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

TL;DR

This paper models excited $\,\, ext{phi}$ mesons using a multichannel approach, identifying potential resonances including a broad state near 2186 MeV, to clarify the nature of the $\, ext{phi}(2170)$.

Contribution

It introduces a generalized Resonance-Spectrum Expansion for multichannel analysis of $\, ext{phi}$ states, including both $qar{q}$ and meson decay channels, to better understand the $\, ext{phi}(2170)$ resonance.

Findings

Identifies candidate resonances consistent with observed states.

Finds a broad dynamical resonance at (2186-i246) MeV.

Model reproduces $\, ext{phi}(1020)$} properties.

Abstract

A multichannel calculation of excited $J^{PC}=1^{--}$ $\phi$ states is carried out within a generalization of the Resonance-Spectrum Expansion, which may shed light on the classification of the $\phi(2170)$ 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 $\phi(1020)$, 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 $\phi(2170)$ somewhat dubious, but further improvements of the model may change this conclusion.