An $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$ due to triangle singularity

Abstract

Triangle mechanisms for $B^0\to (J/\psi {\pi }^{+}{\pi }^{-})K^{+}{\pi }^{-}$ are studied. Experimentally, an $X(3872)$ peak has been observed in this process. When the final $(J/\psi {\pi }^{+}{\pi }^{-})\pi$ invariant mass is around the $D^{\ast }{\bar{D}}^{\ast }$ threshold, one of the triangle mechanisms causes a triangle singularity and generates a sharp $X(3872)$-like peak in the $J/\psi {\pi }^{+}{\pi }^{-}$ invariant mass distribution. The Breit-Wigner mass and width fitted to the spectrum are 3871.68 MeV (a few keV above the $D^{\ast 0}{\bar{D}}^0$ threshold) and $\sim$0.4 MeV, respectively.These Breit-Wigner parameters hardly depends on a choice of the model parameters. Comparing with the precisely measured $X(3872)$ mass and width, $3871.69\pm 0.17$ MeV and $<1.2$ MeV, the agreement is remarkable. When studying the $X(3872)$ signal from this process, this non-resonant contribution has to be understood in advance. We also study a charge analogous process $B^0\to (J/\psi {\pi }^0{\pi }^{-})K^{+}{\pi }^0$. A similar triangle singularity exists and generates an $X^{-}(3876)$-like peak.

arXiv comment6 pages, 4 figures, Contribution to the Proceedings for 8th Asia-Pacific Conference on Few-Body Problems in Physics (APFB2020), March 1-5 2021, Kanazawa, Japan

References in corpus (8)

• Observation of a narrow charmonium-like state in exclusive B+ -> K+ pi+pi- J/psi decays
• Observation of a New Narrow Charmonium State in Exclusive B+-->K+ pi+pi- J/psi Decays
• Novel Method for Precisely Measuring the $X(3872)$ Mass
• Unitary coupled-channels model for three-mesons decays of heavy mesons
• Observation of $X(3872)$ in $B\to X(3872)K\pi$ decays
• $Z_c(4430)$ and $Z_c(4200)$ as triangle singularities
• Triangle singularity appearing as an $X(3872)$-like peak in $B\to (J/\psi {\pi }^{+}{\pi }^{-})K\pi$
• Triangle singularities in ${\bar{B}}^0\to {\chi }_{c1}{K}^{-}{\pi }^{+}$ relevant to $Z_1(4050)$ and $Z_2(4250)$