On the \(\eta_1(1855)\), \(\pi_1(1400)\) and \(\pi_1(1600)\) as dynamically generated states and their SU(3) partners

• Published in: arXiv.org 2023-02
• Main Authors: Mao-Jun, Yan, Dias, Jorgivan M, Guevara, Adolfo, Feng-Kun, Guo, Bing-Song Zou
• Format: Article
• Language: English
• Subjects: Bethe-Salpeter equation; Channels; Quantum numbers; Vector mesons
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2301.04432

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 \(K\bar{K}^*\pi\) 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 \(K^*(1680)\). 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 \(K\bar K\pi\pi\).