Phenomenology of pseudotensor mesons and the pseudotensor glueball

Understand

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 $[ \eta_2 (1870) \rightarrow a_2 (1320) \pi]/[\eta_2 (1870) \rightarrow f_2 (1270) \eta]$ is about $23.5$.