Pseudotensor mesons as three-body resonances

TL;DR

This paper proposes that light pseudotensor mesons can be understood as three-body molecules composed of a pseudoscalar and a tensor meson, with the tensor meson itself being a vector-vector bound state, supported by calculations showing resonant structures.

Contribution

It introduces a novel molecular interpretation of pseudotensor mesons as PVV states using three-body Faddeev equations and fixed center approximation, linking meson interactions to observed resonances.

Findings

Identified resonant structures matching pi_2(1670), eta_2(1645), K*_2(1770) mesons.

Demonstrated strong attraction in PVV interactions leading to quasibound states.

Supported the molecular picture of pseudotensor mesons through theoretical calculations.

Abstract

We show that the lightest pseudotensor mesons J^{PC}=2^-+ can be regarded as molecules made of a pseudoscalar (P) 0^-+ and a tensor 2^++ meson, where the latter is itself made of two vector (V) mesons. The idea stems from the fact that the vector-vector interaction in s-wave and spin 2 is very strong, to the point of generating the 2^++ tensor mesons. On the other hand the interaction of a pseudoscalar with a vector meson in s-wave is also very strong and it generates dynamically the lightest axial-vector mesons. Therefore we expect the PVV interaction to be strongly attractive and thus able to build up quasibound PVV resonances. We calculate the three body PVV interaction by using the fixed center approximation to the Faddeev equations where the two vectors are clustered forming a tensor meson. We find clear resonant structures which can be identified with the pi_2(1670), eta_2(1645) and K^*_2(1770) (2^-+) pseudotensor mesons.