Trigger is one of the main elements of the first stage of event selection of the ATLAS experiment at the Large Hadron Collider. The challenge of the Level-1 system is a reduction of the event rate from a collision rate of 40 MHz by a factor $10^{3}$, using simple algorithms that can be executed with a latency of the order of 1 $mu$s. The input stage of the Level- 1 Muon consists of an array of processors receiving the full granularity of data from a dedicated detector (Resistive Plate Chambers in the Barrel). \nBecause of the different time-of-flights and cables and optical fiber lenghts, signals have to be adjusted in time in order to be correctly aligned before being processed. We present the analysis te chnics developed to allow for a study of time misalignements both among the RPC trigger sectors and globally with the LHC clock. These studies collect and integrate several informations, such as tri gger times from the ATLAS Central Trigger Processor, both from the RPC and external triggers (e.g. the Inner Detector); and offline reconstructed muon tracks, that provide us with the ability to per form topology-based study of the trigger timing by knowing the muon trajectory. These techniques have been tested using a large statistics sample of cosmic muon events in combined runs with the rest of the ATLAS detector; and are expected to provide a fast and detailed mapping of the status of the timing c alibration with the early LHC beam data.