Related papers: Conformal expansions and renormalons
A certain pattern of divergence of perturbative expansions in quantum field theories, related to their small and large momentum behaviour, is known as renormalons. We review formal and phenomenological aspects of renormalon divergence. We…
In both QCD and supersymmetric QCD (SQCD) with N_f flavors there are conformal windows where the theory is asymptotically free in the ultraviolet while the infrared physics is governed by a non-trivial fixed-point. In SQCD, the lower N_f…
We show that the resummation of large perturbative corrections in QCD leads to ambiguities in high energy cross sections that are suppressed by powers of large momentum scales. These ambiguities are caused by infrared renormalons, which are…
Even for short-distance dominated observables the QCD perturbation expansion is never complete. The divergence of the expansion through infrared renormalons provides formal evidence of this fact. In this article we review how this apparent…
We examine the QCD perturbation series at large orders, for different values of the 'large $\beta_0$ renormalization scale'. It is found that if we let this scale grow exponentially with the order, the divergent series can be turned into an…
The difference between fixed-order (FO) and contour-improved (CI) formulations of QCD perturbation theory limits the precision of the strong coupling determined from the hadronic decay of the $\tau$ lepton. Recently, several attempts to…
The renormalization-scheme and scale dependence of the truncated QCD perturbative expansions is one of the main sources of theoretical error of the standard model predictions, especially at intermediate energies. Recently, a class of…
We study the origin of non-analyticity in \alpha_s of a short-distance QCD observable to demonstrate that the infrared renormalons, the same-sign factorial growth of the perturbative expansion, is a universal phenomenon that originates…
We compute the renormalon ambiguity of the static potential, in the limit of a large number of flavors. An extrapolation of the QED result to QCD implies that the large distance behavior of the quark potential is arbitrary in perturbation…
Perturbative expansion in the nonperturbative confining QCD background is formulated. The properly renormalized $\alpha_S(R)$ is shown to be finite at large distances, with the string tension playing the role of an infrared regulator. The…
Ultraviolet renormalons, contrary to their infrared counterparts, lead to a universal contribution to the large-order behaviour of perturbative expansions in QCD. In this letter, we determine nature of the leading ultraviolet renormalon…
Precise extractions of $\alpha_s$ from $\tau\to {\rm (hadrons)}+\nu_\tau$ and from $e^+e^-\to {\rm (hadrons)}$ below the charm threshold rely on finite energy sum rules (FESRs) where the experimental side is given by integrated spectral…
The high order corrections to renormalon are considered. Each new type of insertions into the renormalon chain of graphs generates the correction to the asymptotics of perturbation theory of the order of $\sim 1$. However, this series of…
We examine the large-order behaviour of a recently proposed renormalization-group-improved expansion of the Adler function in perturbative QCD, which sums in an analytically closed form the leading logarithms accessible from…
The general relation between the standard expansion coefficients and the beta function for the QCD coupling is exactly derived in a mathematically strict way. It is accordingly found that an infinite number of logarithmic terms are lost in…
The single renormalon-chain contribution to the correlator of scalar currents in QCD is calculated in the $\bar{MS}$-scheme in the limit of a large $N_f$. We find that in the factorial growth of the coefficients due to renormalons takes…
A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative''…
Higher order renormalons beyond the chain of one-loop bubbles are discussed. A perturbation method for the infrared renormalon residue is found. The large order behavior of the current-current correlation function due to the first infrared…
There are two sources of the factorial large-order behavior of a typical perturbative series. First, the number of the different Feynman diagrams may be large; second, there are abnormally large diagrams known as renormalons. It is well…
The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally…