A study of the CKM angle $\gamma$ using the LHCb experiment and a distributed workload management system

The LHCb experiment, at the Large Hadron Collider (LHC), will make precision $CP$ violation measurements and search for new physics beyond the Standard Model of particle physics. The 14 TeV proton-proton collisions at the LHC will produce the full range of B-hadrons, at a data rate of peta-bytes per year. In order to process this unprecedented amount of data, distributed computing resources (the Grid) located across four continents are coordinated by a series of workload management systems (Grid middlewares). DIRAC, the LHCb distributed workload management system for event simulation, reconstruction and user analysis is extended from the Linux operating platform to the Windows platform, allowing a transparent integration of Windows resources to the existing Linux system. The $B^{\pm} \rightarrow D^0/\bar{D}^0 (K^0_S \pi^{+} \pi^{-}) K^{\pm}$ decay, a key channel for the precision measurement of the CKM angle $\gamma$, is studied using the multiplatform DIRAC system. The expected annual yield from this channel for 2 fb$^{-1}$ of data (a full data taking year) is $\sim$4200 events, with a total physics background to signal ratio (B/S) of < 0.54 at the 90% confidence level. The dominant background is expected to arise from a real $D^0/\bar{D}^0$ candidate reconstructed with a fake kaon from the underlying event, with a B/S = 0.35 $\pm$ 0.03 where the error is statistical. The potential background arising from a real $D^0/\bar{D}^ 0$ candidate reconstructed with a mis-identified pion is greatly reduced, with a B/S < 0.095 at the 90% confidence level, by the use of particle identification information from the RICH sub-detector. The estimated LHCb statistical sensitivity to $\gamma$ is $\sim$12° for 2 fb$^{-1}$ of data, using a model dependent Dalitz analysis with a model error of $\sim$9°.