Light-by-light scattering and muon’s anomalous magnetic moment

A study of hadron production by photons opens unique ways to address a number of fundamental problems in strong interaction physics as well as fundamental questions in Quantum Field Theory. In particular, an understanding of two-photon processes is of crucial importance for constraining the hadronic uncertainties in precision measurements and in searches for new physics. The process of

BCJ-relations in quantum field theory

BCJ-relations have a series of important consequences in Quantum FieldrnTheory and in Gravity. In QFT, one can use BCJ-relations to reduce thernnumber of independent colour-ordered partial amplitudes and to relate nonplanarrnand planar diagrams in loop calculations. In addition, one can usernBCJ-numerators to construct gravity scattering amplitudes through a squaringrn procedure. For these reasons, it is important to nd a prescription tornobtain BCJ-numerators without requiring a diagram by diagram approach.rnIn this thesis, after introducing some basic concepts needed for the discussion,rnI will examine the existing diagrammatic prescriptions to obtainrnBCJ-numerators. Subsequently, I will present an algorithm to construct anrneective Yang-Mills Lagrangian which automatically produces kinematic numeratorsrnsatisfying BCJ-relations. A discussion on the kinematic algebrarnfound through scattering equations will then be presented as a way to xrnnon-uniqueness problems in the algorithm.

The dynamics of ultra-thin polymer films in different confinements studied by resonance enhanced dynamic light scattering

Die Kontroverse über den Glasübergang im Nanometerbereich, z. B. die Glas¬über¬gangs-temperatur Tg von dünnen Polymerfilmen, ist nicht vollständig abgeschlossen. Das dynamische Verhalten auf der Nanoskala ist stark von den einschränkenden Bedingungen abhängig, die auf die Probe wirken. Dünne Polymerfilme sind ideale Systeme um die Dynamik von Polymerketten unter der Einwirkung von Randbedingungen zu untersuchen, wie ich sie in dieser Arbeit variiert habe, um Einblick in dieses Problem zu erhalten.rnrnResonanzverstärkte dynamische Lichtstreuung ist eine Methode, frei von z.B. Fluoreszenzmarkern, die genutzt werden kann um in dünnen Polymerfilmen dynamische Phänomene

Towards a data-driven analysis of hadronic light-by-light scattering

The hadronic light-by-light contribution to the anomalous magnetic moment of the muon was recently analyzed in the framework of dispersion theory, providing a systematic formalism where all input quantities are expressed in terms of on-shell form factors and scattering amplitudes that are in principle accessible in experiment. We briefly review the main ideas behind this framework and discuss the various experimental ingredients needed for the evaluation of one- and two-pion intermediate states. In particular, we identify processes that in the absence of data for doubly-virtual pion–photon interactions can help constrain parameters in the dispersive reconstruction of the relevant input quantities, the pion transition form factor and the helicity partial waves for γ⁎γ⁎→ππ.

Dispersive approach to hadronic light-by-light scattering

Based on dispersion theory, we present a formalism for a model-independent evaluation of the hadronic light-by-light contribution to the anomalous magnetic moment of the muon. In particular, we comment on the definition of the pion pole in this framework and provide a master formula that relates the effect from ππ intermediate states to the partial waves for the process γ * γ * → ππ. All contributions are expressed in terms of on-shell form factors and scattering amplitudes, and as such amenable to an experimental determination.

Accurate evaluation of hadronic uncertainties in spin-independent WIMP-nucleon scattering: Disentangling two- and three-flavor effects

We show how to avoid unnecessary and uncontrolled assumptions usually made in the literature about soft SU(3) flavor symmetry breaking in determining the two-flavor nucleon matrix elements relevant for direct detection of weakly interacting massive particles (WIMPs). Based on SU(2) chiral perturbation theory, we provide expressions for the proton and neutron scalar couplings fp,nu and fp,nd with the pion-nucleon σ term as the only free parameter, which should be used in the analysis of direct detection experiments. This approach for the first time allows for an accurate assessment of hadronic uncertainties in spin-independent WIMP-nucleon scattering and for a reliable calculation of isospin-violating effects. We find that the traditional determinations of Vfpu−fnu and fpd−fnd are off by a factor of 2.

Dispersive approach to hadronic light-by-light scattering and the muon ɡ − 2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (ɡ − 2)μ come from hadronic contributions. In particular, it can be expected that in a few years the subleading hadronic light-by-light (HLbL) contribution will dominate the theory uncertainty. We present a dispersive description of the HLbL tensor. This new, model-independent approach opens up an avenue towards a data-driven determination of the HLbL contribution to the (ɡ − 2)μ.

Hadronic light-by-light scattering and the muon g−2

The largest uncertainties in the Standard Model calculation of the anomalous magnetic moment of the muon (g − 2)μ come from hadronic contributions. In particular, it can be expected that in a few years the subleading hadronic light-by-light (HLbL) contribution will dominate the theory uncertainty. We present a dispersive description of the HLbL tensor, which is based on unitarity, analyticity, crossing symmetry, and gauge invariance. Such a model-independent Approach opens up an avenue towards a data-driven determination of the HLbL contribution to the (g − 2)μ.

Nondestructive quantification of chemical and physical properties of fruits by time-resolved reflectance spectroscopy in the wavelength range 650-1000 nm

Time-resolved reflectance spectroscopy can be used to assess nondestructively the bulk (rather than the superficial) optical properties of highly diffusive media. A fully automated system for time-resolved reflectance spectroscopy was used to evaluate the absorption and the transport scattering spectra of fruits in the red and the near-infrared regions. In particular, data were collected in the range 650-1000 nm from three varieties of apples and from peaches, kiwifruits, and tomatoes. The absorption spectra were usually dominated by the water peak near 970 nm, whereas chlorophyll was detected at 675 nm. For ail species the scattering decreased progressively with increasing wavelength. A best fit to water and chlorophyll absorption line shapes and to Mie theory permitted the estimation of water and chlorophyll content and the average size of scattering centers in the bulls; of intact fruits.

A canonical UTD solution for electromagnetic scattering by an electrically large impedance circular cylinder illuminated by an obliquely incident plane wave

A uniform geometrical theory of diffraction (UTD) solution is developed for the canonical problem of the electromagnetic (EM) scattering by an electrically large circular cylinder with a uniform impedance boundary condition (IBC), when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transform, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the geometrical optics (GO) or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution.

Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder

Con esta tesis ”Desarrollo de una Teoría Uniforme de la Difracción para el Análisis de los Campos Electromagnéticos Dispersados y Superficiales sobre un Cilindro” hemos iniciado una nueva línea de investigación que trata de responder a la siguiente pregunta: ¿cuál es la impedancia de superficie que describe una estructura de conductor eléctrico perfecto (PEC) convexa recubierta por un material no conductor? Este tipo de estudios tienen interés hoy en día porque ayudan a predecir el campo electromagnético incidente, radiado o que se propaga sobre estructuras metálicas y localmente convexas que se encuentran recubiertas de algún material dieléctrico, o sobre estructuras metálicas con pérdidas, como por ejemplo se necesita en determinadas aplicaciones aeroespaciales, marítimas o automovilísticas. Además, desde un punto de vista teórico, la caracterización de la impedancia de superficie de una estructura PEC recubierta o no por un dieléctrico es una generalización de varias soluciones que tratan ambos tipos de problemas por separado. En esta tesis se desarrolla una teoría uniforme de la difracción (UTD) para analizar el problema canónico del campo electromagnético dispersado y superficial en un cilindro circular eléctricamente grande con una condición de contorno de impedancia (IBC) para frecuencias altas. Construir una solución basada en UTD para este problema canónico es crucial en el desarrollo de un método UTD para el caso más general de una superficie arbitrariamente convexa, mediante el uso del principio de localización de los campos electromagnéticos a altas frecuencias. Esta tesis doctoral se ha llevado a cabo a través de una serie de hitos que se enumeran a continuación, enfatizando las contribuciones a las que ha dado lugar. Inicialmente se realiza una revisión en profundidad del estado del arte de los métodos asintóticos con numerosas referencias. As í, cualquier lector novel puede llegar a conocer la historia de la óptica geométrica (GO) y la teoría geométrica de la difracción (GTD), que dieron lugar al desarrollo de la UTD. Después, se investiga ampliamente la UTD y los trabajos más importantes que pueden encontrarse en la literatura. As í, este capítulo, nos coloca en la posición de afirmar que, hasta donde nosotros conocemos, nadie ha intentado antes llevar a cabo una investigación rigurosa sobre la caracterización de la impedancia de superficie de una estructura PEC recubierta por un material dieléctrico, utilizando para ello la UTD. Primero, se desarrolla una UTD para el problema canónico de la dispersión electromagnética de un cilindro circular eléctricamente grande con una IBC uniforme, cuando es iluminado por una onda plana con incidencia oblicua a frecuencias altas. La solución a este problema canónico se construye a partir de una solución exacta mediante una expansión de autofunciones de propagación radial. Entonces, ésta se convierte en una nueva expansión de autofunciones de propagación circunferencial muy apropiada para cilindros grandes, a través de la transformación de Watson. De esta forma, la expresión del campo se reduce a una integral que se evalúa asintóticamente, para altas frecuencias, de manera uniforme. El resultado se expresa según el trazado de rayos descrito en la UTD. La solución es uniforme porque tiene la importante propiedad de mantenerse continua a lo largo de la región de transición, a ambos lados de la superficie del contorno de sombra. Fuera de la región de transición la solución se reduce al campo incidente y reflejado puramente ópticos en la región iluminada del cilindro, y al campo superficial difractado en la región de sombra. Debido a la IBC el campo dispersado contiene una componente contrapolar a causa de un acoplamiento entre las ondas TEz y TMz (donde z es el eje del cilindro). Esta componente contrapolar desaparece cuando la incidencia es normal al cilindro, y también en la región iluminada cuando la incidencia es oblicua donde el campo se reduce a la solución de GO. La solución UTD presenta una muy buena exactitud cuando se compara numéricamente con una solución de referencia exacta. A continuación, se desarrolla una IBC efectiva para el cálculo del campo electromagnético dispersado en un cilindro circular PEC recubierto por un dieléctrico e iluminado por una onda plana incidiendo oblicuamente. Para ello se derivan dos impedancias de superficie en relación directa con las ondas creeping y de superficie TM y TE que se excitan en un cilindro recubierto por un material no conductor. Las impedancias de superficie TM y TE están acopladas cuando la incidencia es oblicua, y dependen de la geometría del problema y de los números de onda. Además, se ha derivado una impedancia de superficie constante, aunque con diferente valor cuando el observador se encuentra en la zona iluminada o en la zona de sombra. Después, se presenta una solución UTD para el cálculo de la dispersión de una onda plana con incidencia oblicua sobre un cilindro eléctricamente grande y convexo, mediante la generalización del problema canónico correspondiente al cilindro circular. La solución asintótica es uniforme porque se mantiene continua a lo largo de la región de transición, en las inmediaciones del contorno de sombra, y se reduce a la solución de rayos ópticos en la zona iluminada y a la contribución de las ondas de superficie dentro de la zona de sombra, lejos de la región de transición. Cuando se usa cualquier material no conductor se excita una componente contrapolar que tiende a desaparecer cuando la incidencia es normal al cilindro y en la región iluminada. Se discuten ampliamente las limitaciones de las fórmulas para la impedancia de superficie efectiva, y se compara la solución UTD con otras soluciones de referencia, donde se observa una muy buena concordancia. Y en tercer lugar, se presenta una aproximación para una impedancia de superficie efectiva para el cálculo de los campos superficiales en un cilindro circular conductor recubierto por un dieléctrico. Se discuten las principales diferencias que existen entre un cilindro PEC recubierto por un dieléctrico desde un punto de vista riguroso y un cilindro con una IBC. Mientras para un cilindro de impedancia se considera una impedancia de superficie constante o uniforme, para un cilindro conductor recubierto por un dieléctrico se derivan dos impedancias de superficie. Estas impedancias de superficie están asociadas a los modos de ondas creeping TM y TE excitadas en un cilindro, y dependen de la posición y de la orientación del observador y de la fuente. Con esto en mente, se deriva una solución UTD con IBC para los campos superficiales teniendo en cuenta las dependencias de la impedancia de superficie. La expansión asintótica se realiza, mediante la transformación de Watson, sobre la representación en serie de las funciones de Green correspondientes, evitando as í calcular las derivadas de orden superior de las integrales de tipo Fock, y dando lugar a una solución rápida y precisa. En los ejemplos numéricos realizados se observa una muy buena precisión cuando el cilindro y la separación entre el observador y la fuente son grandes. Esta solución, junto con el método de los momentos (MoM), se puede aplicar para el cálculo eficiente del acoplamiento mutuo de grandes arrays conformados de antenas de parches. Los métodos propuestos basados en UTD para el cálculo del campo electromagnético dispersado y superficial sobre un cilindro PEC recubierto de dieléctrico con una IBC efectiva suponen un primer paso hacia la generalización de una solución UTD para superficies metálicas convexas arbitrarias cubiertas por un material no conductor e iluminadas por una fuente electromagnética arbitraria. ABSTRACT With this thesis ”Development of a Uniform Theory of Diffraction for Scattered and Surface Electromagnetic Field Analysis on a Cylinder” we have initiated a line of investigation whose goal is to answer the following question: what is the surface impedance which describes a perfect electric conductor (PEC) convex structure covered by a material coating? These studies are of current and future interest for predicting the electromagnetic (EM) fields incident, radiating or propagating on locally smooth convex parts of highly metallic structures with a material coating, or by a lossy metallic surfaces, as for example in aerospace, maritime and automotive applications. Moreover, from a theoretical point of view, the surface impedance characterization of PEC surfaces with or without a material coating represents a generalization of independent solutions for both type of problems. A uniform geometrical theory of diffraction (UTD) is developed in this thesis for analyzing the canonical problem of EM scattered and surface field by an electrically large circular cylinder with an impedance boundary condition (IBC) in the high frequency regime, by means of a surface impedance characterization. The construction of a UTD solution for this canonical problem is crucial for the development of the corresponding UTD solution for the more general case of an arbitrary smooth convex surface, via the principle of the localization of high frequency EM fields. The development of the present doctoral thesis has been carried out through a series of landmarks that are enumerated as follows, emphasizing the main contributions that this work has given rise to. Initially, a profound revision is made in the state of art of asymptotic methods where numerous references are given. Thus, any reader may know the history of geometrical optics (GO) and geometrical theory of diffraction (GTD), which led to the development of UTD. Then, the UTD is deeply investigated and the main studies which are found in the literature are shown. This chapter situates us in the position to state that, as far as we know, nobody has attempted before to perform a rigorous research about the surface impedance characterization for material-coated PEC convex structures via UTD. First, a UTD solution is developed for the canonical problem of the EM scattering by an electrically large circular cylinder with a uniform IBC, when it is illuminated by an obliquely incident high frequency plane wave. A solution to this canonical problem is first constructed in terms of an exact formulation involving a radially propagating eigenfunction expansion. The latter is converted into a circumferentially propagating eigenfunction expansion suited for large cylinders, via the Watson transformation, which is expressed as an integral that is subsequently evaluated asymptotically, for high frequencies, in a uniform manner. The resulting solution is then expressed in the desired UTD ray form. This solution is uniform in the sense that it has the important property that it remains continuous across the transition region on either side of the surface shadow boundary. Outside the shadow boundary transition region it recovers the purely ray optical incident and reflected ray fields on the deep lit side of the shadow boundary and to the modal surface diffracted ray fields on the deep shadow side. The scattered field is seen to have a cross-polarized component due to the coupling between the TEz and TMz waves (where z is the cylinder axis) resulting from the IBC. Such cross-polarization vanishes for normal incidence on the cylinder, and also in the deep lit region for oblique incidence where it properly reduces to the GO or ray optical solution. This UTD solution is shown to be very accurate by a numerical comparison with an exact reference solution. Then, an effective IBC is developed for the EM scattered field on a coated PEC circular cylinder illuminated by an obliquely incident plane wave. Two surface impedances are derived in a direct relation with the TM and TE surface and creeping wave modes excited on a coated cylinder. The TM and TE surface impedances are coupled at oblique incidence, and depend on the geometry of the problem and the wave numbers. Nevertheless, a constant surface impedance is found, although with a different value when the observation point lays in the lit or in the shadow region. Then, a UTD solution for the scattering of an obliquely incident plane wave on an electrically large smooth convex coated PEC cylinder is introduced, via a generalization of the canonical circular cylinder problem. The asymptotic solution is uniform because it remains continuous across the transition region, in the vicinity of the shadow boundary, and it recovers the ray optical solution in the deep lit region and the creeping wave formulation within the deep shadow region. When a coating is present a cross-polar field term is excited, which vanishes at normal incidence and in the deep lit region. The limitations of the effective surface impedance formulas are discussed, and the UTD solution is compared with some reference solutions where a very good agreement is met. And in third place, an effective surface impedance approach is introduced for determining surface fields on an electrically large coated metallic circular cylinder. Differences in analysis of rigorouslytreated coated metallic cylinders and cylinders with an IBC are discussed. While for the impedance cylinder case a single constant or uniform surface impedance is considered, for the coated metallic cylinder case two surface impedances are derived. These are associated with the TM and TE creeping wave modes excited on a cylinder and depend on observation and source positions and orientations. With this in mind, a UTD based method with IBC is derived for the surface fields by taking into account the surface impedance variation. The asymptotic expansion is performed, via the Watson transformation, over the appropriate series representation of the Green’s functions, thus avoiding higher-order derivatives of Fock-type integrals, and yielding a fast and an accurate solution. Numerical examples reveal a very good accuracy for large cylinders when the separation between the observation and the source point is large. Thus, this solution could be efficiently applied in mutual coupling analysis, along with the method of moments (MoM), of large conformal microstrip array antennas. The proposed UTD methods for scattered and surface EM field analysis on a coated PEC cylinder with an effective IBC are considered the first steps toward the generalization of a UTD solution for large arbitrarily convex smooth metallic surfaces covered by a material coating and illuminated by an arbitrary EM source.

Multipole expansion of strongly focussed laser beams

Multipole expansion of an incident radiation field-that is, representation of the fields as sums of vector spherical wavefunctions-is essential for theoretical light scattering methods such as the T-matrix method and generalised Lorenz-Mie theory (GLMT). In general, it is theoretically straightforward to find a vector spherical wavefunction representation of an arbitrary radiation field. For example, a simple formula results in the useful case of an incident plane wave. Laser beams present some difficulties. These problems are not a result of any deficiency in the basic process of spherical wavefunction expansion, but are due to the fact that laser beams, in their standard representations, are not radiation fields, but only approximations of radiation fields. This results from the standard laser beam representations being solutions to the paraxial scalar wave equation. We present an efficient method for determining the multipole representation of an arbitrary focussed beam. (C) 2003 Elsevier Science Ltd. All rights reserved.

Quantitative scattering of melanin solutions

The optical scattering coefficient of a dilute, well-solubilized eumelanin solution has been accurately measured as a function of incident wavelength, and found to contribute < 6% of the total optical attenuation between 210 and 325 nm. At longer wavelengths (325-800 nm), the scattering was less than the minimum sensitivity of our instrument. This indicates that ultraviolet and visible optical density spectra can be interpreted as true absorption with a high degree of confidence. The scattering coefficient versus wavelength was found to be consistent with Rayleigh theory for a particle radius of 38 6 1 nm. Our results shed important light on the role of melanins as photoprotectants.

Measuring and predicting the dynamics of linear monodisperse entangled polymers in rapid flow through an abrupt contraction. A small angle neutron scattering study

Small-angle neutron scattering measurements on a series of monodisperse linear entangled polystyrene melts in nonlinear flow through an abrupt 4:1 contraction have been made. Clear signatures of melt deformation and subsequent relaxation can be observed in the scattering patterns, which were taken along the centerline. These data are compared with the predictions of a recently derived molecular theory. Two levels of molecular theory are used: a detailed equation describing the evolution of molecular structure over all length scales relevant to the scattering data and a simplified version of the model, which is suitable for finite element computations. The velocity field for the complex melt flow is computed using the simplified model and scattering predictions are made by feeding these flow histories into the detailed model. The modeling quantitatively captures the full scattering intensity patterns over a broad range of data with independent variation of position within the contraction geometry, bulk flow rate and melt molecular weight. The study provides a strong, quantitative validation of current theoretical ideas concerning the microscopic dynamics of entangled polymers which builds upon existing comparisons with nonlinear mechanical stress data. Furthermore, we are able to confirm the appreciable length scale dependence of relaxation in polymer melts and highlight some wider implications of this phenomenon.