CLEO-c $D\to K_{S/L}^0 \pi^+\pi^-$ Binned Dalitz-Plot Analyses Optimised for the CKM Angle $\gamma$ Measurement and the Commissioning of the LHCb RICH Front-End Electronics

The best single direct measurement of the CKM angle γ is currently derived from an unbinned maximum likelihood Dalitz analysis of the $B^{\pm}\to D^{(-)0} K^{\pm}$ channel where the neutral $D^{(-)0}$ decays to $K^{0}_{S}\pi^{+}\pi^{-}$ . This technique is limited to a 3 − 9◦ precision on γ arising from uncertainties introduced when modelling the three-body decay of the $D^{(-)}0$. These model uncertainties will dominate the precision on γ at the next generation of B-physics experiments such as LHCb. An alternative binned approach to the analysis of $B^{\pm} \to (K^{0}_{S}\pi^{+}\pi^{-})_{D}K^{\pm}$ data has been proposed that is free of the model-dependent uncertainties. This alternative approach requires external constraints from a set of parameters, so-called ci and si, that depend on both the strong phase difference between $D^{0} \to K^{0}_{S}\pi^{+}\pi^{-}$ and $\overline{D}^{0} \to K^{0}_{s}\pi^{+}\pi^{-}$ and the choice of Dalitzplot binning. A previous analysis of quantum correlated $\overline{D}^{0} \to K^{0}_{s}\pi^{+}\pi^{-}$ data has already yielded a measurement of a set of parameters suitable for making a modelindependent determination of γ from $B \to (K^{0}_{s}\pi^{+}\pi^{-})_{D}K^{\pm}$ data. However, the chosen Dalitz-plot binning leads the $B \to (K^{0}_{s}\pi^{+}\pi^{-})_{D}K^{\pm}$ data-set to be exploited in a way that is statistically non-optimal. Presented here is an analysis of quantum-correlated $D^{(-)0} \to K^{0}_{s}\pi^{+}\pi^{-}$ data using the full 818 ± 8 pb−1 CLEO-c data-set. The choice of Dalitz-plot binning is optimised to best exploit the $B^{\pm}\to D^{(-)0} K^{\pm}$ statistics in the determination of the CKM angle γ at LHCb using the binned Dalitz-plot analysis. In the binned Dalitz analysis, the 3 − 9 degree model error on γ is replaced with a 2 − 4 degree error due primarily to the CLEO-c statistics. The Level-0 front-end electronics modules for the LHCb Ring Imaging Cerenkov (RICH) detectors interface the RICH pixel Hybrid Photon Detectors to the LHCb trigger, data acquisition and control systems. The system operates at 40 MHz with a first-level trigger rate of 1 MHz. The laboratory qualification and fault-finding enabled 278 working Level-0 boards to delivered for operation in the experiment. A simple-touse and functional calibration and controls system has also been developed to read out the RICH detectors at LHCb. The design of this infrastructure facilitates rapid detector operation following front-end hardware installation or replacement. The system has been used to calibrate the HPD analogue voltages and to internally time-align the RICH detectors with a precision of 2 ns. This enables the photon detectors to operate at peak efficiency. The Level-0 module is described, and results are presented on laboratory and in-situ commissioning measurements.