Related papers: Asymptotic Pad\'e Approximants and the SQCD $\beta…
In this note we give a derivation of the asymptotic main term for the q-Gamma function as q approaching 1. This formula is valid on all the complex plan except at the poles of the Euler Gamma function.
Let $\alpha$ and $\beta$ be irrational real numbers and $0<\F<1/30$. We prove a precise estimate for the number of positive integers $q\leq Q$ that satisfy $\|q\alpha\|\cdot\|q\beta\|<\F$. If we choose $\F$ as a function of $Q$ we get…
Convergence of diagonal Pad\'e approximants is studied for a class of functions which admit the integral representation $ {\mathfrak F}(\lambda)=r_1(\lambda)\int_{-1}^1\frac{td\sigma(t)}{t-\lambda}+r_2(\lambda), $ where $\sigma$ is a finite…
We estimate commutators of quadratic operators $Q_a$ in Jordan algebras. These estimates can be used to construct the scattering theory in quantum fields theories formulated in terms of Jordan algebras.
We present new asymptotic series for the Legendre and Jacobi functions of the first and second kinds in terms of Bessel functions with appropriate arguments. The results are useful in the context of scattering problems, improve on known…
We investigate -- as an alternative to usual Monte Carlo Renormalization Group methods -- the feasibility of extracting QCD beta-functions directly from a lattice analysis of correlations between the action and Wilson loops. We test this…
We calculate the small angle expansion of the four-loop QCD cusp anomalous dimension. As a byproduct of our calculation, we also obtain the four-loop anomalous dimension of the heavy-quark field in HQET. The validity of the calculational…
We describe a method to derive, from first principles, the long-distance asymptotic behavior of correlation functions of integrable models in the framework of the algebraic Bethe ansatz. We apply this approach to the longitudinal spin- spin…
We consider sequences of biorthogonal polynomials with respect to a Cauchy type convolution kernel and give the weak and ratio asymptotic of the corresponding sequences of biorthogonal polynomials. The construction is intimately related…
In this contribution we consider the recent computation of the gauge coupling $\beta$-function at four loops and the Yukawa matrix $\beta$-function at three loops in the most general, renormalizable and four-dimensional quantum field…
We establish the asymptotic expansion in $\beta$ matrix models with a confining, off-critical potential, in the regime where the support of the equilibrium measure is a union of segments. We first address the case where the filling…
We apply the exact WKB analysis to the quantum Seiberg-Witten curve for 4-dimensional $\mathcal{N} = 2\ SU(2)\ N_f=2$ SQCD with the flavor symmetry. The discontinuity and the asymptotic behavior of the quantum periods define a…
We report on two recent multiloop results in QED: (i) the four-loop corrections to the conversion relations between the QED charge renormalized in the on-shell and MS-bar schemes; (ii) analytical evaluation of a class of asymptotic…
We obtain an asymptotic formula for the fourth moment of quadratic Dirichlet $L$--functions over $\mathbb{F}_q[x]$, as the base field $\mathbb{F}_q$ is fixed and the genus of the family goes to infinity. According to conjectures of Andrade…
We deduce the gluino contribution to the three-loop QCD \beta function within the minimal supersymmetric Standard Model (MSSM) from its standard QCD expression. The result is a first step in the computation of the full MSSM three-loop \beta…
1. Introduction 2. Massless QCD and Scale Invariance 3. The Renormalisation Group and Asymptotic Freedom 4. More on the Running Coupling 5. Application to Hard Processes 5.1 $R_{e^+e^-}$ and Related Processes 5.2 The Final State in $e^+e^-$…
We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Pad\'e Approximants. We focus on two kind of problems: the first one related with meromorphic…
We address the problems in applying cycle expansions to bound chaotic systems, caused by e.g. intermittency and incompleteness of the symbolic dynamics. We discuss zeta functions associated with weighted evolution operators and in…
The renormalization-group functions of the two-dimensional n-vector \lambda \phi^4 model are calculated in the five-loop approximation. Perturbative series for the \beta-function and critical exponents are resummed by the Pade-Borel-Leroy…
A novel method of summing asymptotic series is advanced. Such series repeatedly arise when employing perturbation theory in powers of a small parameter for complicated problems of condensed matter physics, statistical physics, and various…