Abstract
In this work we study the strong decays of $\phi(2170)$ to final states involving the kaonic resonances $K(1460)$, $K_1(1270)$ and $K_1(1400)$, on which experimental data have recently been extracted by the BESIII Collaboration. The formalism developed here is based on interpreting $\phi(2170)$ and $K(1460)$ as states arising from three-hadron dynamics, which is inspired by our earlier works. For $K_1(1270)$ and $K_1(1400)$ we investigate different descriptions, such as a mixture of states belonging to the nonet of axial resonances, or the former one as a state originating from the vector-pseudoscalar dynamics. The ratios among the partial widths of $K^+(1460)K^-$, $K^+_1(1400)K^-$ and $K^+_1(1270)K^-$ obtained are compatible with the experimental results, reinforcing the three-body nature of $\phi(2170)$. Within our formalism, we can also explain the suppressed decay of $\phi(2170)$ to $K^*(892) \bar K^*(892)$, as found by the BESIII Collaboration. Furthermore, our results can be useful in clarifying the properties of $K(1460)$, $K_1(1270)$ and $K_1(1400)$ when higher statistics data would be available.
Highlights
The BESIII Collaboration has recently [1] studied some properties of φð2170Þ [2,3,4,5,6,7,8,9] via the process eþe− → KþK−π0π0, where a signal with a mass of 2126.5 Æ 16.8 Æ 12.4 MeV and a width of 106.9 Æ 32.1 Æ 28.1 MeV is observed and identified with φð2170Þ
The cross sections for different configurations of the final state KþK−π0π0 are obtained, and the product BrΓeRþe− is determined, where ΓeRþe− corresponds to the partial decay width of φð2170Þ to eþe− and Br is the branching fraction of φð2170Þ to a specific configuration of the final state
We evaluate the cross sections for the φf0ð980Þ configuration of the final state KþK−πþðπ0Þπ−ðπ0Þ, i.e., for the process eþe− → φf0ð980Þ, which is precisely the reaction in which φð2170Þ was observed for the first time
Summary
The BESIII Collaboration has recently [1] studied some properties of φð2170Þ [2,3,4,5,6,7,8,9] via the process eþe− → KþK−π0π0, where a signal with a mass of 2126.5 Æ 16.8 Æ 12.4 MeV and a width of 106.9 Æ 32.1 Æ 28.1 MeV is observed and identified with φð2170Þ. We are going to determine the partial decay widths of φð2170Þ to the channels Kþð1460ÞK−, Kþ1 ð1400ÞK−, and Kþ1 ð1270ÞK− and compare their ratios with the experimental results obtained in Ref. A double pole nature for K1ð1270Þ has been claimed [29,30] In these latter works, K1ð1270Þ is interpreted as a superposition of two states generated from the unitarized dynamics of vector-pseudoscalar channels like φK, ρK, and πKÃð892Þ. As widths of φð2170Þ → Kþ1 ð1400ÞK−, Kþ1 we will show, by considering φð2170Þ ð1270ÞK−. as a φKKstate, we obtain branching fractions which are compatible with those determined from the available BrΓeRþe− results of Ref. [1]
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