Extraindo a fase $\gamma$ de CKM nos decaimentos $B^{\pm} \to K^{\pm} \pi^+ \pi^-$ e $B^0, \bar{B}^0 \to K_S \pi^+ \pi^-$

The Charge-Parity (CP) symmetry violation is implemented in the Standard Model by the presence of a complex phase in the Cabibbo-Kobayashi-Maskawa matrix. The violation magnitude is quantified in the $\alpha$, $\beta$ and $\gamma$ angles, where only $\beta$ is precisely known at present days. The LHCb experiment, in construction phase, has among it's objectives the measurement of $\alpha$ and $\gamma$ angles. In this dissertation we propose a new method for $\gamma$ extraction, using $B^{\pm} \to K^{\pm} \pi^+ \pi^-$ and $B^0, \bar{B}^0 \to K_S \pi^+ \pi^-$ intermediary state interferences in a combined analysis. With the LHCb simulation, we estimate the annual yield for these channels. Using fast Monte Carlo tools we show that for 100k $B^0, \bar{B}^0 \to K_S \pi^+ \pi^-$ events, we can measure $\gamma$ with 5$^{\circ}$ error in one year of data taking. To the $B$ neutral analysis, we developed a new fitting technique that avoids tagging, the joint fit. Besides $\gamma$, we measure direct CP violation in $B \to K \pi \pi$ decays and we measure the relative magnitude and phase difference between tree and penguin contributions of $B^0, \bar{B}^0 \to K^{*\pm} \pi^{\mp}$ channel.