The Simultaneous Fit

Abstract

An accurate determination of the angle \(\gamma \) of the Unitary Triangle is one of the most important goals of the LHCb experiment. The LHCb detector is a single-arm spectrometer at the LHC, optimised for beauty and charm flavour physics. As the angle \(\gamma \) is the least experimentally constrained parameter of the Unitary Triangle, its precise experimental determination can be used to test the validity of the Standard Model. The Unitary Triangle phase \(\gamma \) can be extracted in \(B \rightarrow DK\) decays at tree-level, exploiting the interference between \(b \rightarrow c(\bar{u}s)\) and \(b \rightarrow u(\bar{c}s)\) transitions. This interference is sensitive to \(\gamma \) and can give measurable charge asymmetries. In particular, \(\gamma \ne 0\) is required to produce direct CP violation in \(B\) decays and this is the only CP-violating mechanism for the decay of charged \(B^\pm \) mesons. In this thesis, an analysis of CP violation in \(B^{\pm } \rightarrow DK^{\pm }\) and \(B^{\pm } \rightarrow D\pi ^{\pm }\) decays is presented, where the \(D\) meson is reconstructed in the two-body final states: \(K^{\pm }\pi ^{\mp }\), \(K^+K^-\), \(\pi ^+\pi ^-\) and \(\pi ^{\pm }K^{\mp }\). The analysis uses the full 2011 LHC dataset of 1.0\(\mathrm {\,fb}^{-1}\), collected from \(pp\) collisions at \(\sqrt{s}= 7\mathrm \,TeV .\) Several CP-related quantities, e.g. the ratio of \(B \rightarrow DK\) and \(B \rightarrow D\pi \) branching fractions and their charge asymmetries, are measured via a simultaneous fit to the invariant mass distributions of the modes considered. The suppressed \(B^{\pm }\rightarrow DK^{\pm }\) mode is observed for the first time with \(\approx 10\sigma \) significance. Once all measurements are combined, direct CP violation is established in \(B^{\pm }\) decays with a total significance of \(5.8\sigma \). The measured CP observables are summarised here with their statistical uncertainties and assigned systematic uncertainties: $$\begin{aligned} R_{{ {CP}}+}&= 1.007 \pm 0.038 \pm 0.012 A_{{ {CP}}+}&= 0.145 \pm 0.032 \pm 0.010 R_{\mathrm{ADS}(K)}&= 0.0152 \pm 0.0020 \pm 0.0004 A_{\mathrm{ADS}(K)}&= -0.52 \pm 0.15 \pm 0.02 R_{\mathrm{ADS}(\pi )}&= 0.00410 \pm 0.00025 \pm 0.00005 A_{\mathrm{ADS}(\pi )}&= 0.143 \pm 0.062 \pm 0.011 \end{aligned}$$