The method of unitary clothing transformations in the theory of nucleon-nucleon scattering

The clothing procedure, put forward in quantum field theory by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N-N) scattering. We consider pseudoscalar, vector and scalar meson fields interacting with 1/2 spin fermion ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T-matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation with its huge amount of virtual processes. We have derived the Lippmann-Schwinger-type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space of hadronic states and elaborated a code for its numerical solution in momentum space.Comment: 10 pages, 3 eps figures, proceedings of "19th International IUPAP Conference on Few-Body Problems in Physics"(FB19), 30Aug-05Sep 2009, Bonn, German

Numerical integration of massive two-loop Mellin-Barnes integrals in Minkowskian regions

Mellin-Barnes (MB) techniques applied to integrals emerging in particle physics perturbative calculations are summarized. New versions of AMBRE packages which construct planar and nonplanar MB representations are shortly discussed. The numerical package MBnumerics.m is presented for the first time which is able to calculate with a high precision multidimensional MB integrals in Minkowskian regions. Examples are given for massive vertex integrals which include threshold effects and several scale parameters.Comment: Proceedings for 13th DESY Workshop on Elementary Particle Physics: Loops and Legs in Quantum Field Theory (LL2016), final PoS versio

Some Remarks on Non-Planar Diagrams

Two criteria for planarity of a Feynman diagram upon its propagators (momentum flows) are presented. Instructive Mathematica programs that solve the problem and examples are provided. A simple geometric argument is used to show that while one can planarize non-planar graphs by embedding them on higher-genus surfaces (in the example it is a torus), there is still a problem with defining appropriate dual variables since the corresponding faces of the graph are absorbed by torus generators.Comment: Presented by K. Bielas at the International Conference of Theoretical Physics "Matter To The Deepest", Ustron 201

Complete electroweak two-loop corrections to Z boson production and decay

This article presents results for the last unknown two-loop contributions to the $Z$-boson partial widths and $Z$-peak cross-section. These are the so-called bosonic electroweak two-loop corrections, where "bosonic" refers to diagrams without closed fermion loops. Together with the corresponding results for the $Z$-pole asymmetries $A_l, A_b$, which have been presented earlier, this completes the theoretical description of $Z$-boson precision observables at full two-loop precision within the Standard Model. The calculation has been achieved through a combination of different methods: (a) numerical integration of Mellin-Barnes representations with contour rotations and contour shifts to improve convergence; (b) sector decomposition with numerical integration over Feynman parameters; (c) dispersion relations for sub-loop insertions. Numerical results are presented in the form of simple parameterization formulae for the total width, $\Gamma_{\rm Z}$, partial decay widths $\Gamma_{e,\mu},\Gamma_{\tau},\Gamma_{\nu},\Gamma_{u},\Gamma_{c},\Gamma_{d,s},\Gamma_{b}$, branching ratios $R_l,R_c,R_b$ and the hadronic peak cross-section, $\sigma_{\rm had}^0$. Theoretical intrinsic uncertainties from missing higher orders are also discussed.Comment: 10 page

New prospects for the numerical calculation of Mellin-Barnes integrals in Minkowskian kinematics

During the last several years remarkable progress has been made in numerical calculations of dimensionally regulated multi-loop Feynman diagrams using Mellin-Barnes (MB) representations. The bottlenecks were non-planar diagrams and Minkowskian kinematics. The method has been proved to work in highly non-trivial physical application (two-loop electroweak bosonic corrections to the $Z \to b \bar{{b}}$ decay), and cross-checked with the sector decomposition (SD) approach. In fact, both approaches have their pros and cons. In calculation of multidimensional integrals, depending on masses and scales involved, they are complementary. A powerful top-bottom approach to the numerical integration of multidimensional MB integrals is automatized in the MB-suite AMBRE/MB/ MBtools/MBnumerics/CUBA. Key elements are a dedicated use of the Cheng-Wu theorem for non-planar topologies and of shifts and deformations of the integration contours. An alternative bottom-up approach starting with complex 1-dimensional MB-integrals, based on the exploration of steepest descent integration contours in Minkowskian kinematics, is also discussed. Short and long term prospects of the MB-method for multi-loop applications to LHC- and LC-physics are discussed.Comment: Presented at the Epiphany Cracow conference 2017, refs adde

Multi-scale targeting of land degradation in northern Uzbekistan using satellite remote sensing

Advancing land degradation (LD) in the irrigated agro-ecosystems of Uzbekistan hinders sustainable development of this predominantly agricultural country. Until now, only sparse and out-of-date information on current land conditions of the irrigated cropland has been available. An improved understanding of this phenomenon as well as operational tools for LD monitoring is therefore a pre-requisite for multi-scale targeting of land rehabilitation practices and sustainable land management. This research aimed to enhance spatial knowledge on the cropland degradation in the irrigated agro-ecosystems in northern Uzbekistan to support policy interventions on land rehabilitation measures. At the regional level, the study combines linear trend analysis, spatial relational analysis, and logistic regression modeling to expose the LD trend and to analyze the causes. Time series of 250-m Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index (NDVI), summed over the growing seasons of 2000-2010, were used to determine areas with an apparent negative vegetation trend; this was interpreted as an indicator of LD. The assessment revealed a significant decline in cropland productivity across 23% (94,835 ha) of the arable area. The results of the logistic modeling indicate that the spatial pattern of the observed trend is mainly associated with the level of the groundwater table, land-use intensity, low soil quality, slope, and salinity of the groundwater. To quantify the extent of the cropland degradation at the local level, this research combines object-based change detection and spectral mixture analysis for vegetation cover decline mapping based on multitemporal Landsat TM images from 1998 and 2009. Spatial distribution of fields with decreased vegetation cover is mainly associated with abandoned cropland and land with inherently low-fertility soils located on the outreaches of the irrigation system and bordering natural sandy deserts. The comparison of the Landsat-based map with the LD trend map yielded an overall agreement of 93%. The proposed methodological approach is a useful supplement to the commonly applied trend analysis for detecting LD in cases when plot-specific data are needed but satellite time series of high spatial resolution are not available. To contribute to land rehabilitation options, a GIS-based multi-criteria decision-making approach is elaborated for assessing suitability of degraded irrigated cropland for establishing Elaeagnus angustifolia L. plantations while considering the specific environmental setting of the irrigated agro-ecosystems. The approach utilizes expert knowledge, fuzzy logic, and weighted linear combination to produce a suitability map for the degraded irrigated land. The results reveal that degraded cropland has higher than average suitability potential for afforestation with E. angustifolia. The assessment allows improved understanding of the spatial variability of suitability of degraded irrigated cropland for E. angustifolia and, subsequently, for better-informed spatial planning decisions on land restoration. The results of this research can serve as decision-making support for agricultural planners and policy makers, and can also be used for operational monitoring of cropland degradation in irrigated lowlands in northern Uzbekistan. The elaborated approach can also serve as a basis for LD assessments in similar irrigated agro-ecosystems in Central Asia and elsewhere.Multisclare Bewertung der Landdegradation in Nord-Uzbekistan unter der Verwendung von Satellitenfernerkundung Die zunehmende Landdegradation (LD) in den bewässerten Agrarökosystemen in Usbekistan behindert die nachhaltige Entwicklung dieses vorwiegend landwirtschaftlich geprägten Landes. Bis heute sind nur wenige und veraltete Informationen über die aktuellen Bodenbedingungen der bewässerten Anbauflächen verfügbar. Ein besseres Verständnis dieses Phänomens sowie operationelle Werkzeuge für LD-Monitoring sind daher Voraussetzung für ein nachhaltiges Landmanagement sowie für Landrehabilitationsmaßnahmen. Ziel dieser Studie war es, das räumliche Verständnis der Degradierung von Anbaugebieten in den bewässerten Agrarökosystemsn des nördlichen Usbekistans zu verbessern, um staatliche Interventionen in Bezug auf Landrehabilitationsmaßnahmen zu unterstützen Auf der regionalen Ebene kombiniert die Studie lineare Trendanalyse, räumliche relationale Analyse sowie logistischer Regressionsmodellierung, um den LD-Trend darzustellen und Gründe zu analysieren. Zeitreihen von 250-m Moderate Resolution Imaging Spectroradiometer (MODIS) normalized difference vegetation index (NDVI) Bildern wurden für den Zeitraum der Anbauperioden zwischen 2000-2010 untersucht, um Bereiche mit einem offensichtlich negativen Vegetationstrend zu ermitteln. Dieser negative Trend kann als Indikator für LD interpretiert werden. Die Untersuchung ergab eine signifikante Abnahme der Bodenproduktivität auf 23% (94,835 ha) der Anbaufläche. Zudem deuten die Ergebnisse der logistischen Modellierung darauf hin, dass das räumliche Muster des beobachteten Trends überwiegend mit der Höhe des Grundwasserspiegels, der Landnutzungsintensität, der geringen Bodenqualität, der Hangneigung sowie der Grundwasserversalzung zusammenhängt. Um das Ausmaß der Degradation der Anbauflächen auf der lokalen Ebene zu quantifizieren, kombiniert diese Studie objektbasierte Erkennung von Veränderungen und spektrale Mischungsanalyse für die Abnahme der Vegetationsbedeckung auf der Grundlage von multitemporalen Landsat-TM-Bildern im Zeitraum von 1998 bis 2009. Die räumliche Verteilung der Felder mit abnehmender Vegetationsbedeckung hängt überwiegend mit verlassenen Anbauflächen sowie mit nährstoffarmen Böden in den Randbereichen des Bewässerungssystems und an den Grenzen zu natürlichen Sandwüsten zusammen. Ein Vergleich mit der Karte des LD-Trends ergab insgesamt eine Übereinstimmung von 93%. Der vorgeschlagene Ansatz ist eine nützliche Ergänzung zu der häufig angewendeten Trendanalyse für die Ermittlung von LD in Regionen, für die keine Satellitenbildzeitreihen mit hoher Auflösung verfügbar sind. Als Beitrag zu Landrehabilitationsmöglichkeiten, wird ein GIS-basierter Multi-Kriterien-Ansatz zur Einschätzung der Eignung von degradierten bewässerten Anbauflächen für Elaeagnus angustifolia L. Plantagen beschrieben, der gleichzeitig die spezifischen Umweltbedingungen der bewässerten Agrarökosysteme berücksichtigt. Dieser Ansatz beinhaltet Expertenwissen, Fuzzy-Logik und gewichtete lineare Kombination, um eine Eignungskarte für die bewässerten degradierten Anbauflächen herzustellen. Die Ergebnisse zeigen, dass diese Flächen ein überdurchschnittliches Eignungspotenzial für die Aufforstung mit E. angustifolia aufweisen. Diese Studie trägt zu einem verbesserten Verständnis der räumlichen Variabilität der Eignung von solchen Flächen für E. angustifolia bei. Die Ergebnisse dieser Studie können als Entscheidungshilfe für landwirtschaftliche Planer und politische Entscheidungsträger sowie für verbesserte Landrehabilitationsmaßnahmen und operationelles Monitoring der Degradation von Anbauflächen im nördlichen Usbekistan eingesetzt werden. Zudem kann der beschriebene Ansatz als Grundlage für LD-Untersuchungen in ähnlichen bewässerten Agrarökosystemen in Zentralasien und anderswo dienen

The two-loop electroweak bosonic corrections to sin⁡2θeffb\sin^2\theta_{\rm eff}^{\rm b}

The prediction of the effective electroweak mixing angle $\sin^2\theta_{\rm eff}^{\rm b}$ in the Standard Model at two-loop accuracy has now been completed by the first calculation of the bosonic two-loop corrections to the $Z{\bar b}b$ vertex. Numerical predictions are presented in the form of a fitting formula as function of $M_Z, M_W, M_H, m_t$ and $\Delta{\alpha}$, ${\alpha_{\rm s}}$. For central input values, we obtain a relative correction of $\Delta\kappa_{\rm b}^{(\alpha^2,\rm bos)} = -0.9855 \times 10^{-4}$, amounting to about a quarter of the fermionic corrections, and corresponding to $\sin^2\theta_{\rm eff}^{\rm b} = 0.232704$. The integration of the corresponding two-loop vertex Feynman integrals with up to three dimensionless parameters in Minkowskian kinematics has been performed with two approaches: (i) Sector decomposition, implemented in the packages FIESTA 3 and SecDec 3, and (ii) Mellin-Barnes representations, implemented in AMBRE 3/MB and the new package MBnumerics.Comment: 14 pp; v2: some explanations and Tab.2 added, version published in PL

Побудова концептуальної моделі вибору емітентом оптимального контракту андерайтингу

In light of the research objective, this paper analyzes the dynamics and the structure of the executed contracts under the underwriting conduction in Ukraine in 2008-2012, as well as it was determined the estimation intervals of banks’ efficiency as the investment services providers (according to the dynamics of the issuers’ share prices during the “period of silence”). The major result of this research is separation of the “efficient IBS market” and determine at which of the underwriting models (based on the “firm commitment” of the bank – model “FC”, or “maximum/best efforts” of the bank – model “BE”), as one of the leading investment services, the offering efficiency is higher and therefore it is more suitable for using by issuers for entering the domestic or foreign stock markets. The analysis was conducted by using the elements of the matrix theory of games. The authors draw conclusions on selection of the priority underwriting model, as well as the time of application by the bank maximum market-maker’s (marketing) efforts to promote market-placed securities.У статті проведено порівняльний аналіз ринку інвестиційних банківських послуг (на прикладі послуг андеррайтингу). Визначено, яка із моделей андеррайтингу – на основі «твердих зобов’язань банку» («firm commitment – FC)» чи «максимальних/найкращих зусиль банку» (best efforts – BE)» – забезпечує вищу ефективність розміщення акцій і, відповідно, більше пристосована для використання українськими емітентами при виході на вітчизняні або зарубіжні фондові майданчики. На основі теорії матричних ігор сформульовано алгоритм маркетингового дослідження ринку, за результатами якого керівництво банку може прийняти обґрунтоване рішення щодо пріоритетності для емітента цінних паперів оптимального контракту андеррайтингу

Optimizing the Mellin-Barnes approach to numerical multiloop calculations

The status of numerical evaluations of Mellin–Barnes integrals is discussed, in particular the application of the quasi-Monte Carlo integration method to the efficient calculation of multidimensional integrals

Non-planar Feynman integrals, Mellin-Barnes representations, multiple sums

The construction of Mellin-Barnes (MB) representations for non-planar Feynman diagrams and the summation of multiple series derived from general MB representations are discussed. A basic version of a new package AMBREv.3.0 is supplemented. The ultimate goal of this project is the automatic evaluation of MB representations for multiloop scalar and tensor Feynman integrals through infinite sums, preferably with analytic solutions. We shortly describe a strategy of further algebraic summation.Comment: Contribution to the proceedings of the Loops and Legs 2014 conferenc