Related papers: Fractional Analytic QCD beyond Leading Order in ti…
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…
In the framework of analytic approach to QCD, which has been recently intensively developed, the dependence of nonperturbative contributions in a running coupling of strong interaction on initial perturbative approximation to 3-loop order…
A technique called analytic perturbation theory, which respects the required analytic properties, consistent with causality, is applied to the definition of the running coupling in the timelike region, to the description of inclusive…
A recently developed linear algebraic method for the computation of perturbation expansion coefficients to large order is applied to the problem of a hydrogenic atom in a magnetic field. We take as the zeroth order approximation the $D…
In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
We argue that a technique called analytic perturbation theory leads to a well-defined method for analytically continuing the running coupling constant from the spacelike to the timelike region, which allows us to give a self-consistent…
In this paper, we develop a numerical algorithm for an inverse problem on determining fractional orders of time derivatives simultaneously in a coupled subdiffusion system. Following the theoretical uniqueness, we reformulate the order…
We derive the analytical expression of the coordinate time $t$ in terms of the eccentric anomaly $u$ at the second post-Newtonian order in General Relativity for a compact binary system moving on eccentric orbits. The parametrization of $t$…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
In this paper, we study quantitative spatial analytic bounds and unique continuation inequalities of solutions for fractional heat equations with an analytic lower order term on the whole space. At first, we show that the solution has a…
This article develops how to generalize the invariant subspace method for deriving the analytical solutions of the multi-component (N+1)-dimensional coupled nonlinear time-fractional PDEs (NTFPDEs) in the sense of Caputo fractional-order…
We present several key steps towards the computation of differential Higgs boson cross sections at N$^3$LO in perturbative QCD. Specifically, we work in the framework of Higgs-differential cross sections that allows to compute precise…
We present QCD predictions for the transverse momentum (q_T) distribution of the Higgs boson at the LHC. At small q_T the logarithmically-enhanced terms are resummed to all orders up to next-to-next-to-leading logarithmic accuracy. The…
This article analysis differential equations which represents damped and fractional oscillators. First, it is shown that prior to using physical quantities in fractional calculus, it is imperative that they are turned dimensionless.…
The paper is devoted to application of recently devised ghost-free Analytic Perturbation Theory (APT) for analysis of some QCD observables. We start with the discussion of the main problem of the perturbative QCD -- ghost singularities and…
We develop methods to obtain the fully differential cross-section for the $f \bar{f} \to Z(\ell\ell)\,h$ process to any desired order in effective field theory (EFT). To achieve this, we first derive a mapping between the partial wave…
This article proves the uniqueness for two kinds of inverse problems of identifying fractional orders in diffusion equations with multiple time-fractional derivatives by pointwise observation. By means of eigenfunction expansion and Laplace…
We provide new methods to straightforwardly obtain compact and analytic expressions for epsilon-expansions of functions appearing in both field and string theory amplitudes. An algebraic method is presented to explicitly solve for…
We discuss the resummation approach in QCD Analytic Perturbation Theory (APT). We start with a simple example of asymptotic power series for a zero-dimensional analog of the scalar $g\,\phi^4$ model. Then we give a short historic preamble…