Direct instantons, topological charge screening, and QCD glueball sum rules

Abstract

Nonperturbative Wilson coefficients of the operator product expansion (OPE) for the spin-0 glueball correlators are derived and analyzed. A systematic treatment of the direct instanton contributions is given, based on realistic instanton size distributions and renormalization at the operator scale. In the pseudoscalar channel, topological charge screening is identified as an additional source of (semi-) hard nonperturbative physics. The screening contributions are shown to be vital for consistency with the anomalous axial Ward identity, and previously encountered pathologies (positivity violations and the disappearance of the 0 −+ glueball signal) are traced to their neglect. On the basis of the extended OPE, a comprehensive quantitative analysis of eight Borel-moment sum rules in both spin-0 glueball channels is then performed. The nonperturbative OPE coefficients turn out to be indispensable for consistent sum rules and for their reconciliation with the underlying low-energy theorems. The topological short-distance physics strongly affects the sum rule results and reveals a rather diverse pattern of glueball properties. New predictions for the spin-0 glueball masses and decay constants and an estimate of the scalar glueball width are given, and several implications for glueball structure and experimental glueball searches are discussed. I. INTRODUCTIONAmong exotic hadrons, i.e. those which evade classification according to the constituent quark model, glueballs [1, 2, 3] occupy an extreme position. In fact, they contain no valence quarks at all and are the only hadrons which would persist in a world without quarks. Even the exclusion of sea quarks from QCD, as in quenched lattice simulations, is not expected to alter their properties drastically [94]. Hence glueball structure provides a unique source of information on nonperturbative gluon dynamics and may even shed light on the often elusive gluon component of the light classical hadrons (and potentially hybrids). A suggestive way to access this information is to investigate the role of known coherent gluon fields, with instantons as the most prominent example, in glueball structure.The operator product expansion (OPE) [4] of glueball correlation functions provides an effective analytical framework for such investigations. In fact, it exhibits several exceptional features of the gluonium channels already at the qualitative level. The probably most instructive one is directly associated with the defining characteristic of the OPE, i.e. its factorization of the short-distance correlators into contributions from hard and soft field modes. Indeed, since the glueball's gluon content should be mostly nonperturbative, one might expect it to manifest itself primarily in the soft contributions, i.e. in the gluon condensates. Surprisingly, this is not the case: the condensate contributions are unusually weak [5,6,7] and cannot fully reflect the nonperturbative nature of low-lying gluonia. This suggests that a major part of the nonperturbative physics is relatively hard ...

Topological charge screening and pseudoscalar glueballs

“…Two of the consequences were recently observed in [8]: any reliable signal for a pseudoscalar glueball resonance disappears (in contradiction to lattice evidence), and even the fundamental spectral positivity bound is violated. In addition, the crucial low-energy theorem for the zero-momentum 0 −+ glueball correlator, and therefore the underlying anomalous axial Ward identity, is strongly violated [4]. As pointed out in [4], these problems have an appealing solution in the form of additional nonperturbative short-range contributions to the IOPE, associated with topological charge screening.…”

“…In addition, the crucial low-energy theorem for the zero-momentum 0 −+ glueball correlator, and therefore the underlying anomalous axial Ward identity, is strongly violated [4]. As pointed out in [4], these problems have an appealing solution in the form of additional nonperturbative short-range contributions to the IOPE, associated with topological charge screening. Below, we will sketch the implementation of the screening contributions and their impact on the sum rule analysis.…”

“…(for three light flavors and m u,d m s ) which derives from the axial anomaly and imposes stringent consistency requirements on the sum rule analysis [4].…”

“…(See also the subsequent gaussian sum rule analysis [7], based on the same instanton contributions.) The Borel sum rule analysis has recently been improved and extended (to realistic instanton size distributions and renormalized instanton contributions) in [4]. Hard nonperturbative contributions to the pseudoscalar glueball IOPE and sum rules were also investigated.…”

“…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].…”