It is well known that, because of the axial anomaly in QCD, mesons with J P ¼ 0 − are close to SUð3Þ V eigenstates; the η 0 ð958Þ meson is largely a singlet, and the η meson an octet. In contrast, states with J P ¼ 1 − are flavor diagonal; e.g., the ϕð1020Þ is almost puress. Using effective Lagrangians, we show how this generalizes to states with higher spin, assuming that they can be classified according to the unbroken chiral symmetry of G fl ¼ SUð3Þ L × SUð3Þ R . We construct effective Lagrangians from terms invariant under G fl and introduce the concept of hetero-and homochiral multiplets. Because of the axial anomaly, only terms invariant under the Zð3Þ A subgroup of the axial Uð1Þ A enter. For heterochiral multiplets, which begin with that including the η and η 0 ð958Þ, there are Zð3Þ A invariant terms with low mass dimension which cause states to mix according to SUð3Þ V flavor. For homochiral multiplets, which begin with that including the ϕð1020Þ, there are no Zð3Þ A invariant terms with low mass dimension, and so states are diagonal in flavor.In this way, we predict the flavor mixing for the heterochiral multiplet with spin 1 as well as for hetero-and homochiral multiplets with spin 2 and spin 3.

We study the decays of the pseudotensor mesons [π2 (1670), K2(1770), η2(1645), η2(1870)] interpreted as the ground-state nonet of 1 1 D2qq states using interaction Lagrangians which couple them to pseudoscalar, vector, and tensor mesons. While the decays of π2(1670) and K2(1770) can be well described, the decays of the isoscalar states η2(1645) and η2 (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 • , 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, theqq assignment of pseudotensor states predicts that the ratio [η2(1870) → a2(1320) π]/[η2(1870) → f2 (1270) η] 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 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 conventionalqq states: a sizable decay into K * 2 (1430) K and a2(1230) π together with a vanishing decay into pseudoscalar-vector pairs [such as ρ(770) π 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. arXiv:1608.08777v2 [hep-ph] 15 Dec 2016 2 THE MODEL 2 parity P are connected by chiral transformations. For instance, scalar (1 3 P 0 , J P C = 0 ++ ) and pseudoscalar mesons (1 1 S 0 , J P C = 0 −+ ) as well as vector (1 3 S 1 , J P C = 1 −− ) and axial-vector mesons (1 3 P 1 , J P C = 1 ++ ) are chiral partners, e.g. Ref. [4]. In addition to explicit breaking, chiral symmetry is -even more importantly -also broken spontaneously,pseudoscalar mesons (e.g., the pions) are the corresponding quasi-Goldstone bosons. Tensor mesons (1 3 P 2 , J P C = 2 ++ ) are another example of a very well-understoodqq nonet: their decays fit nicely into this scheme [2,[5][6][7]. The chiral partners of tensor mesons, the pseudotensor mesons (1 1 D 2 , J P C = 2 −+ ), are not so well understood, e.g. Refs. [8,9] and Refs. therein. The standard assignment [1,2] contains the isotriplet state π 2 (1670), the isodoublet states K 2 (1770), and the isoscalar states η 2 (1645) and η 2 (1870). We plan to study the decays of these resonances in order to test the validity of this assignment and to investigate the mixing in the isoscalar sector. To this end, we build two effective interaction Lagrangians which describe the decays of pseudotensor states into vector-pseudoscalar and into tensor-pseudoscalar pairs. The isotriplet and isodoublet states ...

In this paper, we review classical and quantum field theory of massive non-interacting spin-two fields. We derive the equations of motion and Fierz-Pauli constraints via three different methods: the eigenvalue equations for the Casimir invariants of the Poincaré group, a Lagrangian approach, and a covariant Hamilton formalism. We also present the conserved quantities, the solution of the equations of motion in terms of polarization tensors, and the tree-level propagator. We then discuss canonical quantization by postulating commutation relations for creation and annihilation operators. We express the energy, momentum, and spin operators in terms of the former. As an application, quark-antiquark currents for tensor mesons are presented. In particular, the current for tensor mesons with quantum numbers J P C = 2 −+ is, to our knowledge, given here for the first time.