Low-lying even parity meson resonances and spin-flavor symmetry

TL;DR

This paper investigates low-lying even parity meson resonances using an SU(6) spin-flavor symmetric approach, identifying most as multiplets and predicting new exotic states, with some resonances possibly being glueballs or hybrids.

Contribution

It extends the SU(3) Weinberg-Tomozawa Lagrangian to SU(6), incorporating symmetry breaking and solving the Bethe Salpeter equation to classify meson resonances and predict exotic states.

Findings

Most low-lying meson resonances fit SU(6) multiplets.

Some resonances are candidates for glueballs or hybrids.

Predicted five exotic resonances in the 1.4-1.6 GeV range.

Abstract

A study is presented of the $s-$wave meson-meson interactions involving members of the $\rho-$nonet and of the $\pi-$octet. The starting point is an SU(6) spin-flavor extension of the SU(3) flavor Weinberg-Tomozawa Lagrangian. SU(6) symmetry breaking terms are then included to account for the physical meson masses and decay constants, while preserving partial conservation of the axial current in the light pseudoscalar sector. Next, the $T-$matrix amplitudes are obtained by solving the Bethe Salpeter equation in coupled-channel with the kernel built from the above interactions. The poles found on the first and second Riemann sheets of the amplitudes are identified with their possible Particle Data Group (PDG) counterparts. It is shown that most of the low-lying even parity PDG meson resonances, specially in the $J^P=0^+$ and $1^+$ sectors, can be classified according to multiplets of the spin-flavor symmetry group SU(6). The $f_0(1500)$, $f_1(1420)$ and some $0^+(2^{++})$ resonances cannot be accommodated within this SU(6) scheme and thus they would be clear candidates to be glueballs or hybrids. Finally, we predict the existence of five exotic resonances ($I \ge 3/2$ and/or $|Y|=2$) with masses in the range 1.4--1.6 GeV, which would complete the $27_1$, $10_3$, and $10_3^*$ multiplets of SU(3)$\otimes$SU(2).