Related papers: Scheme variations of the QCD coupling and tau deca…
The Quantum Chromodynamics (QCD) coupling, $\alpha_s$, is not a physical observable of the theory since it depends on conventions related to the renormalization procedure. We introduce a definition of the QCD coupling, denoted by…
The Quantum Chromodynamics (QCD) coupling $\alpha_s$ is a central parameter in the Standard Model of particle physics. However, it depends on theoretical conventions related to renormalisation and hence is not an observable quantity. In…
A novel, non-power, expansion of QCD quantities replacing the standard perturbative expansion in powers of the renormalized couplant a has recently been introduced and examined by two of us. Being obtained by analytic continuation in the…
The perturbative QCD corrections to the semileptonic decay width of the tau lepton are evaluated in the next-next-to-leading order from the contour integral representation in various renormalization schemes, using numerical solution of the…
The QCD corrections to the R_{\tau}^{12} moment of the invariant mass distribution in hadronic decays of the tau lepton are discussed. The next-to-next-to-leading order prediction is shown to be stable with respect to change of the…
Physical quantities in QCD do not depend upon $\alpha_s(Q)$. There is no way to measure $\alpha_s(Q)$ experimentally. If those statements sound shocking, please read on. They are actually well-known facts, though ones that are constantly…
Conventionally, one adopts typical momentum flow of a physical observable as the renormalization scale for its perturbative QCD (pQCD) approximant. This simple treatment leads to renormalization scheme-and-scale ambiguities due to the…
The QCD corrections to the moments of the invariant mass distribution in the semileptonic $\tau$ decays are considered. The effect of the renormalization scheme dependence on the fitted values of alpha_s(m^2_tau) and the condensates is…
Hadronic tau decays offer the possibility of determining the strong coupling alpha_s at relatively low energy. Precisely for this reason, however, good control over the perturbative QCD corrections, the non-perturbative condensate…
We discuss the St\"uckelberg-Peterman extended renormalization group equations in perturbative QCD, which express the invariance of physical observables under renormalization-scale and scheme-parameter transformations. We introduce a…
The question of the renormalization scheme dependence of the $\tau$ semileptonic decay rate is revisited in response to a recent criticism. Particular attention is payed to a distinction between a consistent quantitative description of this…
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…
We present a new approach to determining the strong coupling $\alpha_s(Q)$, over the entire range of validity of perturbative QCD, for scales above $\Lambda_{\mathrm{QCD}}$ and up to the Planck scale $\sim1.22\cdot10^{19}$\,GeV, with the…
The next-to-next-to-leading order perturbative QCD corrections to R_tau and the higher moments of the invariant mass distribution in the hadronic tau decays are considered. The renormalization scheme dependence of these corrections is…
In this work, the perturbative QCD series of the scalar correlation function $\Psi(s)$ is investigated. Besides ${\rm Im}\Psi(s)$, which is relevant for Higgs decay into quarks, two other physical correlators, $\Psi^{"}(s)$ and $D^L(s)$,…
The QCD running coupling $\alpha_s(Q^2)$ sets the strength of the interactions of quarks and gluons as a function of the momentum transfer $Q$. The $Q^2$ dependence of the coupling is required to describe hadronic interactions at both large…
The hadronic decay rate of the tau lepton serves as one of the most precise determinations of the QCD coupling alpha_s. The dominant theoretical source of uncertainty at present resides in the seeming disparity of two approaches to…
As a basic requirement of the renormalization group invariance, any physical observable must be independent of the choice of both the renormalization scheme and the initial renormalization scale. In this paper, we show that by using the…
The calculation of perturbative corrections to the spectral moments observable in hadronic $\tau$ decays is reconsidered. The exact order-$\alpha_s^3$ results and the resummation procedure of Le~Diberder and Pich are compared with a partial…
We apply an analytic description to the inclusive decay of the $\tau$ lepton. We argue that this method gives not only a self-consistent description of the process both in the timelike region by using the initial expression for $R_\tau$ and…