Related papers: RG/Pade Estimate of the Three-Loop Contribution to…
A full analytic calculation of the two-loop diagrams contributing to the static potential in QCD is presented in detail. Using a renormalization group improvement, the ``three-loop'' potential in momentum space is thus derived and the third…
The perturbative QCD static potential and ultrasoft contributions, which together give the static energy, have been calculated to three- and four-loop order respectively, by several authors. Using the renormalization group, and Pad\'e…
Asymptotic Pade-approximant methods are utilized to estimate the leading-order unknown (i.e., not-yet-calculated) contributions to the perturbative expansions of two-current QCD correlation functions obtained from scalar-channel fermion and…
We discuss Pad\'e-improvement of known four-loop order results based upon an asymptotic three-parameter error formula for Pad\'e-approximants. We derive an explicit formula estimating the next-order coefficient $R_4$ from the previous…
We utilize asymptotic Pade-approximant methods to estimate the three-loop order MS bar-scheme coefficients within the inclusive semileptonic b to u decay rate for four and five active quark flavours. The estimates we obtain for the three…
Utilizing asymptotic Pade-approximant methods, we estimate the three-loop order MS-bar coefficients of alpha_s^3[\log(\mu^2/m^2_b(\mu)]^k terms [k = {0,1,2,3}] within the $b \to u\ell^-\bar{\nu}_\ell$ decay rate. Except for the coefficient…
We compute the purely gluonic contribution to the static QCD potential at three--loop order. This completes the computation of the static potential at this order.
The renormalization-scale ($\mu$) dependence of the two-loop inclusive semileptonic $b\to c\ell^-\bar\nu_\ell$ decay rate is shown to be significant in the pole mass scheme, and the decay rate is shown to be poorly convergent in the MS-bar…
The semi-analytical expression for the forth coefficient of 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 three-loop…
The three-loop contribution to the MS bar single-Higgs-doublet standard-model cross-section $\sigma(W_L^+ W_L^- \to Z_L Z_L)$ at s = (5M_H)^2 is estimated via least-squares matching of the asymptotic Pade-approximant prediction of the next…
We resum the leading ultrasoft logs of the singlet and octet static QCD potentials within potential NRQCD. We then obtain the complete three-loop renormalization group improvement of the singlet QCD static potential. The discrepancies…
It had been known that the Borel transforms of the twice quark pole mass 2*mq and of the QCD q-barq static potential V(r) have leading infrared renormalons at b=1/2 such that they cancel in the sum. The renormalon residue of 2*mq had been…
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…
We assess the accuracy of our previous Asymptotic Pad\'e predictions of the five-loop QCD $\beta$-function and quark mass anomalous dimension in the light of subsequent exact results. We find the low-order coefficients in an expansion in…
Renormalization Group (RG) and optimized Pade-approximant methods are used to estimate the three-loop perturbative contributions to the inclusive semileptonic b \to u and b \to c decay rates. It is noted that the \bar{MS} scheme works…
The renormalization-group (RG) functions for the three-dimensional n-vector cubic model are calculated in the five-loop approximation. High-precision numerical estimates for the asymptotic critical exponents of the three-dimensional impure…
In this talk the methods and computer tools which were used in our recent calculation of the three-loop Standard Model renormalization group coefficients are discussed. A brief review of the techniques based on special features of…
The complete analysis of a model with three quartic coupling constants associated with an O(2N)--symmetric, a cubic, and a tetragonal interactions is carried out within the three-loop approximation of the renormalization-group (RG) approach…
We compute the static energy of QCD at short distances at next-to-next-to-next-to leading-logarithmic accuracy in terms of the three-loop singlet potential. By comparing our results with lattice data we extract the value of the unknown…
The three loop anomalous dimension for the gauge invariant, renormalizable, non-local mass operator for a gluon is computed in the MSbar scheme. In addition the anomalous dimensions of the associated localizing ghost fields are also deduced…