Multichannel calculation of excited vectorϕresonances and theϕ(2170)

A multichannel calculation of excited $J^{PC}=1^{--}\varphi$ states is carried out within a generalization of the resonance-spectrum expansion, which may shed light on the classification of the $\varphi (2170)$ resonance, discovered by BABAR and originally denoted $X(2175)$. In this framework, a complete spectrum of bare $s\overline{s}$ states is coupled to those Okubo-Zweig-Iizuka–allowed decay channels that should be most relevant for the considered energy range. The included $S$- and $P$-wave two-meson channels comprise the lowest pseudoscalar, vector, scalar, and axial-vector mesons, while in the $q\overline{q}$ sector both the ${}^{3}S_1$ and ${}^{3}D_1$ states are coupled. The only two free parameters are tuned so as to reproduce mass and width of the $\varphi (1020)$, but come out reasonably close to previously used values. Among the model’s $T$-matrix poles, there are good candidates for observed resonances, as well as other ones that should exist according to the quark model. Besides the expected resonances as unitarized confinement states, a dynamical resonance pole is found at $(2186-i246)\mathrm{MeV}$. The huge width makes its interpretation as the $\varphi (2170)$ somewhat dubious, but further improvements of the model may change this conclusion.