Multichannel calculation of excited vector $ϕ$ resonances and the $ϕ(2170)$

A multichannel calculation of excited $J^{PC}=1^{--}$ $ϕ$ states is carried out within a generalization of the Resonance-Spectrum Expansion, which may shed light on the classification of the $ϕ(2170)$ resonance, discovered by BABAR and originally denoted X(2175). In this framework, a complete spectrum of bare $s\bar{s}$ states is coupled to those OZI-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 $q\bar{q}$ 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 $ϕ(1020)$, 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 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 $(2186-i246)$ MeV. The huge width makes its interpretation as the $ϕ(2170)$ somewhat dubious, but further improvements of the model may change this conclusion.

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