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

Abstract

$Z_1(4050)$ and $Z_2(4250)$ observed in ${\bar{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ by the Belle Collaboration are candidates of charged charmonium-like states that minimally includes 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 ${\chi }_{c1}{\pi }^{+}$ invariant mass distribution resonance-like 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 $X(3872){\pi }^{+}$ channel near the triangle-singularity energy. This characteristic lineshape could be used to discriminate different interpretations of $Z_1(4050)$. An interesting prediction from interpretting $Z_1(4050)$ and $Z_2(4250)$ as the triangle singularities is that similar bumps caused by the same mechanisms possibly appear also in ${\bar{B}}^0\to J/\psi K^{-}{\pi }^{+}$ data; the already observed $Z_c(4200)$ corresponds to $Z_2(4250)$ of $J^P=1^{+}$.

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

References in corpus (15)

• Observation of a resonance-like structure in the pi^+- psi' mass distribution in exclusive B-->K pi^+- psi' decays
• Observation of the resonant character of the $Z(4430{)}^{-}$ state
• X(3872) and Other Possible Heavy Molecular States
• Are Y(4260) and {\rm Z${}_2^{+}$(4250)} ${\mathrm{D}}_1\mathrm{D}$ or ${\mathrm{D}}_0{\mathrm{D}}^{\ast }$ Hadronic Molecules?
• Observation of a new charged charmoniumlike state in B -> J/psi K pi decays
• A Discussion on Triangle Singularities in the ${\Lambda }_b\to J/\psi K^{-}p$ Reaction
• Excited heavy tetraquarks with hidden charm
• On the nature of $a_1(1420)$
• The "$a_1(1420)$" peak as the $\pi f_0(980)$ decay mode of the $a_1(1260)$
• The bound state problem of S-wave heavy quark meson-aitimeson systems
• Width of exotics from QCD sum rules : tetraquarks or molecules?
• Triangular singularity and a possible $\varphi p$ resonance in the ${\Lambda }_c^{+}\to {\pi }^0\varphi p$ decay
• Model-independent observation of exotic contributions to $B^0\to J/\psi K^{+}{\pi }^{-}$ decays
• Another tetraquark structure in the ${\pi }^{+}{\chi }_{c1}$ invariant mass distribution
• Abnormal isospin violation and $a_0-f_0$ mixing in the $D_s^{+}\to {\pi }^{+}{\pi }^0{a}_0(980)(f_0(980))$ reactions

Cited by in corpus (11)

• Pentaquark and Tetraquark states
• Electron-Ion Collider in China
• Heavy hadronic molecules with pion exchange and quark core couplings: a guide for practitioners
• Classifying Pole of Amplitude Using Deep Neural Network
• Triangle singularity appearing as an $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$
• The role of charged exotic states in $e^{+}{e}^{-}\to \psi (2S){\pi }^{+}{\pi }^{-}$
• Detecting the pure triangle sigularity effect through the $\psi (2S)\to p\bar{p}\eta /p\bar{p}{\pi }^0$ process
• The role of triangle singularity in isospin breaking process $J/\psi \to \Lambda \bar{\Lambda }\pi$ and the possible evidence of ${\Sigma }^{\ast }({\frac{1}{2}}^{-})$ states
• $S$-wave contributions to the $B_{(s)}\to {\chi }_{c1}(\pi \pi ,K\pi ,KK)$ decays
• $Z_c(4430)$, $Z_c(4200)$, $Z_1(4050)$, and $Z_2(4250)$ as triangle singularities
• An $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$ due to triangle singularity