The spin parity of $Z_c^{-}$(4100), $Z_1^{+}$(4050) and $Z_2^{+}$(4250)

Abstract

We conjecture that $Z_c^{-}$(4100) found by LHCb group from a Dalitz plot analysis of $B^0\to {\eta }_c{K}^{+}{\pi }^{-}$ decay is the charge conjugate of $Z_1^{+}$(4050) observed in ${\chi }_{c1}{\pi }^{+}$ distribution from Belle collaboration. Some interesting conclusions are inferred from this assumption. The $Z_2$(4250) would be assigned to be a $J^P=1^{+}$ or $1^{-}$ state because of its absence in ${\eta }_c{\pi }^{-}$ invariant mass distribution, while $Z_1^{+}$(4050)/$Z_c^{-}$(4100) could be a $0^{+}$ or $1^{-}$ state but $2^{+}$ is unfavored because it would be coupled to ${\eta }_c\pi$ in $D$-wave. The null observation of $Z_1{Z}_2$, $Z_1{Z}_1$ and $Z_2{Z}_2$ production in $e^{+}{e}^{-}$ annihilation and ${\rm Y}(1S,2S)$ decay by Belle collaboration would further allocate the spin parity combination of $Z_1^{+}$(4050)/$Z_c^{-}$(4100) and $Z_2$(4250). Our deductions can be used to exclude a set of proposed models and could be further tested by future experiment, e.g. in $\gamma \gamma$ collisions.

Comments: 10 pages,published version