The ${\chi }_{cJ}$ decay to $\varphi K^{\ast }\bar{K},\varphi h_1(1380)$ testing the nature of axial vector meson resonances

Abstract

We perform a theoretical study of the ${\chi }_{cJ}\to \varphi K^{\ast }\bar{K}\to \varphi K\pi \bar{K}$ reaction taking into account the $K^{\ast }\bar{K}$ final state interaction, which in the chiral unitary approach is responsible, together with its coupled channels, for the formation of the low lying axial vector mesons, in this case the $h_1(1380)$ given the selection of quantum numbers. Based on this picture we can easily explain why in the ${\chi }_{c0}$ decay the $h_1(1380)$ resonance is not produced, and, in the case of ${\chi }_{c1}$ and ${\chi }_{c2}$ decay, why a dip in the $K^{+}{\pi }^0{K}^{-}$ mass distribution appears in the 1550-1600 MeV region, that in our picture comes from a destructive interference between the tree level mechanism and the rescattering that generates the $h_1(1380)$ state. Such a dip is not reproduced in pictures where the nominal $h_1(1380)$ signal is added incoherently to a background, which provides support to the picture where the resonance appears from rescattering of vector-pseudoscalar components.

arXiv comment11 pages, 3 figures; V2: version accepted for publication in Phys. Lett. B

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