Gaussian sum-rules and prediction of resonance properties

Abstract

Techniques for using Gaussian QCD sum-rules to predict hadronic resonance properties are developed for single-resonance and two-resonance phenomenological models, and criteria are developed for determining which of these models is required for analyzing a particular hadronic channel. The vector current sum-rule coupled to the ρ meson is shown to be consistent with a single resonance model, and the Gaussian sum-rule analysis results in an accurate ρ mass prediction which exhibits excellent agreement between the theoretical prediction of the Gaussian sum-rule and the phenomenological model. A two-resonance model is shown to be necessary for the Gaussian sum-rule for the non-strange quark scalar (nn) currents. The two-resonance Gaussian sum-rule analysis of the isoscalar and isovector (I = 0, 1)nn scalar mesons exhibits excellent agreement between the theoretical prediction and phenomenological model. The prediction of the resonance properties of the I = 0, 1 nn scalar mesons in this two-resonance model provides valuable information for the interpretation of the scalar mesons, including the X(1775).

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

“…Thus, the information contained in the GSRs which is independent of the FESRs can be isolated by considering the normalized Gaussian sum-rules (NGSRs) [14] …”

“…For non-diagonal correlators the possibility of state mixing implies that ρ had (t) could change sign, so it is possible that either M k,0 (τ, s 0 ) or the denominator on the right-hand sides of (14) or (16) could be zero. In such situations, the GSRs would have to be analyzed instead of the NGSRs.…”

Gaussian Sum-Rule Analysis of Scalar Gluonium and Quark Mesons

“…[16]), ρ is the instanton radius, and n(ρ) is the instanton density function. Before substituting (13) into (9), it is convenient to first simplify (9) by employing a particularly useful identity relating the Borel transform (10) to the inverse Laplace transform [8] …”

“…Substituting the right-hand side of (7) into (9) and again making use of the identity (11), it is simple to show that…”

“…In this paper, we focus exclusively on the k = 0, −1 Gaussian sum-rules. Substituting (13) into (36) and recalling (31) gives 4 (for details on simplifying the relevant integrals in (31), see [6,9])…”