Measurement of the semileptonic $CP$ violating asymmetry $a_{sl}^{s}$ in $B_s^0$ decays and the $D_{s}^{+}$ -- $D_{s}^{-}$ production asymmetry in 7 TeV $pp$ collisions

The large hadron collider (LHC) at the European Organization for Nuclear Research (CERN) in Geneva is the world's largest and highest-energy particle accelerator. It is located in a tunnel with a circumference of 27 kilometers (17 miles) whose synchrotron is designed to mainly collide opposing particle beams of protons with energy up to 7 TeV in 2011 and 8 TeV in 2012. LHC is designed to address some of the fundamental open questions in physics regarding the basic laws governing the interactions and forces among the elementary particles. Among the four major experiments at LHC: A Toroidal LHC Apparatus (ATLAS), Compact Muon Solenoid (CMS), Large Hadron Collider beauty (LHCb) and A Large Ion Collider Experiment (ALICE), LHCb is the one that is specialized on heavy flavor physics whose goal is to measure the Charge Parity Violation ($CPV$) parameters and rare decays of the Beauty and Charm hadrons. Such studies can help to explain the Matter-Antimatter asymmetry of the Universe. $CP$ violation searches are performed at LHCb in quite a few probing decay channels and systems. In $B_{s}^{0}$-$\bar{B_{s}^{0}}$ mixing, the $CP$ violation is expected to be tiny in the Standard Model, but can be significantly enhanced in the presence of new $CP$ violation phases in general physics models. This thesis presents, in Chapter 5, the measurement of semileptonic asymmetry $a_{\text{sl}}^{\text{s}}$ in $B_{s}^{0}$-$\bar{B_{s}^{0}}$ mixing system at LHCb. The CP-violating asymmetry $a_{\text{sl}}^{\text{s}}$ is studied using samples of $B_{s}^{0}$ and $\bar{B_{s}^{0}}$ semileptonic decays in $pp$ collisions at a centre-of-mass energy of 7 TeV using a data sample, corresponding to an integrated luminosity of 1 fb$^{-1}$ collected by LHCb. The detected final states are $D_s^{\pm}\mu ^{\mp}$, with the $D_s^{\pm}$ particle reconstructed in the $\phi\pi^{\pm}$ mode. The $D_s^{\pm}\mu ^{\mp}$ yields are summed over untagged $\bar{B_{s}^{0}}$ and $B_{s}^{0}$ initial states, and integrated with respect to decay time. Data-driven methods are used to measure all the efficiency ratios needed to determine $a_{\text{sl}}^{\text{s}}$ . We obtain $a_{\text{sl}}^{\text{s}}$ = $(-0.06\pm0.50\pm0.36)$\%, where the first uncertainty is statistical and the second systematic. Specific attention is drawn to an elegant data-driven approach that is developed to determine the relative pion detection efficiency as described in Chapter 3. It is a key building block of the $a_{\text{sl}}^{\text{s}}$ measurement and can open many other doors to $CPV$ searches at LHCb. As a ``litmus test" for this tool, we measure the $D_{s}^{+}$ - $D_{s}^{-}$ production asymmetry using $\phi\pi^{\pm}$ mode in 7 TeV $pp$ collisions at LHC in Chapter 4. Heavy quark production in 7 TeV center-of-mass energy of $pp$ collisions at the LHC is not necessarily flavor symmetric. The production asymmetry, $A_{\rm P}$, between $D_s^+$ and $D_s^-$ mesons is studied using the $\phi\pi^{\pm}$ decay mode in a data sample of 1.0 fb$^{-1}$ collected with the LHCb detector. The difference between $\pi^+$ and $\pi^-$ detection efficiencies is determined using the ratios of fully reconstructed to partially reconstructed $D^{*\pm}$ decays. The overall production asymmetry in the $D_s^{\pm}$ rapidity region 2.0 to 4.5 with transverse momentum larger than 2\,GeV is measured to be $A_{\rm P}=(-0.33\pm0.22 \pm0.10)\%$. While theoretical predictions are difficult and vague, a precise measure of the production asymmetry constrains future heavy quark models and can be used as inputs for other $CPV$ measurements.