Consistent Laplace sum rules for pseudoscalar glueball in the instanton vacuum model

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.…”

“…[19]. However, this state lies considerably lower than the theoretical expectations: the lattice QCD predictions suggest a glueball around 2.5 GeV [36,59]; the mass scale of the pseudoscalar glueball obtained in the QCD sum rule approach is above 2 GeV [7,15,16,60]. Moreover, there are attractive arguments for the scalar and pseudoscalar glueballs being approximately degenerate in mass [61], and even the scenario that a pseudoscalar glueball may be lower in mass than the scalar one was recently discussed in Ref.…”

“…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.…”

“…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].…”