It is demonstrated that the well-regularized hypergeometric functions can be evaluated directly and numerically. The package NumExp is presented for expanding hypergeometric functions and/or other transcendental functions in a small regularization parameter. The hypergeometric function is expressed as a Laurent series in the regularization parameter and the coefficients are evaluated numerically by using the multi-precision finite difference method. This elaborate expansion method works for a wide variety of hypergeometric functions, which are needed in the context of dimensional regularization for loop integrals. The divergent and finite parts can be extracted from the final result easily and simultaneously. In addition, there is almost no restriction on the parameters of hypergeometric functions.

Based on the principle of Lorentz covariance the transition matrix elements from an off-shell photon state to the vacuum are decomposed into the light-cone photon distribution amplitudes (DAs), in which only two transversal DAs survive in the on-shell limit. The eight off-shell lightcone photon 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 DAs multiplied by their corresponding coupling constants are 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.

A semi-classical expansion based on the instanton vacuum model of quantum chromodynamics is taken to obtain the correlation function of the 0 −+ pseudoscalar glueball current. Working on the framework of Gaussian sum rules with a Gaussian-tail instantons size distribution, we find the contributions arising from the interaction between the classical instanton fields and quantum fluctuation ones are comparable to the pure classical and quantum ones, and thus impact the sum rule results; whereas the usual condensate contribution turned out to be negligible and may be understood as a small part of the corresponding instanton contributions. In consideration of axial U(1) anomaly, and inspired by the correlation function's behavior, we assume that the spectral function is saturated by the three zero-width resonances (the mesons η and η , and the pseudoscalar glueball G) plus continuum, and the corresponding Gaussian sum rules are constructed. The optimal mass and the coupling constant of the lowest pseudoscalar glueball are predicted to be consistent in a series Gaussian sum rules and almost the same as that of our previous Laplace sum rules.

respectively. In addition, the M 2 γγ-dependent partial widths of the inclusive decay are also presented.

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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.

In the framework of a semiclassical expansion for quantum chromodynamics (QCD) 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 Breit-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 QCD with and without light quarks are studied. A consistency between the subtracted and unsubtracted sum rules is 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.