The LHCb experiment is a single-arm forward spectrometer situated at the Large Hadron Collider, CERN. LHCb is optimised for the precision study of beauty and charm flavoured hadrons and in 2011 collected 1 fb-1 of proton- proton collision data at a centre-of-mass energy of 7TeV. The aim of LHCb is to search for rare decays and make precise measurements of Charge-Parity (CP) violation in the beauty and charm sectors. In the Standard Model the decay B°→ ΦK*(892)° is described by a loop mediated process, providing a sensitive test for new physics. In this decay, signs of CP violation could indicate the presence of physics beyond the Standard Model. This thesis presents a study of the flavour eigenstate B° → Φ(→ K+K-)K*(892)°(→ K+π-) and its charge conjugate -B°-decay. The decay products form an admixture of CP-even and CP-odd eigenstates, which can have longitudinal or transverse polarisation. An angular analysis is performed to disentangle these different contributions and the polarisation amplitudes and strong phases are measured. No difference is observed between B0 and -B0 amplitudes, supporting the hypothesis that CP is conserved in this decay. In addition, the Triple Product Asymmetries (TPAs) are determined from the products of the polarisation amplitudes and strong phases. True TPAs are zero in the event that CP symmetry is conserved, while fake TPAs can arise due to final-state interactions. Although the measured true TPAs are consistent with zero, several significant fake TPAs are observed.

Recently, there has been an increasing interest in looking at urban environment as a complex system. More and more researchers are paying attention to the study of the configuration of urban space as well as human social activities within it. It has been found that correlation exists between the morphological properties of urban street network and observed human social movement patterns. This correlation implies that the influence of urban configurations on human social movements is no longer only revealed from the sense of metric distance, but also revealed from topological and geometrical perspectives. Metric distances, topological relationships and angular changes between streets should be considered when applying space syntax analysis to an urban street network. This thesis is mainly focused on the comparison among metric, topological and angular analyses based on three kinds of urban street representation models: natural streets, axial lines and axial segments. Four study areas (London, Paris, Manhattan and San Francisco) were picked up for empirical study. In the study, space syntax measures were calculated for different combinations of analytical methods and street models. These theoretical space syntax accessibility measures (connectivity, integration and choice) were correlated to the corresponding practical human movement to evaluate the correlations. Then the correlation results were compared in terms of analytical methods and street representation models respectively. In the end, the comparison of results show that (1) natural-street based model is the optimal street model for carrying out space syntax analysis followed by axial lines and axial segments; (2) angular analysis and topological analysis are more advanced than metric analysis; and (3) connectivity, integration and local integration (two-step) are more suitable for predicting human movements in space syntax. Furthermore, it can be hypothesized that topological analysis method with natural-street based model is the best combination for the prediction of human movements in space syntax, for the integration of topological and geometrical thinking.

We present a first measurement of time-dependent CP-violation in B0 → D∗∓ ρ± , where D∗∓ → D0 π. The analysis was performed using the final Belle dataset containing 772 × 106 B ¯B pairs collected at the KEKB e+ e− collider. Three D0 decay modes are analyzed, K∓ π± , K∓ π± π0 , and K∓ π± π∓ π± . Since the studied decay is a scalar → vector vector decay, three helicity configurations are present. Exploiting the helicity configura- tions via angular analysis, the time-dependent CP-violation parameters encoding 2ϕ1 +ϕ3 are obtained from the fit. 1

Title: Study of b-quark processes in the Belle experiment Author: Daniel Červenkov Department: Institute of Particle and Nuclear Physics Supervisor: Zdeněk Doležal Co-Supervisor: Karim Trabelsi Abstract: A study regarding the plausability of using the B0 → D∗ ρ± decay channel and the data set of the Belle experiment to measure sin(2φ1+φ3) has been carried out. Two fitters have been created. A time-independent one, which ex- hibits high stability and reports gratifying fit uncertainties, and a time-dependent one. During the testing of the latter we have discovered an EvtGen flaw and pro- posed a temporary workaround. Nevertheless, the time-dependent fitter fails to recover the correct values. More work will be needed to reach conclusive results. Keywords: B meson, CP violation, angular analysis, time-dependent, fitter

Cette thèse concerne quatre thèmes apparemment différents, mais en fait intimement liés : problèmes variationnels sur les algèbres de Jordan euclidiennes, problèmes de complémentarité sur l’espace des matrices symétriques, analyse angulaire entre deux cônes convexes fermés et analyse du chemin central en programmation conique symétrique.Dans la première partie de ce travail, le concept de “commutation au sens opérationnel” dans les algèbres de Jordan euclidiennes est étudié en fournissant un principe de commutation pour problèmes variationnels avec données spectrales.Dans la deuxième partie, nous abordons l’analyse et la résolution numérique d’une large classe de problèmes de complémentarité sur l’espace des matrices symétriques. Les conditions de complémentarité sont exprimées en termes de l’ordre de Loewner ou, plus généralement, en termes d’un cône du type Loewnerien.La troisième partie de ce travail est une tentative de construction d’une théorie générale des angles critiques pour une paire de cônes convexes fermés. L’analyse angulaire pour une paire de cônes spécialement structurés est également considérée. Par-exemple, nous travaillons avec des sous-espaces linéaires, des cônes polyédriques, des cônes de révolution, des cônes “topheavy” et des cônes de matrices.La dernière partie de ce travail étudie la convergence et le comportement asymptotique du chemin central en programmation conique symétrique. Ceci est fait en utilisant des techniques propres aux algèbres de Jordan. / This thesis deals with four different but interrelated topics: variational problems on Euclidean Jordan algebras, complementarity problems on the space of symmetric matrices, angular analysis between two closed convex cones and the central path for symmetric cone linear programming.In the first part of this work we study the concept of “operator commutation” in Euclidean Jordan algebras by providing a commutation principle for variational problems involving spectral data.Our main concern of the second part is the analysis and numerical resolution of a broad class of complementarity problems on spaces of symmetric matrices. The complementarity conditions are expressed in terms of the Loewner ordering or, more generally, with respect to a dual pair of Loewnerian cones.The third part of this work is an attempt to build a general theory of critical angles for a pair of closed convex cones. The angular analysis for a pair of specially structured cones is also covered. For instance, we work with linear subspaces, polyhedral cones, revolution cones, topheavy cones and cones of matrices.The last part of this work focuses on the convergence and the limiting behavior of the central path in symmetric cone linear programming. This is done by using Jordan-algebra techniques.