On the ${\eta }_1(1855)$, ${\pi }_1(1400)$ and ${\pi }_1(1600)$ as dynamically generated states and their SU(3) partners

Abstract

In this work, we interpret the newly observed ${\eta }_1(1855)$ resonance with exotic $J^{PC}=1^{-+}$ quantum numbers in the $I=0$ sector, reported by the BESIII Collaboration, as a dynamically generated state from the interaction between the lightest pseudoscalar mesons and axial-vector mesons. The interaction is derived from the lowest order chiral Lagrangian from which the Weinberg-Tomozawa term is obtained, describing the transition amplitudes among the relevant channels, which are then unitarized using the Bethe-Salpeter equation, according to the chiral unitary approach. We evaluate the ${\eta }_1(1855)$ decays into the $\eta {\eta }^{\prime }$ and $K{\bar{K}}^{\ast }\pi$ channels and find that the latter has a larger branching fraction. We also investigate its SU(3) partners, and according to our findings, the ${\pi }_1(1400)$ and ${\pi }_1(1600)$ structures may correspond to dynamically generated states, with the former one coupled mostly to the $b_1\pi$ component and the latter one coupled to the $K_1(1270)\bar{K}$ channel. In particular, our result for the ratio $\Gamma ({\pi }_1(1600)\to f_1(1285)\pi )/\Gamma ({\pi }_1(1600)\to {\eta }^{\prime }\pi )$ is consistent with the measured value, which supports our interpretation for the higher ${\pi }_1$ state. We also report two poles with a mass about 1.7~GeV in the $I=1/2$ sector, which may be responsible for the $K^{\ast }(1680)$. We suggest searching for two additional ${\eta }_1$ exotic mesons with masses around 1.4 and 1.7~GeV. In particular, the predicted ${\eta }_1(1700)$ is expected to have a width around 0.1~GeV and can decay easily into $K\bar{K}\pi \pi$.

Comments: Accepted for publication in Universe with a DOI link https://doi.org/10.3390/universe9020109