A gaussian sum-rule analysis of scalar glueballs

Abstract

Although marginally more complicated than the traditional Laplace sum-rules, Gaussian sum-rules have the advantage of being able to probe excited and ground states with similar sensitivity. Gaussian sum-rule analysis techniques are applied to the problematic scalar glueball channel to determine masses, widths and relative resonance strengths of low-lying scalar glueball states contributing to the hadronic spectral function. A feature of our analysis is the inclusion of instanton contributions to the scalar gluonic correlation function. Compared with the next-to-leading Gaussian sum-rule, the analysis of the lowest-weighted sum-rule (which contains a large scale-independent contribution from the low energy theorem) is shown to be unreliable because of instability under QCD uncertainties. However, the presence of instanton effects leads to approximately consistent mass scales in the lowest weighted and next-lowest weighted sum-rules. The analysis of the next-to-leading sum-rule demonstrates that a single narrow resonance model does not provide an adequate description of the hadronic spectral function. Consequently, we consider a wide variety of phenomenological models which distribute resonance strength over a broad region-some of which lead to excellent agreement between the theoretical prediction and phenomenological models. Including QCD uncertainties, our results indicate that the hadronic contributions to the spectral function stem from a pair of resonances with masses in the range 0.8-1.6 GeV, with the lighter of the two potentially having a large width.

Near-maximal mixing of scalar gluonium and quark mesons: A Gaussian sum-rule analysis

“…The significance of instanton contributions in the overall consistency of the LET-sensitive k = −1 sum-rule and the LET-insensitive k ≥ 0 sum-rules was first demonstrated for Laplace sum-rules [27,28]. A similar consistency is observed for Gaussian sum-rules, but theoretical uncertainties are better controlled in the k ≥ 0 GSRs [13]; hence, we focus here on the k = 0 GSRs for both the diagonal gluonic and quark channels. QCD expressions for the GSRs G (ŝ, τ, s 0 ) corresponding to the diagonal correlation functions (23), (24) can be found in [13,14].…”

“…From the correlation function, the k = 0 GSR can be calculated as outlined in Section 2 and Ref. [13]:…”

“…GSR analyses of gluonium have employed single and double narrow resonance models in addition to a variety of models that incorporate resonance widths [13,15]. However, inclusion of width effects do not lead to appreciable improvement in the agreement between the QCD expression and phenomenological model.…”

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

“…The research of glueballs may give a unique insight into the non-Abelian dynamics of QCD. Theoretical investigations including lattice simulations [1][2][3], model researches [4][5][6] and sum rule analyses [7][8][9][10][11][12][13][14][15][16][17][18] have been going on for a long time, but no decisive evidence of the existence of glueballs has been confirmed by experimental research up to now [19,20]. Further investigation on glueballs still makes sense.…”

Topological charge screening and pseudoscalar glueballs

“…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.) The Borel sum rule analysis has recently been improved and extended (to realistic instanton size distributions and renormalized instanton contributions) in [4].…”