Phenomenology of pseudotensor mesons and the pseudotensor glueball

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) (q) over barq 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.2(1645) and eta(2)(1870) can be brought in agreement with the present experimental data only if the mixing angle between nonstrange and strange states is surprisingly large (about -42 degrees, 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 (q) over barq assignment of pseudotensor states predicts that the ratio [eta(2)(1870) -> a(2)(1320) pi]/[eta(2)(1870) -> f(2)(1270)eta] is about 23.5. This value is in agreement with Barberis et al., (20.4 +/- 6.6), but disagrees with the recent reanalysis of Anisovich et al., (1.7 +/- 0.4). Future experimental studies are necessary to understand this puzzle. If Anisovich's value is confirmed, a simple nonet of pseudoscalar mesons cannot be able to describe data (different assignments and/or additional states, such as an hybrid state, will be needed). In the end, we also evaluate the decays of a pseudoscalar glueball into the aforementioned conventional (q) over barq states: a sizable decay into K-2* (1430) K and a(2)(1230) pi together with a vanishing decay into pseudoscalar-vector pairs (such as rho(770) pi and K*(892) K) are expected. This information can be helpful in future studies of glueballs at the ongoing BESIII and at the future PANDA experiments.