Preliminary study for a measurement of the CKM angle $\gamma$ using the tree $B^{\pm} \to D^{(*)0} K^{\pm}$ decays with the LHCb detector at CERN

The Large Hadron Collider (LHC) offers the possibility to collect hints of New Physics (NP) in proton-proton collisions at high energy. The LHC experiments' collaborations are exploring direct and indirect techniques to reveal the existence of NP. General purpose detectors, as ATLAS and CMS, search for the decay of predicted particles to complete the Standard Model or its extensions. ALICE is dedicated to sudies of a high density and temperature environment, testing the theoretical predictions for quark gluon plasma state. LHCb tests the Standard Model (SM) in the sector of the Heavy Flavors and the global consistency of the description of the CP violation (CPV) phenomena. Since CPV manifestations involve in particular beauty mesons and because of the large b-antib production cross section at LHC, LHCb is already starting to contribute to world averages for B-meson physics and CPV parameters. The measurement of the gamma angle of the bd unitarity triangle of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is a key test of the Standard Model (SM), as gamma approximates the complex phase delta of the CKM matrix explaining the CP violation within the quark sector of the SM. The measurement of the gamma angle can be achieved through theoretically clean tree-only processes B^{\pm}-> D^{(*)0}K^{\pm}, excluding any contribution from NP. A precise measure of gamma with tree transitions would set a very stable reference for the global consistency test of the CKM mechanism within the SM. A discrepancy between the measurement of gamma achieved through tree-only decays and through processes involving loops would be evidence of NP virtual particles arising in the loops. Furthermore the world average for gamma is less precise than that of the other angles of the unitarity triangle (alpha and beta). The test of the geometrical relation alpha + beta + gamma = pi is a fundamental test for the three-generation quark model. The work presented here is a feasibility study for contributing to tree-processes gamma measurement with the channel B -> D^{*0}K. The methods exploiting this decay are called GLW and ADS after the authors Gronau-London-Wyler and Awood- Dunietz-Soni, respectively. I conclude the theoretical introduction by reviewing the GLW and ADS methods for the B^{\pm}-> D^{0}K^{\pm} channel and their extension to B^{\pm}-> D^{*0}K^{\pm}. The LHC offers the world highest b-antib pairs production cross section, while the LHCb detector has been designed to efficiently measure B-mesons, achieving a high background rejection thanks to a powerful multi-level trigger. The comparison of LHCb, TeVatron (CDF) and b-factories yields shows that the LHCb data sample is already competitive, and before the end of 2011 LHCb is expected to obtain the best gamma measurement, based on 1 fb^{-1} (2 fb^{-1}) collected at the end of 2011 (2012). I describe the official LHCb analysis of B^{\pm}-> D^0 K^{\pm} decays that I have repeated during my training period, as well as the computing techniques used. Finally I describe the first reconstruction attempts for B^{\pm}-> D^{*0}h^{\pm} channels. The aim is to verify whether B^{\pm} -> D^{*0}K^{\pm} channel can significantly improve LHCb gamma measurement, contributing with a significant data sample. I have thus applied the same techniques used for the B^\pm -> D^0h^\pm analyses to the B^\pm -> D^{*0} pi^\pm, developing a C++ framework named Leaf which is parallel calculation oriented and usable for both analyses. Using Leaf and some additional utilities (as RooFit and TMVA), I achieved the first observation of B-> D^{*0} pi with D^{*0} -> D^0 gamma, and D^{*0} -> D^0 pi^0 at LHCb. Even if the current statistics is not sufficient to measure gamma through D^{*0} channels, this result encourages to improve the reconstruction efficiency algorithms in order to increase their efficiency.