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Related papers: Asymptotic Pad\'e Approximants and the SQCD $\beta…

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We propose a novel Bayesian method to analytically continue observables to real baryochemical potential $\mu_B$ in finite density QCD. Taylor coefficients at $\mu_B=0$ and data at imaginary chemical potential $\mu_B^I$ are treated on equal…

High Energy Physics - Lattice · Physics 2021-03-11 Attila Pásztor , Zsolt Szép , Gergely Markó

In this paper we present a full set of 2- and 3-point functions for massless QCD at three-loop order in the MSbar scheme. The vertex functions are evaluated at the asymmetric point with one vanishing momentum. These results are used to…

High Energy Physics - Phenomenology · Physics 2007-05-23 K. G. Chetyrkin , A. Retey

We address whether Pad\'e-summations of the $\bar{MS}$ QCD $\beta$-function for a given number of flavours exhibit an infrared-stable fixed point, or alternatively, an infrared attractor of a double valued couplant as noted by Kogan and…

High Energy Physics - Phenomenology · Physics 2009-09-25 F. A. Chishtie , V. Elias , V. A. Miransky , T. G. Steele

We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…

High Energy Physics - Lattice · Physics 2009-10-22 Sergio Caracciolo , Andrea Pelissetto

We propose a generalization of Grunberg's method of effective charges in which, starting with the effective charge for some dimensionless QCD observable dependent on the single energy scale $Q, R(Q)$, we introduce an infinite set of…

High Energy Physics - Phenomenology · Physics 2009-10-30 C. J. Maxwell

The leading order coefficients of the beta-function of QCD are computed in a large N_f expansion. They are in agreement with the three loop MSbar calculation. The method involves computing the anomalous dimension of the operator (G^2_{mu…

High Energy Physics - Phenomenology · Physics 2009-10-28 J. A. Gracey

The recent QCD calculations of the five-loop beta function and of R(e+e-) to O(alpha_s^4) provide one more term in the Banks-Zaks expansion in (16.5-nf). There is no longer any hope that the expansion could extend, even crudely, to low nf.…

High Energy Physics - Phenomenology · Physics 2016-12-21 P. M. Stevenson

Asymptotic Pade-approximant methods are utilized to estimate the order $\alpha_s^5$ contribution to the $H\to gg$ rate and the order $\alpha_s^4$ contribution to the $H \to b \bar{b}$ rate. The former process is of particular interest…

High Energy Physics - Phenomenology · Physics 2008-11-26 V. Elias , F. A. Chishtie , T. G. Steele

We report first results of an ongoing project devoted to the analytical calculation of the QCD $\beta$-function and the quark mass anomalous dimension at the five loop level.

High Energy Physics - Phenomenology · Physics 2014-02-27 P. A. Baikov , K. G. Chetyrkin , J. H. Kühn

In this paper we study linear and non-linear Fourier-Pad\'e approximation for Angelesco systems of functions. This construction is similar to that of Hermite-Pad\'e approximation. Instead of considering power series expansions of the…

Classical Analysis and ODEs · Mathematics 2016-08-16 M. Bello-Hernández , G. López-Lagimasino , J. Mínguez-Ceniceros

Asymptotic approximations of Jacobi polynomials are given for large values of the $\beta$-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the…

Classical Analysis and ODEs · Mathematics 2018-07-18 Amparo Gil , Javier Segura , Nico M. Temme

In ${\cal N}=1$ SQED with $N_f$ flavors regularized by higher derivatives we obtain the four-loop beta function using a method based on calculating vacuum supergraphs. For this purpose we use a special C++ program which obtain contributions…

High Energy Physics - Theory · Physics 2024-03-12 Ilya Shirokov , Valentina Shirokova

The semi-analytical $O(\alpha_s^4)$ expression for the renormalization group $\beta$-function in the ${\rm{V}}$-scheme is obtained in the case of the $SU(N_c)$ gauge group. In the process of calculations we use the existing information…

High Energy Physics - Phenomenology · Physics 2015-10-13 A. L. Kataev , V. S. Molokoedov

For population genetics models with recombination, obtaining an exact, analytic sampling distribution has remained a challenging open problem for several decades. Recently, a new perspective based on asymptotic series has been introduced to…

Probability · Mathematics 2012-05-03 Paul A. Jenkins , Yun S. Song

Asymptotic approximations of Jacobi polynomials are given in terms of elementary functions for large degree $n$ and parameters $\alpha$ and $\beta$. From these new results, asymptotic expansions of the zeros are derived and methods are…

Classical Analysis and ODEs · Mathematics 2020-07-22 Amparo Gil , Javier Segura , Nico M. Temme

The $ \beta $-functions of marginal couplings are known to be closely related to the $ A $-function through Osborn's equation, derived using the local renormalization group. It is possible to derive strong constraints on the…

High Energy Physics - Theory · Physics 2019-10-02 Colin Poole , Anders Eller Thomsen

We demonstrate that the asymptotic approximant applied to the Blasius boundary layer flow over a flat plat (Barlow et al., 2017 Q. J. Mech. Appl. Math., 70(1): 21-48) yields accurate analytic closed-form solutions to the Falkner-Skan…

The properties of the new analytic running coupling are investigated at the higher loop levels. The expression for this invariant charge, independent of the normalization point, is obtained by invoking the asymptotic freedom condition. It…

High Energy Physics - Phenomenology · Physics 2007-05-23 A. V. Nesterenko , I. L. Solovtsov

I present a general method for determining the massive cusp anomalous dimension in QCD to a very high degree of accuracy using its asymptotic behavior at small and large quark velocities. I show that the method works exceedingly well at two…

High Energy Physics - Phenomenology · Physics 2023-03-15 Nikolaos Kidonakis

We have applied Pade approximants to perturbative QCD calculations of event shape observables in e+e- --> hadrons. We used the exact O(alpha_s^2) prediction and the [0/1] Pade approximant to estimate the O(alpha_s^3) term for 15…

High Energy Physics - Phenomenology · Physics 2009-10-28 P. N. Burrows , T. Abraha , M. Samuel , E. Steinfelds , H. Masuda