Long-Range Coulomb Forces in DIS: Missed Radiative Corrections?

The Born approximation, one photon exchange, used for DIS is subject to virtual radiative corrections which are related to the long-range Coulomb forces. They may be sizeable for heavy nuclei since Z\alpha is not a small parameter. So far these corrections are known only for two processes, elastic scattering and bremsstrahlung on the Coulomb field of a point-like target. While the former amplitude acquires only a phase, in the latter case the cross section is modified also. Although the problem of Coulomb corrections for DIS on nuclei is extremely difficult, it should be challenged rather than 'swept under the carpet'. The importance of these radiative corrections is questioned in present paper. We show that in the simplest case of a constant hadronic current the Coulomb corrections provide a phase to the Born amplitude, therefore the cross section remains the same. Inclusion of more realistic hadronic dynamics changes this conclusion. The example of coherent production of vector mesons off nuclei reveals large effects. So far a little progress has been made deriving exact lepton wave functions in the Coulomb field of an extended target. Employing available results based on the first-order approximation in Z\alpha, we conclude that the Coulomb corrections are still important for heavy nuclei. We also consider an alternative approach for extended nuclear targets, the eikonal approximation, which we demonstrate to reproduce the known exact results for Coulomb corrections. Calculating electroproduction of vector mesons we again arrive at a large deviation from the Born approximation. We conclude that one should accept with caution the experimental results for nuclear effects in DIS based on analyses done in the Born approximation.Comment: 24 pages including 4 figures. Fig.4 is modified and stylistic corrections are made. The final version to appear in Eur.Phys.J.

Fractional Generalization of Gradient Systems

We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these systems.Comment: 11 pages, LaTe

A Complete Version of the Glauber Theory for Elementary Atom - Target Atom Scattering and Its Approximations

A general formalism of the Glauber theory for elementary atom (EA) - target atom (TA) scattering is developed. A second-order approximation of its complete version is considered in the framework of the optical-model perturbative approach. A `potential' approximation of a second-order optical model is formulated neglecting the excitation effects of the TA. Its accuracy is evaluated within the second-order approximation for the complete version of the Glauber EA-TA scattering theory.Comment: PDFLaTeX, 10 pages, no figures; an updated versio

Highest coefficient of scalar products in SU(3)-invariant integrable models

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of their highest coefficients. We obtain various different representations for the highest coefficient in terms of sums over partitions. We also obtain multiple integral representations for the highest coefficient.Comment: 17 page

Quantum properties of a non-Abelian gauge invariant action with a mass parameter

We continue the study of a local, gauge invariant Yang-Mills action containing a mass parameter, which we constructed in a previous paper starting from the nonlocal gauge invariant mass dimension two operator F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}. We return briefly to the renormalizability of the model, which can be proven to all orders of perturbation theory by embedding it in a more general model with a larger symmetry content. We point out the existence of a nilpotent BRST symmetry. Although our action contains extra (anti)commuting tensor fields and coupling constants, we prove that our model in the limit of vanishing mass is equivalent with ordinary massless Yang-Mills theories. The full theory is renormalized explicitly at two loops in the MSbar scheme and all the renormalization group functions are presented. We end with some comments on the potential relevance of this gauge model for the issue of a dynamical gluon mass generation.Comment: 17 pages. v2: version accepted for publication in Phys.Rev.

Quantum-mechanical description of in-medium fragmentation

We present a quantum-mechanical description of quark-hadron fragmentation in a nuclear environment. It employs the path-integral formulation of quantum mechanics, which takes care of all phases and interferences, and which contains all relevant time scales, like production, coherence, formation, etc. The cross section includes the probability of pre-hadron (colorless dipole) production both inside and outside the medium. Moreover, it also includes inside-outside production, which is a typical quantum-mechanical interference effect (like twin-slit electron propagation). We observe a substantial suppression caused by the medium, even if the pre-hadron is produced outside the medium and no energy loss is involved. This important source of suppression is missed in the usual energy-loss scenario interpreting the effect of jet quenching observed in heavy ion collisions. This may be one of the reasons of a too large gluon density, reported by such analyzes.Comment: 20 pages, 7 figure

The inverse problem of spectral reflection prediction: Problems of framework selection

Digital image processing requires substantial computations for characterization. It is since the reliable color reproduction can be achieved by establishing the correspondence between the spectral reflectance of the printed surface and the amounts of deposited inks. The processing is implemented by using different mathematical models. Most of the color prediction models engage some mathematical techniques to predict spectral reflectance for a mixture of colorants that are characterized by absorption and scattering during the light propagation. However, few attempts were made to make a model for prediction the colorants values based on an observing spectrum. This work is devoted to application of artificial neural network approach for solving the inverse problem of spectral reflection prediction. This task has been considered unsolvable as it involves solving a system of the linear differential equations, in which the number of unknowns exceeds the number of equations. Our attempt is based on the assumption that the prediction of the initial colorants from spectral data is possible by analogy with the work of the color perception system in humans. The aim of our study is to offer an approach to the framework selection. The model is built in Matlab and shows satisfactory prediction accuracy. © 2020 American Institute of Physics Inc.. All rights reserved

The forward problem of spectral reflection prediction: Mutual match between framework selection and the training set volume

Novel technology of the color reproduction is closely related to a variety of color prediction techniques. Along with the deterministic models, those based on the use of artificial neural networks have recently begun to appear. An important problem in the application of a neural network approach is the choice of the training set and network training algorithms. In our work, we describe the results of a computational experiment where various configurations of the artificial neural networks along the different volumes of training subsamples were simultaneously determined providing a satisfactory accuracy of the spectral reflection prediction. The results show that each subsample might be mapped to a particular network configuration. © 2020 American Institute of Physics Inc.. All rights reserved