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

Abstract

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.

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

“…The predicted mass of the lowest lying tensor glueball is only a little bit higher than that of the scalar one (1500MeV) determined recently according to the same approach [14]. The reason may be that although there is a lack of the leading instanton contribution in the tensor channel of glueballs, there is still a strong attractive force arising from the interference between the quantum gluon fields and the classical one, so as to govern the final result almost alone.…”

“…In this paper, we investigate the mass scale and the magnitude of the width for the lowest state of tensor glueballs along the same line with our previous works [13][14][15][16][17][18]. This issue is first considered in a nonrelativistic approach by assuming a large value of the effective gluon mass [35], and the mass, m 2 ++ , of the lowest tensor glueball was predicted to be about 1.6GeV; later, relying on the construction of an efficient quasiparticle gluon basis for Hamiltonian QCD in Coulomb gauge, m 2 ++ is exploited to be 2.42GeV.…”

“…The possibly non-vanishing gluonium content of the ground state η and η ′ mesons is discussed in [12,[63][64][65]. Up to now, only the topological model of the glueball as a closed flux tube [61] predicts a degeneracy of the 0 ++ and 0 −+ glueball masses and admits the region 1.3 − 1.5 GeV before our recent result [13,14,17,18] published.…”

“…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.…”

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

“…(3) After choosing an appropriate gauge, for example the fixed-point gauge, where the gauge link becomes a unit operator, we are in a position to express the leading order of the correlation functions in terms of the spectral densities of the effective quark propagator. An important point is that this quark propagator is derived from the instanton vacuum model of QCD in the singular gauge of the gauge potential, which obeys the fixed-point gauge too, as checked in the same way as in [39,40]. (4) Completing the integrations with the help of Lorentz covariance and a straightforward manipulation, we obtain the explicit analytical forms for the light-cone photon DAs and their coupling constants, and we display the dependence of the photon DAs on the momentum fraction u carried by the quark for various photon virtualities P 2 , and the dependence of the corresponding coupling constants on P 2 .…”