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

TL;DR

This paper analyzes the spin and parity assignments of the exotic states Zc(4100), Z1(4050), and Z2(4250), proposing their possible quantum numbers and implications based on experimental data and theoretical considerations.

Contribution

It introduces a conjecture linking Zc(4100) and Z1(4050), and deduces their possible spin-parity assignments, providing a framework to test these states in future experiments.

Findings

Zc(4100) and Z1(4050) are likely charge conjugates with related quantum numbers.

Z2(4250) is probably a J^P = 1^+ or 1^- state based on decay patterns.

Null results in certain production channels help constrain the spin-parity assignments.

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 $\Upsilon(1S,2S)$ 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.