Virtual Compton scattering in baryon chiral perturbation theory

This thesis is concerned with the calculation of virtual Compton scattering (VCS) in manifestly Lorentz-invariant baryon chiral perturbation theory to fourth order in the momentum and quark-mass expansion. In the one-photon-exchange approximation, the VCS process is experimentally accessible in photon electro-production and has been measured at the MAMI facility in Mainz, at MIT-Bates, and at Jefferson Lab. Through VCS one gains new information on the nucleon structure beyond its static properties, such as charge, magnetic moments, or form factors. The nucleon response to an incident electromagnetic field is parameterized in terms of 2 spin-independent (scalar) and 4 spin-dependent (vector) generalized polarizabilities (GP). In analogy to classical electrodynamics the two scalar GPs represent the induced electric and magnetic dipole polarizability of a medium. For the vector GPs, a classical interpretation is less straightforward. They are derived from a multipole expansion of the VCS amplitude. This thesis describes the first calculation of all GPs within the framework of manifestly Lorentz-invariant baryon chiral perturbation theory. Because of the comparatively large number of diagrams - 100 one-loop diagrams need to be calculated - several computer programs were developed dealing with different aspects of Feynman diagram calculations. One can distinguish between two areas of development, the first concerning the algebraic manipulations of large expressions, and the second dealing with numerical instabilities in the calculation of one-loop integrals. In this thesis we describe our approach using Mathematica and FORM for algebraic tasks, and C for the numerical evaluations. We use our results for real Compton scattering to fix the two unknown low-energy constants emerging at fourth order. Furthermore, we present the results for the differential cross sections and the generalized polarizabilities of VCS off the proton.

Black hole scattering from Worldline Quantum Field Theory and the Classical Double Copy of Spinning particles

This PhD thesis focuses on studying the classical scattering of massive/massless particles toward black holes, and investigating double copy relations between classical observables in gauge theories and gravity. This is done in the Post-Minkowskian approximation i.e. a perturbative expansion of observables controlled by the gravitational coupling constant κ = 32πGN, with GN being the Newtonian coupling constant. The investigation is performed by using the Worldline Quantum Field Theory (WQFT), displaying a worldline path integral describing the scattering objects and a QFT path integral in the Born approximation, describing the intermediate bosons exchanged in the scattering event by the massive/massless particles. We introduce the WQFT, by deriving a relation between the Kosower- Maybee-O’Connell (KMOC) limit of amplitudes and worldline path integrals, then, we use that to study the classical Compton amplitude and higher point amplitudes. We also present a nice application of our formulation to the case of Hard Thermal Loops (HTL), by explicitly evaluating hard thermal currents in gauge theory and gravity. Next we move to the investigation of the classical double copy (CDC), which is a powerful tool to generate integrands for classical observables related to the binary inspiralling problem in General Relativity. In order to use a Bern-Carrasco-Johansson (BCJ) like prescription, straight at the classical level, one has to identify a double copy (DC) kernel, encoding the locality structure of the classical amplitude. Such kernel is evaluated by using a theory where scalar particles interacts through bi-adjoint scalars. We show here how to push forward the classical double copy so to account for spinning particles, in the framework of the WQFT. Here the quantization procedure on the worldline allows us to fully reconstruct the quantum theory on the gravitational side. Next we investigate how to describe the scattering of massless particles off black holes in the WQFT.

Thermal instability in a gravity-like scalar theory

We study the question of stability of the ground state of a scalar theory which is a generalization of the phi(3) theory and has some similarity to gravity with a cosmological constant. We show that the ground state of the theory at zero temperature becomes unstable above a certain critical temperature, which is evaluated in closed form at high temperature.

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially nonperturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with nontrivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.

Scattering of massless scalar waves by Reissner-Nordstrom black holes

We present a study of scattering of massless planar scalar waves by a charged nonrotating black hole. Partial wave methods are applied to compute scattering and absorption cross sections, for a range of incident wavelengths. We compare our numerical results with semiclassical approximations from a geodesic analysis, and find excellent agreement. The glory in the backward direction is studied, and its properties are shown to be related to the properties of the photon orbit. The effects of the black hole charge upon scattering and absorption are examined in detail. As the charge of the black hole is increased, we find that the absorption cross section decreases, and the angular width of the interference fringes of the scattering cross section at large angles increases. In particular, the glory spot in the backward direction becomes wider. We interpret these effects under the light of our geodesic analysis.

Structure, stability, depolarized light scattering, and vibrational spectra of fullerenols from all-electron density-functional-theory calculations

We have investigated the stability, electronic properties, Rayleigh (elastic), and Raman (inelastic) depolarization ratios, infrared and Raman absorption vibrational spectra of fullerenols [C(60)(OH)(n)] with different degrees of hydroxylation by using all-electron density-functional-theory (DFT) methods. Stable arrangements of these molecules were found by means of full geometry optimizations using Becke's three-parameter exchange functional with the Lee, Yang, and Parr correlation functional. This DFT level has been combined with the 6-31G(d,p) Gaussian-type basis set, as a compromise between accuracy and capability to treat highly hydroxylated fullerenes, e.g., C(60)(OH)(36). Thus, the molecular properties of fullerenols were systematically analyzed for structures with n=1, 2, 3, 4, 8, 10, 16, 18, 24, 32, and 36. From the electronic structure analysis of these molecules, we have evidenced an important effect related to the weak chemical reactivity of a possible C(60)(OH)(24) isomer. To investigate Raman scattering and the vibrational spectra of the different fullerenols, frequency calculations are carried out within the harmonic approximation. In this case a systematic study is only performed for n=1-4, 8, 10, 16, 18, and 24. Our results give good agreements with the expected changes in the spectral absorptions due to the hydroxylation of fullerenes.

Cross section of a resonant-mass detector for scalar gravitational waves

Gravitationally coupled scalar fields, originally introduced by Jordan, Brans and Dicke to account for a non-constant gravitational coupling, are a prediction of many non-Einsteinian theories of gravity not excluding perturbative formulations of string theory. In this paper, we compute the cross sections for scattering and absorption of scalar and tensor gravitational waves by a resonant-mass detector in the framework of the Jordan-Brans-Dicke theory. The results are then specialized to the case of a detector of spherical shape and shown to reproduce those obtained in general relativity in a certain limit. Eventually we discuss the potential detectability of scalar waves emitted in a spherically symmetric gravitational collapse.

Scattering of quantum particles by gravitational plane waves

We consider the coupling of quantum massless and massive scalar particles with exact gravitational plane waves. The cross section for scattering of the quantum particles by the waves is shown to coincide with the classical cross section for scattering of geodesics. The expectation value of the scalar field stress tensor between scattering states diverges at the points where classical test particles focus after colliding with the wave. This indicates that back-reaction effects cannot be ignored for plane waves propagating in the presence of quantum particles and that classical singularities are likely to develop.

The domain derivative in rough-surface scattering and rigorous estimates for first-order perturbation theory

We investigate Fréchet differentiability of the scattered field with respect to variation in the boundary in the case of time–harmonic acoustic scattering by an unbounded, sound–soft, one–dimensional rough surface. We rigorously prove the differentiability of the scattered field and derive a characterization of the Fréchet derivative as the solution to a Dirichlet boundary value problem. As an application of these results we give rigorous error estimates for first–order perturbation theory, justifying small perturbation methods that have a long history in the engineering literature. As an application of our rigorous estimates we show that a plane acoustic wave incident on a sound–soft rough surface can produce an unbounded scattered field.

Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Duffin-Kemmer-Petiau theory in the causal approach

In this paper we consider the scalar sector of Duffin-Kemmer-Petiau theory in the framework of Epstein-Glaser causal method. We calculate the lowest order distributions for Compton scattering, vacuum polarization, self-energy and vertex corrections. By requiring gauge invariance of the theory we recover, in a natural way, the scalar propagator of the usual effective theory.

alpha alpha scattering in halo effective field theory

We study the two-alpha-particle (alpha alpha) system in an Effective Field Theory (EFT) for halo-like systems. We propose a power Counting that incorporates the subtle interplay of strong and electromagnetic forces leading to a narrow resonance at an energy of about 0.1 MeV. We investigate the EFT expansion in detail, and compare its results with existing low-energy aa phase shifts and previously determined effective-range parameters. Good description of the data is obtained with a surprising amount of fine-tuning. This scenario can be viewed as an expansion around the limit where, when electromagnetic interactions are turned off, the (8)Be ground state is at threshold and exhibits conformal invariance. We also discuss possible extensions to systems with more than two alpha particles. (c) 2008 Elsevier B.V. All rights reserved.

Scalar quantum field theory in disordered media

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

NONLINEAR SCALAR COUPLING MODELS AND PROTON-NUCLEUS SCATTERING OBSERVABLES

The effects of nonlinear scalar field couplings on elastic proton-nucleus scattering observables are investigated using a relativistic impulse approximation. Nonlinear couplings affect in a nontrivial way the effective nucleon mass and the nuclear scalar and vector densities. Modifications on the densities might have observable consequences on scattering observables. Our investigation indicates that the description of the observables for the reactions p-O-16 and p-Ca-40 at 200 MeV are not greatly modified with the use of nonlinear models in comparison with the description using linear models.

Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)