Erratum: Scalar glueball mixing and decay [Phys. Rev. D 59, 014022 (1999)]

Abstract

We provide the first explanation of the counter-intuitive scalar glueball couplings to pseudoscalar mesons found in lattice QCD and predict hitherto uncalculated decay modes. Significant a 1 π and (ππ) S (ππ) S couplings are found. We demonstrate the equivalence of linear and quadratic mass matrices for glueballquarkonium mixing. The equivalence of formalisms which deal with a glueballquarkonium basis and only a quarkonium basis is demonstrated. We show that the f 0 (1500) is not the heaviest state arising from glueball-quarkonium mixing for a glueball mass consistent with lattice QCD. The masses and couplings of scalar mesons, as well as their valence content, are calculated.

Scalar glueball, scalar quarkonia, and their mixing

“…Consequently, the mass of the f 0 (1370) state is predicted to be 1218 MeV in [35]. In our case, M S is larger than M N by only ∼ 25 MeV which reflects the result from the recent lattice calculation [6].…”

ON THE MIXING OF THE SCALAR MESONS f0(1370), f0(1500) AND f0(1710)

“…Furthermore, in both cases, the results exhibit destructive interference between the states |N and |S for f 0 (1500) while constructive interference between the states |N and |S for f 0 (1710) and f 0 (1370), which is also consistent with the conclusion given by Ref. [8][9][10][11].…”

“…(18) and (23), in both cases, a large mixing effect on the f 0 (1710), f 0 (1500) and f 0 (1370) exists, which is consistent with our above results that in the scalar sector, pure glueball and quarkonia lie in a vicinal mass region. The largest components of f 0 (1370) and f 0 (1500) are quarkonia and the quarkonia content of the f 0 (1500) and f 0 (1370) differs due to the different mass level order of the bar states |N and |S , which is consistent with the main property of the mass matrix (1) that upon mixing the higher mass bare state becomes more massive, while the lower mass bare state becomes less massive (i.e., the mass splitting between the higher and lower mass bare states increases as a result of the mixing) [11]. The largest component of f 0 (1710) is glueball, which supports the argument that f J (1710) is a mixed qq glueball having a large glueball component if its spin is determined to be 0 [8].…”

“…The convenient but not convincing recent tendency is to put aside the f 0 (400 − 1200) and f 0 (980), and focus on f 0 (1370), f 0 (1500) and f 0 (1710) [7], although the spin-parity of the f J (1710) J P C = 0 ++ or ( and ) 2 ++ is controversial. Recently, several authors have discussed the quarkonia-glueball content of the f 0 (1370), f 0 (1500) and f 0 (1710) by studying the mixing of the three states [8][9][10][11]. The different assumption about the mass level order of the bare states |G = |gg , |S = |ss and |N = |uū + dd / √ 2 leads to the different quantitative predictions about the glueball-quarkonia content of the three states.…”

Glueball production via gluonic penguin $$B$$ B decays

“…These results support that the scalar meson f 0 (1710) is a glueball. Phenomenologically, f 0 (1710) could be an impure glueball since it may be contaminated by possible mixings with the colorless quarkantiquark states that have total isospin zero [3][4][5][6][7][8][9]. These mixing effects can be either small [5][6][7][8] or large [3][4][5]9], depending largely on the mixing schemes one chose to do the fits in and these may complicate the analysis.…”