Triangle singularities in Bˉ0→χc1K?π+ relevant to Z1(4050) and Z2(4250)

摘要

Z 1 ( 4050 ) and Z 2 ( 4250 ) observed in B ˉ 0 → χ c 1 K ? π + by the Belle Collaboration are candidates of charged charmoniumlike states that minimally include two quarks and two antiquarks. While Z 1 ( 4050 ) and Z 2 ( 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 χ c 1 π + invariant mass distribution resonancelike bumps that fit very well the Belle data. If these bumps are simulated by the Z 1 ( 4050 ) and Z 2 ( 4250 ) resonance excitations, the spin-parity of them are predicted to be 1 ? for Z 1 ( 4050 ) and 1 + or 1 ? for Z 2 ( 4250 ) . The bump corresponding to Z 1 ( 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 Z 1 ( 4050 ) . An interesting prediction from interpreting Z 1 ( 4050 ) and Z 2 ( 4250 ) as the triangle singularities is that similar bumps caused by the same mechanisms possibly appear also in B ˉ 0 → J / ψ K ? π + data; the already observed Z c ( 4200 ) corresponds to Z 2 ( 4250 ) of J P = 1 + .