A Study of the RICH Detector Performance and Search for New Physics in $B^{0}_{d} \to K^{*}\mu^{+}\mu^{-}$ Decays with the LHCb Experiment

The LHCb experiment will make precision \ensuremath{\mathcal{C}\mathcal{P}\text{-violation}} and rare decay measurements at the Large Hadron Collider which is due to start running in 2008. These will provide an indirect window onto new physics beyond the Standard Model (SM). The Ring Imaging Cherenkov (RICH) sub-detectors provide essential particle identification for many LHCb physics analyses. A system test of the RICH photon detectors and electronics has been successfully performed at CERN. The reconstructed mean Cherenkov angle and photon yields are in good agreement with expectations. The Cherenkov angle resolution of the RICH Hybrid Photon Detectors (HPDs) is measured to be \ensuremath{1.66\;\pm\;0.03\:\mathrm{mrad}} where the quoted error is the systematic error and the statistical error is negligible. The resolution is in good agreement with the Monte Carlo (MC) simulation. The rare decay \ensuremath{\mathrm{B}^{0}_{\mathrm{d}}\;\rightarrow\;\mathrm{K}^{*}\,\mu^{+}\,\mu^{-}} provides a sensitive test of the SM. The reconstruction and selection of these events has been studied using the full LHCb MC simulation. With a \ensuremath{2\:\;\mathrm{fb}^{-1}} data set, \ensuremath{7200\;\pm\;180^{\;+\;2200}_{\;-\;1900}} signal events are expected where the first error is the statistical error from the MC event sample and the second error is from the measured branching ratio. A total background of \ensuremath{1770\;\pm\;310} even ts is expected excluding a potential background of \ensuremath{1730} events from non-resonant \ensuremath{\mathrm{B}^{0}_{\mathrm{d}}\;\rightarrow\;\mathrm{K}^{+}\,\pi^{-}\,\mu^{+}\,\mu^{-}} decays. The background is expected to be dominated by events with muons from real b-decays. The forward-backward asymmetry (\ensuremath{\mathrm{A_{FB}}}) in \ensuremath{\mathrm{B}^{0}_{\mathrm{d}}\;\rightarrow\;\mathrm{K}^{*}\,\mu^{+}\,\mu^{-}} events is sensitive to new physics. The large number of signal events expected means that the \ensuremath{\mathrm{A_{FB}}} distribution can be measured as a function of the invariant mass of the muon pair. The sensitivity to the zero-crossing point of \ensuremath{\mathrm{A_{FB}}}, i.e. the expected statistical precision, is estimated to be \ensuremath{0.60\:\mathrm{GeV}^{2}/c\,^{4}} with \ensuremath{2\:\;\mathrm{fb}^{-1}} and \ensuremath{0.29\:\mathrm{GeV}^{2}/c\,^{4}} with \ensuremath{10\:\;\mathrm{fb}^{-1}} of data and corresponds to approximately 1 and 5 years of data taking respectively.