Where is the pseudoscalar glueball?

Abstract

The pseudoscalar mesons π(1300), K(1460), η(1295), η(1405) and η(1475) are assumed to form the meson decuplet which includes the glueball as the basis state supplementing the standard SU (3)F nonet of light qq states (q = u, d, s). The decuplet is investigated by using the algebraic approach based on the hypothesis of vanishing exotic commutators (VEC) of SU (3)F "charges" and their time derivatives. This leads to a system of master equations (ME) determining: (a) octet contents of the physical isoscalar mesons, (b) the mass formula relating all masses of the decuplet and (c) the mass ordering rule. The states of the physical isoscalar mesons η(1295), η(1405), η(1475) are expressed as superpositions of the "ideal" qq (N and S) states and the glueball G one. The "mixing matrix" realizing transformation from the unphysical states to the physical ones follows from the octet contents and is expressed totaly by the decuplet meson masses. Among four one-parameter families of the resulting mixing matrices (multitude of the solutions arising from bad quality of data on the π(1300) and K(1460) meson masses) there is a family attributing the glueball-dominated composition to the η(1405) meson. The pseudoscalar decuplet is similar in some respects to the scalar one: both are composed of the excited qq states and G; the mass ordering of their N, S, G -dominated isoscalars is the same. Contrary to the Lattice QCD and other predictions, the mass m G −+ of the pseudoscalar pure glueball state is smaller than the scalar m G

Categorizing resonancesX(1835),X(2120), andXYu1, Sun2, Liu3 et al. 2011Phys. Rev. D661620View full textAdd to dashboardCite

“…[24,26,27]. In most theoretical studies [28][29][30][31][32][33], the decay patterns of ð1405Þ indicate it as being a possible candidate of 0 Àþ glueball with the mass consistent with the prediction of the flux tube model [34]. In any case, if one leaves ð1405Þ as a pseudoscalar glueball and to be investigated separately, it is interesting to recognize a pseudoscalar nonet of the second radial excitations formed by ð1800Þ, Kð1830Þ, ð1760Þ, and Xð1835Þ.…”

Localization of the glueball and possible decuplets of tensor mesons

“…The MOR restrictions for the decuplet masses have been formulated long ago in several approaches e.g. [9,11] but they are most apparently seen from fig.1 of [12]. We give now their simple algebraic proof.…”

“…The functions l 2 i being the solution of the ME, are not a priori positive; therefore we require them to satisfy the conditions (12). These conditions restrict the masses of particles belonging to the multiplet; the particles may form multiplet only if their masses satisfy these conditions.…”

Abelian decomposition and glueball-quarkonium mixing in QCD

“…The popular view that PDG endorses is that η(548) and η (958) are predominantly the uū + d d and ss states, and that η(1295) and η(1475) are the first radial excitations of η(548) and η (958) [87][88][89]. But it is widely agreed that η(1405) is indeed a pseudo-scalar glueball [90][91][92][93][94][95]. This is endorsed by PDG and by our analysis, although there exists a lattice result which might contradict with this view [12].…”