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

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 Added by Xu Cao
 Publication date 2018
  fields
and research's language is English




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We conjecture that $Z_c^-$(4100) found by LHCb group from a Dalitz plot analysis of $B^0to eta_c K^+pi^-$ 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 $Upsilon(1S,2S)$ 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.

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The spin and parity of the $Z_c(3900)^pm$ state are determined to be $J^P=1^+$ with a statistical significance larger than $7sigma$ over other quantum numbers in a partial wave analysis of the process $e^+e^-to pi^+pi^-J/psi$. We use a data sample of 1.92 fb$^{-1}$ accumulated at $sqrt{s}=4.23$ and 4.26 GeV with the BESIII experiment. When parameterizing the $Z_c(3900)^pm$ with a Flatte-like formula, we determine its pole mass $M_textrm{pole}=(3881.2pm4.2_textrm{stat}pm52.7_textrm{syst})textrm{MeV}/c^2$ and pole width $Gamma_textrm{pole}=(51.8pm4.6_textrm{stat}pm36.0_textrm{syst})textrm{MeV}$. We also measure cross sections for the process $e^+e^-to Z_c(3900)^+pi^-+c.c.to J/psipi^+pi^-$ and determine an upper limit at the 90% confidence level for the process $e^+e^-to Z_c(4020)^+pi^-+c.c.to J/psipi^+pi^-$.
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