Testing the Bethe ansatz with large N renormalons

The ground-state energy of integrable asymptotically free theories can be conjecturally computed using the Bethe ansatz once the theory has been coupled to an external potential through a conserved charge. This leads to a precise prediction for the perturbative expansion of the energy. We provide a non-trivial test of this prediction in the non-linear sigma model and its supersymmetric extension, by calculating analytically the associated Feynman diagrams at next-to-leading order in the 1/N expansion, and at all loops. By investigating the large order behavior of the diagrams, we locate the position of the renormalons of the theory and we obtain an analytic expression for the large N trans-series associated to each. As a spin-off of our calculation, we provide a direct derivation of the beta function of these theories, at next-to-leading order in the 1/N expansion.

Review of the direct derivation method: quantitative phase analysis with observed intensities and chemical composition data

The direct derivation (DD) method is a technique for quantitative phase analysis (QPA). It can be characterized by the use of the total sums of scattered/diffracted intensities from individual components as the observed data. The crystal structure parameters are required when we calculate the intensities of reflections or diffraction patterns. Intensity can, however, be calculated only with the chemical composition data if it is not of individual reflections but of a total sum of diffracted/scattered intensities for that material. Furthermore, it can be given in a form of the scattered intensity per unit weight. Therefore, we can calculate the weight proportion of a component material by dividing the total sum of observed scattered/diffracted intensities by the scattered intensity per unit weight. The chemical composition data of samples under investigation are known in almost all cases at the stage of QPA. Thus, a technical problem is how to separate the observed diffraction pattern of a mixture into individual component patterns. Various pattern decomposition techniques currently available can be used for separating the pattern of a mixture. In this report, the theoretical background of the DD method and various techniques for pattern decompositions are reviewed along with the examples of applications.

Heavy Minerals Study of Sandstone from the Late Miocene-Early Pliocene Mukdadiya Formation; Kirkuk, Iraq: Implications for Provenance

Mukdadiya Formation (Late Miocene-Pliocene) exposed in the northeastern limb of Baba anticline fold in Kirkuk structure. The selected section was located in the Shoraw area, northeastern Kirkuk city, Iraq. Twenty sandstone samples were collected to study heavy minerals. The study indicates that opaque and epidote group minerals forming the main heavy minerals, followed by amphibole, pyroxene, garnet, and chlorite. According to heavy minerals assemblage, the source rocks are interpreted to be composed essentially of sedimentary followed by igneous and metamorphic rocks and the high contents of unstable and metastable minerals confirm their direct derivation from the adjacent primary source. Ultra-stable and metastable heavy minerals relationship indicated that the sandstone of the Mukdadiya Formation is immature and moderate stability and showed that these minerals couldn't be transported for very long distances close to the source area and not represents polycyclic grain. MF-MT-GM Ternary diagram showed that the studied samples fall within the field of active continental margins which is characterized by a relatively high percentage of minerals (MF˃GM) derived from mafic magmatic rocks.

Decomposition of Feynman integrals by multivariate intersection numbers

We present a detailed description of the recent idea for a direct decomposition of Feynman integrals onto a basis of master integrals by projections, as well as a direct derivation of the differential equations satisfied by the master integrals, employing multivariate intersection numbers. We discuss a recursive algorithm for the computation of multivariate intersection numbers, and provide three different approaches for a direct decomposition of Feynman integrals, which we dub thestraight decomposition, thebottom-up decomposition, and thetop-down decomposition. These algorithms exploit the unitarity structure of Feynman integrals by computing intersection numbers supported on cuts, in various orders, thus showing the synthesis of the intersection-theory concepts with unitarity-based methods and integrand decomposition. We perform explicit computations to exemplify all of these approaches applied to Feynman integrals, paving a way towards potential applications to generic multi-loop integrals.

Pilot study of microelimination in hepatitis C: direct derivation between drug centers and the hepatology unit in a university hospital.

Resumen Introducción: Siguiendo las recomendaciones de la OMS para eliminar la hepatitis C (2030) se han elaborado múltiples estrategias de micro/macroeliminación. Dentro de las estrategias de microeliminación debe incluirse la búsqueda activa y la simplificación del manejo de la infección en poblaciones de riesgo como los usuarios adictos a drogas. Material y métodos: Se han analizado de manera descriptiva variables demográficas, clínicas, analíticas, virológicas, de adherencia y de tratamiento de los pacientes derivados desde dos centros de drogodependencia de Málaga capital a la Unidad de Hepatología de un Hospital Universitario en Málaga durante el año 2019 mediante un proceso de derivación simplificado. Resultados: Se incluyeron un total de 24 pacientes de los cuales 17 (70,8%) acudieron a la primera consulta, resultando el 70,6% virémicos. Se pautaron 10 tratamientos con antivirales de acción directa. La adherencia al tratamiento fue del 80% y a consulta tras una primera visita en Hepatología fue del 91,6%. Conclusiones: La estrategia implantada en este estudio piloto ha simplificado el diagnóstico y el tratamiento de los pacientes con adicciones y hepatitis C reduciendo el número de visitas de 9 a un máximo de 3 para la prescripción del tratamiento antiviral permitiendo el aumento de pacientes que acuden a la consulta especializada. A pesar de este avance, sigue habiendo un 29% de los pacientes enviados desde estos centros que no acuden a su primera visita. Por lo tanto, creemos de importancia seguir avanzando en la accesibilidad y la simplificación en el diagnóstico y tratamiento de estos pacientes.

Size of bulk fermions in the SYK model

The study of quantum gravity in the form of the holographic duality has uncovered and motivated the detailed investigation of various diagnostics of quantum chaos. One such measure is the operator size distribution, which characterizes the size of the support region of an operator and its evolution under Heisenberg evolution. In this work, we examine the role of the operator size distribution in holographic duality for the Sachdev-Ye-Kitaev (SYK) model. Using an explicit construction of AdS2 bulk fermion operators in a putative dual of the low temperature SYK model, we study the operator size distribution of the boundary and bulk fermions. Our result provides a direct derivation of the relationship between (effective) operator size of both the boundary and bulk fermions and bulk SL(2; ℝ) generators.

Accurate and time-saving quantification of a component present in a very small amount in a mixture by the direct derivation method

In quantitative phase analysis (QPA) using the direct derivation (DD) method, total sums of diffracted/scattered intensities for individual components are used as observed quantities. Fluctuation in their relative intensity ratios induces errors in derived weight fractions, and it ought to be suppressed for improving the accuracy in QPA, in particular, of a component that is present in a small amount. The fluctuation is primarily caused by the termination in summing/integrating diffracted/scattered intensities on the high-angle side. It is usually associated with changing the 2θ range in whole-powder-pattern fitting (WPPF) used to decompose the mixture pattern into individual component patterns. In this study, calculated patterns for individual components, fitted in WPPF, are normalized so as to give the unit area when they are separately integrated over their definition ranges in 2θ. The termination effect could effectively be reduced by extending the definition range to a certain high-angle limit. Scale parameters for adjusting the calculated patterns become non-fluctuating against the change of the 2θ range in WPPF. Thus, the time spent for intensity data collection of mixture patterns can be reduced by shortening the scan range. The present procedure has been tested with binary mixtures containing small amounts of crystalline phases of 0.02–0.4 wt%. QPA could be conducted with errors of 0.01–0.03 wt% for both inorganic materials chosen as ideal samples and pharmaceutical materials as practical ones. QPA of an amorphous component present in a small amount is also discussed.