Phenomenology of pseudotensor mesons and the pseudotensor glueball

Abstract

We study the decays of the pseudotensor mesons $[{\pi }_2(1670),K_2(1770),{\eta }_2(1645),{\eta }_2(1870)]$ interpreted as the ground-state nonet of $1^1{D}_2$ $\bar{q}q$ states using interaction Lagrangians which couple them to pseudoscalar, vector, and tensor mesons. While the decays of ${\pi }_2(1670)$ and $K_2(1770)$ can be well described, the decays of the isoscalar states ${\eta }_2(1645)$ and ${\eta }_2(1870)$ can be brought in agreement with experimental data only if the mixing angle between nonstrange and strange states is surprisingly large (about $-42^{\circ }$, similar to the mixing in the pseudoscalar sector, in which the chiral anomaly is active). Such a large mixing angle is however at odd with all other conventional quark-antiquark nonets: if confirmed, a deeper study of its origin will be needed in the future. Moreover, the $\bar{q}q$ assignment of pseudotensor states predicts that the ratio $[{\eta }_2(1870)\to a_2(1320)\pi ]/[{\eta }_2(1870)\to f_2(1270)\eta ]$ is about $23.5$. This value is in agreement with Barberis et al., ($20.4\pm 6.6$), but disagrees with the recent reanalysis of Anisovich et al., ($1.7\pm 0.4$). Future experimental studies are necessary to understand this puzzle. If Anisovich's value shall be confirmed, a simple nonet of pseudoscalar mesons cannot be able to describe data (different assignments and/or additional state, such as an hybrid state, will be needed). In the end, we also evaluate the decays of a pseudoscalar glueball into the aforementioned conventional $\bar{q}q$ states: a sizable decay into $K_2^{\ast }(1430)K$ and $a_2(1230)\pi$ together with a vanishing decay into pseudoscalar-vector pairs [such as $\rho (770)\pi$ and $K^{\ast }(892)K$] are expected. This information can be helpful in future studies of glueballs at the ongoing BESIII and at the future PANDA experiments.

arXiv comment22 pages (15 main text, 4 appendix, 3 references), 8 tables, 2 figures, v2: more references, additional information and minor changes due to referee comments, published version

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