Coorientador: Alfredo Pio Noronha Rodrigues Galeão. / Orientador: Gastão Inacio Krein. / Doutor

This thesis uses a variety of numerical and statistical techniques to perform high precision calculations in high energy physics using quantum field theory. It introduces the experimental motivation for the calculation of B meson form factors and includes a discussion of previous work. It then describes the modern theoretical framework describing these phenomena, outlining quantum chromodynamics and electroweak theory, and then illustrating the procedure of gauge fixing, the quantum effective action and background field gauge which is required for subsequent perturbative work. Details of the basic methodology of lattice quantum field theory are given as well as the specific formulation of the relativistic theory and nonrelativistic approximations used in this work to describe quantum chromodynamics. A comprehensive calculation of the zero recoil B to D* form factor is then presented, using state of the art lattice techniques with relativistic charm sea quarks and light sea quarks with correct physical masses, leading to a discussion of the dominant sources of uncertainty and possible resolutions of experimental tensions. Also included is preliminary work towards the full calculation of nonzero recoil matrix elements, with the aim of outlining possible future work. Finally, this thesis presents the computation of parameters correcting for radiative one loop phenomena and corrections to the kinetic coupling parameters in nonrelativistic quantum chromodynamics in order to achieve a desirable level of precision in future calculations. This is done using Monte-Carlo integration to evaluate integrals from diagrams generated using automated lattice perturbation theory in background field gauge in order to match the coefficients of the effective action between the lattice and the continuum.

Recent results at the LHCb and B-factory experiments have suggested that rare processes in B →Vγ and B → V ℓ¯ℓ decays, where V is a vector meson, show some deviation from Standard Model predictions. Although these anomalies are not yet at the level to constitute a formal discovery, they are certainly suggestive of potential New Physics effects in flavour-changing neutral currents. However, explanations within the Standard Model cannot yet be ruled out. This thesis contributes to the understanding of such anomalies in two ways. Firstly, the angular distribution of the B → KJ (→ Kπ)ℓ1¯ℓ2 decay is derived, for the full dimension-six effective weak Hamiltonian, using a generalisation of the helicity formalism to effective theories mediating b → sℓ1¯ℓ2 transitions. This approach sheds light on the origin of the underlying structure, and in the process extends the general angular distribution to decays in which the two leptons in the final state, ℓ1¯ℓ2, are not necessarily identical. An additional benefit of the derivation of the angular distribution presented in this manner is that it lends itself to a moments analysis of the decay. It is shown how the angular distribution changes in the presence of new operators, predicted to be vanishingly small in the Standard Model. Such operators could be sizeable in the presence of New Physics, but using a moments analysis enables the contribution of such operators to be assessed. Secondly, an analysis is presented of the three-particle vector and axial meson distribution amplitudes. It is shown that the distribution amplitudes of both particles are, up to QCD corrections, nearly identical. These results are applied to a new calculation of the long-distance charm loop contribution to radiative B → Vγ decays, and it is shown that the approximate symmetry can be exploited to provide an improved theoretical control in the search for New Physics contributions to right-handed currents in radiative decays.

A representação Fock-Tani é um formalismo de teoria de campos para tratar problemas envolvendo simultaneamente partículas compostas e seus constituintes. O formalismo foi originalmente desenvolvido para problemas de física atômica e nesta tese este é estendido para problemas de física hadrônica. Uma mudança de representação é implementada através de um operador unitário tal que estados mesônicos no espaço de Fock compostos por um par quark-anti- quark sejam redescritos em termos de operadores de campo de mésons elementares num espaço de Hilbert estendido. A aplicação do operador unitário a um Hamiltoniano microscópico de quarks leva a um Hamiltoniano efetivo que descreve todos os possíveis processos envolvendo quarks, anti-quarks e mésons. Esse Hamiltoniano efetivo é utilizado para estudar as interações entre mésons em baixa energia num modelo de quarks constituintes onde os quarks e anti-quarks interagem através da troca de um glúon e são confinados por um potencial fenomenológico. Este mesmo Hamiltoniano efetivo é empregado para estudar as propriedades de estados ligados mesônicos num meio a temperatura finita. Apresentamos também uma generalização do formalismo Fock-Tani para modelos de quarks sofisticados. / The Fock-Tani representation is a field theoretic formalism to deal with problems involving simultaneously composite particles and their constituents. The formalism was originally developed for problems in atomic physics and in this thesis it is extended to problems in hadron physics. A change of representation is implemented by means of a unitary operator such that Fock-space bound meson states composed by a quark- anti-quark pair are redescribed by elementary-meson field operators in an extended Hilbert space. Application of the unitary operator on a microscopic quark Hamiltonian gives rise to an effective Hamiltonian which describes all possible processes involving quarks, anti-quarks, and mesons. This effective Hamiltonian is used to study meson interactions at low energies in a constituent quark model in which quarks and anti-quarks interact through one-gluon-exchange and are confined by a phenomenological potential. This same effective Hamiltonian is employed to study the properties of meson bound states in a medium at finite temperature. We also present a generalization of the Fock-Tani formalism for sophisticated quark models.

Radiative decays of B mesons, a good example of Flavor Changing Neutral Currents, are interesting for the study of physics beyond the Standard Model, as new high-energy phenomena can enter in the loop. The LHCb experiment, designed to study b- and c-hadron physics at the LHC, is an ideal candidate for the study of this type of decays. However, in order to effectively study radiative B decays, good trigger performance is needed. Two trigger strategies have been studied, one exclusive and one inclusive: on one side, the already existing exclusive lines have been modified, and, on the other side, a new set of inclusive topological lines, specific for radiative B decays, has been introduced. Their performance in 2011 has been assessed both on simulation and on data, and the strategy for 2012 has been outlined. In addition, the full 2011 dataset collected by LHCb has been used to extract the ratio of branching fractions BR(B → K∗γ)/BR(Bs → ϕγ), which has been measured to be 1.31 ± 0.08(stat) ± 0.04(syst) ± 0.10(fs/fd). From this result, and using the well-known value for B → K∗γ, the branching fraction of Bs → ϕγ has been found to be (3.3 ± 0.3 )x10−5, largely improving previous results. This work puts the basis for future developments within the radiative decays group in LHCb, as it settles the trigger strategy on one hand and provides a detailed study of the backgrounds involved in the two studied decays, on the other. This will be very useful for future analyses, such as the CP asymmetry measurements in B → K∗γ or the photon polarization in Bs → ϕγ. / Les desintegracions dels mesons B són interessants per a l'estudi de Física més enllà del Model Estàndard, ja que són un bon exemple de Corrents Neutres amb Canvi de Sabor, molt sensibles a nova Física a altes energies a través del loop. L'experiment LHCb, dedicat a l'estudi de la física d'hadrons b i c a l'LHC, és un candidat ideal per a l'estudi d'aquest tipus de desintegracions. Tot i així, per a poder estudiar d'una manera efectiva les desintegracions radiative de mesons B a LHCb és necessària una bona resposta del trigger de l'experiment. S'han estudiat dues estratègies de trigger, una d'exclusiva i una d'inclusiva: per un costat, les línies exclusives ja existents han estat modificades, i, per l'altre, s'ha introduït un nou conjunt de línies topològiques específic per a desintegracions radiatives. S'ha estudiat el seu rendiment durant 2011 i, basant-se en els resultats obtinguts, s'ha dissenyat l'estratègia de trigger per a 2012. A més, s'han usat les dades preses per LHCb durant tot 2011 per a extreure la raó de les fraccions d'embrancament BR(B → K∗γ)/BR(Bs → ϕγ), obtenint el resultat de 1.31 ± 0.08(est) ± 0.04(sist) ± 0.10(fs/fd). A partir d'aquest resultat, i fent servir el valor ben mesurat de BR(B → K∗γ), s'ha trobat una raó d'embrancament per a Bs → ϕγ de (3.3 ± 0.3 )x10−5, millorant significativament els resultat anteriors. Aquest treball posa les bases per a futurs desenvolupaments dins del grup de desintegracions radiatives a LHCb, ja que per un costat fixa l'estratègia de trigger i, per l'altre, proporciona un estudi detallat de les diferents fonts de contaminació en la selecció de les desintegracions estudiades. Això resultarà molt útil en futurs anàlisis, tals com les mesures d'asimetria CP en B → K∗γ o la polarització del fotó en Bs → ϕγ.

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 125-160).

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This thesis presents an investigation of the charged B meson decay to the pseudoscalar-vector final state p°π±..The results presented in this thesis have been published in Physics Letters B, Volume 542, Issues 3-4, 29 August 2002, Pages 183-192.

Thesis (Ph. D.)--Ohio State University, 2008. / Title from first page of PDF file. Includes bibliographical references (p. 163-166).