Related papers: Conformal mappings in perturbative QCD
The essence of the potential algebra concept [3] is that quantum mechanical free motions of scalar particles on curved surfaces of given isometry algebras can be mapped on 1D Schroedinger equations with particular potentials. As long as the…
The semihadronic tau decay width allows a clean extraction of the strong coupling constant at low energies. We present a modification of the standard "contour improved" method based on a derivative expansion of the Adler function. The…
Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution. In this article, we…
We investigate the relation between a postulated skeleton expansion and the conformal limit of QCD. We begin by developing some consequences of an Abelian-like skeleton expansion, which allows one to disentangle running-coupling effects…
Conformal symmetry is broken in physical QCD; nevertheless, one can use conformal symmetry as a template, systematically correcting for its nonzero $\beta$ function as well as higher-twist effects. For example, commensurate scale relations…
The conformal nature of smooth curves in $\mathbb{R}^3$ is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges .…
Bounds on the expansion coefficients of the strangeness changing $K\pi$ form factors were derived recently from analyticity and unitarity, using as input suitable correlation functions calculated by perturbative QCD in the Euclidian region.…
The Brodsky--Lepage--Mackenzie procedure is sequentially and unambiguously extended to any fixed order of perturbative QCD beyond the so called ``large--\beta_0 approximation''. As a result of this procedure, the obtained perturbation…
In this paper we show that the apparent failure of QCD lattice perturbation theory to account for Monte Carlo measurements of perturbative quantities results from choosing the bare lattice coupling constant as the expansion parameter. Using…
The Taylor expansion of thermodynamic observables at a finite baryon chemical potential $\mu_B$ is an oft-used method to circumvent the well-known sign problem of Lattice QCD. Owing to the associated difficulty and limitations of precision…
Contact adaption is an essential capability when manipulating objects. Two key contact modes of non-prehensile manipulation are sticking and sliding. This paper presents a Trajectory Optimization (TO) method formulated as a Mathematical…
We investigate the origin of the quark-hadron duality-violating terms in the expansion of the QCD two-point vector correlation function at large energies in the complex $q^2$ plane. Starting from the dispersive representation for the…
The factorization theorems for transverse momentum distributions of dilepton/boson production, recently formulated by Collins and Echevarria-Idilbi-Scimemi in terms of well-defined transverse momentum dependent distributions (TMDs), allows…
Conformal symmetry-based relations between concrete perturbative QED and QCD approximations for the Bjorken, the Ellis-Jaffe sum rules of polarized lepton- nucleon deep-inelastic scattering (DIS), the Gross-Llewellyn Smith sum rules of…
Perturbative QCD results in the MSbar scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the ``MSR…
We propose a hypothesis on the detailed structure for the representation of the conformal symmetry breaking term in the basic Crewther relation generalized in the perturbation theory framework in QCD renormalized in the ${\rm \bar{MS}}$…
For high energy processes ($M\gg \Lambda_{QCD}$) there are infrared safe hadronic shape variables that have a calculable perturbative expansion in $\alpha_s(M^2)$. However, nonperturbative power suppressed corrections to these variables are…
The dispersive approach to QCD is applied to the study of the inclusive tau lepton hadronic decay. This approach provides the unified integral representations for the hadronic vacuum polarization function, related R function, and Adler…
The QCD-coupling is a necessary input in the computation of many observables, and the parametric error on input parameters can be a dominant source of uncertainty. The coupling can be extracted by comparing high order perturbative…
Using a full resummation of the Adler function in the large-$\beta_0$ approximation of QCD and a mathematical framework of resurgence suitable for the specific properties of the Borel transform in this particular case, we derive a compact…