Contribution to the Development of the LHCb acquisition electronics and Study of polarized radiative $\Lambda_b$ decays

LHCb is one of the four main experiments that will take place at the future Large Hadron Collider at CERN. The data taking is foreseen to start in 2007. The LHCb detector is a forward single-arm spectrometer to precision measurements of CP violation and rare decays in the b-quark sector. The goal is to over-constrain the Standard Model (SM) and - hopefully - to exhibit inconsistencies which will be a signal of new physics beyond. Building such a large experiment as LHCb is a big challenge, and many contributions are needed. The Lausanne institute is responsible for the development of a common "off-detector" readout board (TELL1), which provides the interface to the copper and optical links used for the detector readout, and outputs them to the data acquisition system, after performing intensive processing. It performs: event synchronization, pedestal calculation and subtraction, common mode subtraction and monitoring, zero suppression. The TELL1 board will be used by the majority of the LHCb subdetectors. We present here a contribution to the R&D necessary for the realization of the final board. In particular the feasibility of a mixed architecture using DSP and FPGA technologies has been studied. We show that the performance of this architecture satisfies LHCb electronics requirements at the time of the study (2002). Within the rich LHCb physics program, b -> s transitions represent an interesting sector to look for evidence of physics beyond the SM. Even if the measured decay rate is in good agreement with the SM prediction up to now, new physics may still be hidden in more subtle observables. One of the most promising is the polarization of the emitted photon, which is predicted to be mainly left-handed in the SM. However right-handed components are present in a variety of new physics models. The photon polarization can be tested at LHCb by exploiting decays of polarized b baryons. If the initial baryon is polarized, asymmetries appear in the final states angular distributions, which can be used to probe the chirality of the effective Hamiltonian, and possibly to unveil new sources of CP violation. We present a phenomenological approach to the study of radiative decays of the type /\b ->/\(X) gamma, where /\(X) can be any /\ baryon of mass X. Calculations of the angular distributions are carried out employing the helicity formalism, for decays which involve /\ baryons of spin 1/2 and 3/2. Finally, detailed simulation studies of these channels in the LHCb environment allow us to assess the LHCb sensitivity to the photon polarization in b -> s transitions.