Gaussian sum rules for 0⁻⁺glueball in the instanton vacuum model

Abstract

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.

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

“…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.…”

“…It plays a great role in sum rule analysis in accordance with the spirit of semiclassical expansion. The imaginary part of the correlation function including this interference contribution is positive as shown in FIG.6 in appendix D. Moreover, it is excluded in the correlation function the traditional condensate contribution to avoid the double counting [7] because condensates can be reproduced by the instanton distributions [29][30][31][32]; another cause to do so is that the usual condensate contribution is proven to be unusually weak, and cannot fully reflect the nonperturbative nature of the low-lying gluonia [7,15,16,54]; in our opinion, the condensate contribution may be considered as a small fraction of the corresponding instanton one, so it is naturally taken into account already.…”

“…For the finiteness of the pion mass, we have (15) without consideration of the possibility of a 2 ++ meson or glueball decaying into two photons. There are, as well, another argument for the low-energy theorem, (15), for the tensor glueball current. Inserting the full intermediate states into the correlation function between the two currents O µν (x) and O µν (0), it is easy to see that all intermediate states have certainly no contribution with the possible exceptions of the vacuum |Ω and the multi-massless pions |nπ with n = 2, 4, · · · because of the energy-momentum conservations.…”

“…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.…”

“…To avoid it, a semiclassical expansion in instanton background fields is suggested in our previous works to analyze the properties of the lowest 0 ++ scalar glueball [13,34] and 0 −+ pseudoscalar one [15][16][17][18], where the correlation functions of the glueball currents are calculated by just including the contributions from the pure instantons, the pure quantum gluons, and the interference between both, instead of working with both instantons and condensates at the same time. In fact, the condensate contributions turned out to be very small as compared with those of instantons (including the classical and quantum interference contribution) in the glueball channels, and may be understood as a small fraction of the latter in the local limit [13,15,16].…”