QCD sum-rule study of scalar mesons

Abstract

In this thesis, QCD Laplace sum-rules for the light quark 'qq ' currents are employed to study the properties of the non-strange ' I' = 0 and 'I' = 1 light quark scalar mesons. This QCD sum-rule analysis allows us to interpret the experimentally observed ' I' = 0 and 'I' = 1 scalar mesons. The Holder inequality technique is employed to determine the region of validity for the QCD sum-rule, and a stability analysis of the QCD sum-rule prediction is conducted through a Monte-Carlo uncertainty simulation of uncertainties. The field theoretical content of the QCD sum rules incorporates purely-perturbative QCD contributions to two-loop order, leading contributions from QCD-vacuum condensates, and the direct single-instanton contributions in the instanton-liquid QCD vacuum model. Single-instanton contributions are the only components of the QCD field theory that distinguish between isospin states, and therefore they are responsible for breaking the mass degeneracy between the lowest-lying isovector and isoscalarmesons. A novel treatment of instanton effects in QCD continuum contribution is included in this thesis. There is also a need to go beyond the narrow resonance approximation for the scalar channels which are likely to exhibit sensitivity to broad resonance structure. A finite-width effect anticipated from physical resonance widths is incorporated for the hadronic content of the 'I' = 0 and 'I' = 1 QCD sum rules. In the 'I' = 0 channel, our results support interpretation of the 'f'0(980) as the lowest-lying light quark scalar meson, indicating that 'f'0(400 - 1200) is unnaturally decoupled from a light quark non-strange current. In the ' I' = 1 channel, the results identify 'a'0(1450) as the lowest-lying 'qq' resonance, and are indicative of a non-'qq' interpretation for 'a'0(980).