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:
Keywords
- Charge Asymmetry
- Systematic Uncertainties
- Invariant Mass Distribution
- Crystal Ball Function
- Detectable Asymmetry
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Notes
- 1.
Toy experiments are MC simulated experiments where every dataset is generated from the expected PDFs and then fitted with the same model used for data.
- 2.
\(\bar{u}\) quarks must be extracted from the quark sea in the proton.
- 3.
although the sigmas of the Crystal Ball function (Sect. 5.1.2) must be fixed to ensure convergence. The tail parameters are allowed to vary, instead.
References
W. Verkerke, D. Kirkby, The RooFit toolkit for data modeling, arXiv:physics/0306116
LHCb collaboration, R. Aaij, and others, Measurements of the branching fractions and CP asymmetries of \(B^+ \rightarrow J/\psi \pi ^+\) and \(B^+ \rightarrow \psi (2S) \pi ^+\) decays. Phys. Rev. D85 091105, arXiv:1203.3592 (2012)
R. Aaji and others, Measurement of the production asymmetry in 7 TeV pp collisions. Phys. Lett. B 713(3), p. 186 (2012)
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Gandini, P. (2014). The Simultaneous Fit. In: Observation of CP Violation in B± → DK± Decays. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-01029-8_5
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DOI: https://doi.org/10.1007/978-3-319-01029-8_5
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