Abstract:A pedagogical introduction to the heavy quark theory is given. It is explained that various expansions in the inverse heavy quark mass 1/m Q present a version of the Wilson operator product expansion in QCD. A systematic approach is developed and many practically interesting problems are considered. I show how the 1/m Q expansions can be built using the background field technique and how they work in particular applications. Interplay between perturbative and nonperturbative aspects of the heavy quark theory i… Show more
“…where I used the fact that β 0 αs(Q 2 ) 8π = 1 2 ln(Q 2 /Λ 2 ) = 1/n * . Of course, we 10 A remarkable feature making the model different from QCD is the fact of OPE convergence at the level of O(N 0 ) and O(N −1 ) terms. This is due the fact that at this level particle production thresholds do not extend to infinite energies in the O(N ) sigma model, unlike QCD.…”
Section: Ope and Renormalons In Qcdmentioning
confidence: 92%
“…All terms in (16) have the same sign, which means that the asymptotic series per se is not Borel-summable. Now let us briefly consider the large k 2 domain in (10). At large k 2…”
I summarize what we know of renormalons from the 1970s and 80s: their uses and theoretical status. It is emphasized that renormalons in QCD are closely related to the Wilsonean operator product expansion (OPE) -a setup ideally suited for dealing with the factorially divergent series reflecting infrared dynamics. I discuss a breakthrough proposal due to Uraltsev et al. to use renormalons to evaluate nonperturbative (power) corrections in the processes without OPE. Some fresh ideas which were put forward recently are briefly discussed too, with emphasis on a possible relationship between resurgence via trans-series and OPE.This article is devoted to the memory of my friend Kolya Uraltsev. I should emphasize that these are my personal recollections. Other people who closely knew Kolya may or may not agree with my opinions.
“…These are quantities amenable to study via the OPE. Local quark-hadron duality was given a new consideration a few years ago by M. Shifman [112], who related its violations to the asymptotic nature of the power expansion in inverse large energy scale provided by the 'practical' OPE. These ideas were later reiterated and developed in a number of papers, in particular in connection to heavy quark physics (see, e.g., Refs.…”
Achievements in the heavy quark theory over the last decade are reviewed, with the main emphasis put on dynamical methods which quantify nonperturbative effects via application of the Operator Product Expansion. These include the total weak decay rates of heavy flavor hadrons and nonperturbative corrections to heavy quark sum rules. Two new exact superconvergent sum rules are derived; they differ from the known ones in that they are finite and normalization point independent in perturbation theory. A new hadronic parameter Σ is introduced which is a spinnonsinglet analogue of Λ = M B −m b ; it is expected to be about 0.25 GeV. The first sum rule implies the bound ρ 2 > 3/4 for the slope of the Isgur-Wise function. The heavy quark potential is discussed and its connection to the infrared contributions in the heavy quark mass. Among applications extraction of |V cb | from the total semileptonic and from the B → D * zero recoil rates is addressed, as well as extracting |V ub | from Γ sl (b → u). Practical aspects of local quark-hadron duality are briefly discussed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.