Related papers: About Fractional Analytic QCD beyond Leading Order
We consider the two-fold expansion in powers of the conformal anomaly and of the strong coupling $\alpha_s$ for the non-singlet contributions to Adler $D$-function and Bjorken polarized sum rule calculated previously in the $\MSbar$-scheme…
We recall the physical features of the parton distributions in the quantum statistical approach of the nucleon. Some predictions from a next-to-leading order QCD analysis are compared to recent experimental results. We also consider their…
Several topics in QCD are reviewed, including: the light-cone Fock state representation, which encodes the flavor, spin and other quark and gluon correlations of hadrons in the form of universal process-independent amplitudes; the…
The paper presents derivation and interpretation of one type of variable order derivative definitions. For mathematical modelling of considering definition the switching and numerical scheme is given. The paper also introduces a numerical…
Digital System Research has pioneered the mathematics and design for a new class of computing machine using residue numbers. Unlike prior art, the new breakthrough provides methods and apparatus for general purpose computation using several…
If connecting properties of a multiquark hadron with those exhibited by its constituents, QCD sum rules inferred along the routes of traditional wisdom necessarily involve contributions not related at all to and thus not presenting…
Let $R$ be an order in an algebraic number field. If $R$ is a principal order, then many explicit results on its arithmetic are available. Among others, $R$ is half-factorial if and only if the class group of $R$ has at most two elements.…
Going back to Kreisel in the Sixties, hyperarithmetical analysis is a cluster of logical systems just beyond arithmetical comprehension. Only recently natural examples of theorems from the mathematical mainstream were identified that fit…
In this paper, we introduce two new non-singular kernel fractional derivatives and present a class of other fractional derivatives derived from the new formulations. We present some important results of uniformly convergent sequences of…
We prove an analytic KAM-Theorem, which is used in [1], where the differential part of KAM-theory is discussed. Related theorems on analytic KAM-theory exist in the literature (e. g., among many others, [7], [8], [13]). The aim of the…
In this article, the existence and uniqueness about the solution for a class of stochastic fractional-order differential equation systems are investigated, where the fractional derivative is described in Caputo sense. The fractional…
In this short review we elaborate the significance of resummation in $k_T$ factorization theorem, and summarize the recent progresses in the calculations of the next-to-leading order contributions to B meson decays from the perturbative QCD…
We present an overview of a novel approach to the QCD Light-Cone Sum Rule method, employing $B$-meson Light-Cone Distribution Amplitudes. This method circumvents the semi-global quark-hadron duality (QHD) approximation, which can introduce…
In recent years, as fractional calculus becomes more and more broadly used in research across different academic disciplines, there are increasing demands for the numerical tools for the computation of fractional…
The analytic continuation of the Mellin transforms to complex values of N for the basic functions $g_i(x)$ of the momentum fraction x emerging in the quantities of massless QED and QCD up to two-loop order, as the unpolarized and polarized…
A new representation of the next to leading QCD corrections to the nucleon structure functions is given in terms of parton distributions. All $~\alpha_{s}~$ corrections to the leading logarithmic approximation (LLA) are included. In…
The QCD factorization approach provides the theoretical basis for a systematic analysis of nonleptonic decay amplitudes of B mesons in the heavy-quark limit. After recalling the basic ideas underlying this formalism, several tests of QCD…
We briefly summarize theoretical methods for carrying out QCD calculations to next-to-leading order in perturbation theory. In particular, we describe a new general algorithm that can be used for computing arbitrary jet cross sections in…
I discuss recent applications of QCD light-cone sum rules to various form factors of pseudoscalar mesons. In this approach both soft and hard contributions to the form factors are taken into account. Combining QCD calculation with the…
We generalize the generalized-squeezing problem to include fractional values of the squeezing order $n$. This approach allows us to determine the locations of critical points at which qualitative changes in behaviour occur and accurately…