Related papers: Comment on "Infrared freezing of Euclidean QCD obs…
We propose a conjecture about the detailed structure of the conformal symmetry breaking term in the generalized Crewther relation. We conclude that this conjecture leads to new relations between the QCD expansion coefficients of the Adler…
We consider Euler flows on two-dimensional (2D) periodic domain and are interested in the stability, both linear and nonlinear, of a simple equilibrium given by the 2D Taylor-Green vortex. As the first main result, numerical evidence is…
We study the dependence on the pion mass of the QCD effective charge by employing the dispersion relations for the Adler D function. This new massive analytic running coupling is compared to the effective coupling saturated by the…
Estimates of higher-order contributions for perturbative series in QCD, in view of their asymptotic nature, are delicate, though indispensable for a reliable error assessment in phenomenological applications. In this work, the Adler…
We discuss the structure of infrared and ultraviolet singularities in on-shell QCD and supersymmetric QCD amplitudes at one-loop order. Previous results, valid for massless partons, are extended to the case of massive partons. Using…
Let $D$ be a smoothly bounded pseudoconvex domain in $\mathbf C^n$, $n > 1$. Using the Robin function $\Lambda(p)$ that arises from the Green function $G(z, p)$ for $D$ with pole at $p \in D$ associated with the standard sum-of-squares…
There are no square $L^2$-flat sequences of polynomials of the type $$\frac{1}{\sqrt q}( \epsilon_0 + \epsilon_1z + \epsilon_2z^2 + \cdots + \epsilon_{q-2}z^{q-2} +\epsilon_q z^{q-1}),$$ where for each $j,~~ 0 \leq j\leq q-1,~\epsilon_j =…
We provide the last missing ingredient necessary to approximate one-loop amplitudes in QCD with massive quarks in the limit of vanishing energy of a single gluon up to terms suppressed by this energy. Our main result is a soft operator…
Following the prequel work \cite{VO3}, we prove a generalization of "Mazur's conjecture" for $L$-functions of elliptic curves in abelian extensions of imaginary quadratic fields, including the assertion that the Mordell-Weil rank of an…
We show that some spectral properties of the almost Mathieu operator with frequency well approximated by rationals can be as poor as at all possible in the class of all one-dimensional discrete Schroedinger operators. For the class of…
We give a comprehensive study of interpolation inequalities for periodic functions with zero mean, including the existence of and the asymptotic expansions for the extremals, best constants, various remainder terms, etc. Most attention is…
We compute the one-particle spectral function and the optical conductivity for the 2-d Hubbard model on a square lattice. The computational method is cellular dynamical mean-field theory (CDMFT) in which a 4-site Hubbard plaquette is…
We derive the structure of three-loop anomalous dimensions governing infrared singularities of QCD amplitudes with one massive and an arbitrary number of massless external partons. The contributions of tripole and quadrupole correlations…
We show that the existence of the fundamental ultraviolet cut-off (minimal scale) fixed by weak interactions enhances the QCD running coupling evaluated at one quantum loop level, starting at the scale in the vicinity of the cut-off. The…
We discuss phenomenological tests for the frozen infrared behavior of the running coupling constant and gluon propagators found in some solutions of Schwinger-Dyson equations of the gluonic sector of QCD. We verify that several observables…
Following Lortz, we construct a family of smooth steady states of the ideal, incompressible Euler equation in three dimensions that possess no continuous Euclidean symmetry. As in Lortz, they do possess a planar reflection symmetry and, as…
The removal of unphysical singularities in the perturbatively calculable part of the pion form factor--a classic example of a three-point function in QCD--is discussed. Different ``analytization'' procedures in the sense of Shirkov and…
It is well-known that direct analytic continuation of DGLAP evolution kernel (splitting functions) from space-like to time-like kinematics breaks down at three loops. We identify the origin of this breakdown as splitting functions are not…
We discuss the renormalon-based approach to power corrections in non-singlet deep inelastic scattering structure functions and compare it with the general operator product expansion. The renormalon technique and its variations relate the…
We establish existence of an ergodic invariant measure on $H^1(D,\mathbb{R}^3)\cap L^2(D,\mathbb{S}^2)$ for the stochastic Landau-Lifschitz-Gilbert equation on a bounded one dimensional interval $D$. The conclusion is achieved by employing…