Off-shell photon distribution amplitudes in the low-energy effective theory of QCD

Based on the principle of the Lorentz covariance the transition matrix elements from an off-shell photon state to the vacuum are decomposed into the light-cone photon DAs, in which only two transversal DAs survive in the on-shell limit. The eight off-shell light-cone photon distribution amplitudes (DAs) corresponding to chiral-odd and chiral-even up to twist-four and the corresponding coupling constants are studied systematically in the instanton vacuum model of quantum chromodynamics (QCD). The various individual photon DA multiplied by its corresponding coupling constant is expressed in terms of the correlation functions, which are connected with the spectral densities of an effective quark propagator, and then evaluated in the low-energy effective theory derived from the instanton vacuum model of QCD. The explicit analytical expressions and the numerical results for the photon DAs and their coupling constants are given

Finite-width Gaussian sum rules for 0−+0^{-+} pseudoscalar glueball based on correction from instanton-gluon interference to correlation function

Based on correction from instanton-gluon interference to correlation function, the properties of the $0^{-+}$ pseudoscalar glueball is investigated in a family of finite-width Gaussian sum rules. In the framework of semiclassical expansion for quantum chromodynamics $(\textrm{QCD})$ in the instanton liquid background, the contribution arising from the the interference between instantons and the quantum gluon fields is calculated, and included in the correlation function together with pure-classical contribution from instantons and the perturbative one. The interference contribution is turned to be gauge-invariant, free of infrared divergence, and has a great role to restore the positivity of the spectra of the full correlation function. The negligible contribution from vacuum condensates is excluded in our correlation function to avoid the double counting. Instead of the usual zero-width approximation for the resonances, the usual Breit-Wigner form with a suitable threshold behavior for the spectral function of the finite-width resonances is adopted. A consistency between the subtracted and unsubtracted sum rules is very well justified. The values of the mass, decay width and coupling constants for the $0^{-+}$ resonance in which the glueball fraction is dominant are obtained, and agree with the phenomenological analysis.Comment: 18 pages, 10 figure

0++0^{++} scalar glueball in finite-width Gaussian sum rules

Based on a semiclassical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the $0^{++}$ scalar glueball current is given, and the properties of the $0^{++}$ scalar glueball are studied in the framework of Gaussian sum rules. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are come into play. Instead of the usual zero-width approximation for the resonance, the Breit-Wigner form for the spectral function of the finite-width resonance is adopted. The family of the Gaussian sum rules for the scalar glueball in quantum chromodynamics with and without light quarks is studied. A consistency between the subtracted and unsubtracted sum rules is very well justified, and the values of the decay width and the coupling to the corresponding current for the $0^{++}$ resonance, in which the scalar glueball fraction is dominant, are obtained.Comment: 18pages, 9figure

The finite-width Laplace sum rules for 0++0^{++} scalar glueball in instanton liquid model

In the framework of a semi-classical expansion for quantum chromodynamics in the instanton liquid background, the correlation function of the $0^{++}$ scalar glueball current is given. Besides the pure classical and quantum contributions, the contributions arising from the interactions between the classical instanton fields and quantum gluons are taken into account as well. Instead of the usual zero-width approximation for the resonance, the Brite-Wigner form for the spectral function of the finite-width resonance is adopted. The family of the Laplace sum rules for the scalar glueball in quantum chromodynamics with and without light quarks are studed. A consistency between the subtracted and unsubtracted sum rules are very well justified, and the values of the mass, decay width, and the coupling to the corresponding current for the $0^{++}$ resonance in which the glueball fraction is dominant, are obtained.Comment: 6 figure