Triangle singularities in $\bar{B}^0\to \chi_{c1}K^-\pi^+$ relevant to $Z_1(4050)$ and $Z_2(4250)$

Z1(4050) and Z2(4250) observed in B¯0→χc1K-π+ by the Belle Collaboration are candidates of charged charmoniumlike states that minimally include two quarks and two antiquarks. While Z1(4050) and Z2(4250) have been interpreted as tetraquark states previously, we propose a completely different scenario based on a kinematical effect called the triangle singularity. We demonstrate that the triangle singularities cause in the χc1π+ invariant mass distribution resonancelike bumps that fit very well the Belle data. If these bumps are simulated by the Z1(4050) and Z2(4250) resonance excitations, the spin-parity of them are predicted to be 1- for Z1(4050) and 1+ or 1- for Z2(4250). The bump corresponding to Z1(4050) has a highly asymmetric shape, which the Belle data exactly indicate. We show that the asymmetric shape originates from an interplay between the triangle singularity and the opening of the X(3872)π+ channel near the triangle-singularity energy. This characteristic lineshape could be used to discriminate different interpretations of Z1(4050). An interesting prediction from interpreting Z1(4050) and Z2(4250) as the triangle singularities is that similar bumps caused by the same mechanisms possibly appear also in B¯0→J/ψK-π+ data; the already observed Zc(4200) corresponds to Z2(4250) of JP=1+.

Note:

6 pages, 5 figures, (v2) numerical results corrected; changes are small, discussion on B0 -> J/psi K pi added; (v3) published version: relativistic energy-momentum relation is used for all particles; study on cutoff-dependence added

anti-B0: hadronic decay
anti-B0: branching ratio
Z(4050)
Z2(4250)
X(3872)
tetraquark
excited state
kinematics: effect
singularity
electron positron: annihilation

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Figures(6)

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