Scalar gluonium and instantons

Abstract

The impact of QCD instantons on scalar glueball properties is studied in the framework of an instanton-improved operator product expansion (IOPE) for the 0 ++ glueball correlation function. Direct instanton contributions are found to strongly dominate over those from perturbative fluctuations and soft vacuum fields. All IOPE sum rules, including the one involving a subtraction constant, show a high degree of stability and are, in contrast to previous glueball sum rules, consistent with the low-energy theorem for the zero-momentum correlator. The predicted glueball mass m G = 1.53 ± 0.2 GeV is less sensitive to the instanton contributions then the glueball coupling (residue) f G = 1.01 ± 0.25 GeV, which increases by about half an order of magnitude. Both glueball properties are shown to obey scaling relations as a function of the average instanton size and density.

Topological charge screening and pseudoscalar glueballs

“…Direct instantons are the paradigm for such physics, and their contributions to the spin-0 glueball correlators are indeed exceptionally large. We have improved on the previous evaluation of these contributions [3] by implementing a realistic instanton size distribution and the renomalization of the instanton-induced coefficients (both of these improvements should be useful in other hadron channels as well). A further new development is very specific to the 0 −+ glueball channel: we have found compelling evidence for topological charge screening to provide crucial contributions to the unit operator coefficient of the pseudoscalar glueball IOPE.…”

“…The implementation of the direct instanton contributions in the 0 −+ channel is straightforward: the expressions from the 0 ++ channel [3] can simply be taken over, with their signs inverted. This is a consequence of the (Minkowski) (anti-) self-duality of the (anti-) instanton's field strength,…”

“…One such opportunity was recently exploited in OCD sum rule analyses, which found nonperturbative short-distance physics in the form of direct instantons [2] to play a crucial role in the structure and dynamics of the scalar (0 ++ ) glueball [3,4]. Indeed, the instanton-improved operator product expansion (IOPE) of the 0 ++ glueball correlator resolves two longstanding problems of the conventional sum rules (the mutual inconsistency of different Borel moment sum rules and the conflict with the underlying low-energy theorem [5,6]), generates new scaling relations between fundamental glueball and instanton properties, and leads to improved sum rule predictions for scalar glueball properties [3]. (See also the subsequent gaussian sum rule analysis [7], based on the same instanton contributions.)…”

Finite-width Laplacian sum rules for 2++ tensor glueball in the instanton vacuum model

“…For short distance region, we assume that the contribution from a single instanton is dominant over multi-instantons [50]. At the leading loop level, the gluon propagator, (33) ,in the background field Feynman gauge becomes the puregluon one in the usual Feynman gauge which is used actually in our calculation.…”

“…Moreover, the values of condensates can be reproduced from instanton distribution [29][30][31][32]. The contributions of instanton and those of the condensates may reveal the same non-perturbative effects, and thus including both contributions at the same time will cause the so-called double counting problem [33]. To avoid it, a semiclassical expansion in instanton background fields is suggested in our previous works to analyze the properties of the lowest 0 ++ scalar glueball [13,34] and 0 −+ pseudoscalar one [15][16][17][18], where the correlation functions of the glueball currents are calculated by just including the contributions from the pure instantons, the pure quantum gluons, and the interference between both, instead of working with both instantons and condensates at the same time.…”