Related papers: Renormalization-scale-invariant continuation of tr…
A method of resummation of truncated perturbation series, related to diagonal Pad\'e approximants but giving results independent of the renormalization scale, was developed more than ten years ago by us with a view of applying it in…
Truncated perturbative series (TPS's) of any observable have the unphysical dependence on the choice of the renormalization scale (RScl). The diagonal Pad\'e approximants (dPA's) to any TPS of an observable possess the favorable property of…
Recently it has been pointed out that diagonal Pad\'e approximants to truncated perturbative series in gauge theories have the remarkable property of being independent of the choice of the renormalization scale as long as the gauge coupling…
We advocate the replacement of standard alphas(mu)-based QCD perturbation theory, in which the coupling and truncated perturbative predictions are dependent on the chosen renormalisation scheme, by a Lambda-based approach in which QCD…
In this lecture I present some of the new developments concerning the use of Pade Approximants (PA's) for resumming perturbative series in QCD. It is shown that PA's tend to reduce the renormalization scale and scheme dependence as compared…
Applicability of the previously introduced method of modified diagonal Baker-Gammel approximants is extended to truncated perturbative series (TPS) of any order in gauge theories. The approximants reproduce the TPS when expanded in power…
A key problem in making precise perturbative QCD predictions is to set the proper renormalization scale of the running coupling. The conventional scale-setting procedure assigns an arbitrary range and an arbitrary systematic error to…
A short survey of the renormalization problem in QCD and its non-perturbative solution by means of numerical simulations on the lattice is given. Most emphasis is on scale dependent renormalizations, which can be reliably addressed via a…
Previously developed Pade-related method of resummation for QCD observables, which achieves exact renormalization-scale-invariance, is extended so that the scheme-invariance is obtained as well. The dependence on the leading scheme…
A key issue in making precise predictions in perturbative QCD is the uncertainty in setting the renormalization scale. If in principle, the entire perturbative series is void of this issue, in practice the perturbative corrections are known…
We analyze truncated series generated as divergent formal solutions of non-linear ordinary differential equations. Motivating the study is a specific non-linear, first-order differential equation, which is the basis of the resurgent…
We formulate a general scheme to improve the truncated perturbative expansion in alpha_s by means of the renormalization group in QCD for the single-scale quantities. The procedure is used for the evaluation of hadronic decay rates of…
The QED renormalization is restudied by using a mass-dependent subtraction which is performed at a time-like renormalization point. The subtraction exactly respects necessary physical and mathematical requirements such as the gauge…
The conventional approach to fixed-order perturbative QCD predictions is based on an arbitrary choice of the renormalization scale, together with an arbitrary range. This {\it ad hoc} assignment of the renormalization scale causes the…
We introduce a generalization of the conventional renormalization schemes used in dimensional regularization, which illuminates the renormalization scheme and scale ambiguities of pQCD predictions, exposes the general pattern of…
Based on the renormalization group summation method of McKeon ${\it et\; al.}$, it is shown that the renormalization group equation, while related to the radiatively mass scale $\mu$, would perform a summation over QCD perturbative terms.…
We explain how scale dependent renormalized quantities can be computed using lattice QCD. Two examples are used: the running coupling and quark masses. A reliable computation of the $\Lambda$-parameter in the quenched approximation is…
We present in detail a new systematic method which can be used to automatically eliminate the renormalization scheme and scale ambiguities in perturbative QCD predictions at all orders. We show that all of the nonconformal \beta-dependent…
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…
We give an introduction to renormalisation, focusing first on a pedagogical description of fundamental concepts of the procedure and its features, then we introduce the renormalisation group and its equations. We discuss then the case of…