Eur. Phys. J. C (2024) 84: 147
https://doi.org/10.1140/epjc/s10052-024-12501-6

Regular Article - Theoretical Physics

Productions of X(3872), $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in $B_{(s)}$ decays offer strong clues on their molecular nature

¹ Institute of Particle and Nuclear Physics, Henan Normal University, 453007, Xinxiang, China
² School of Physics and Center of High Energy Physics, Peking University, 100871, Beijing, China
³ Frontiers Science Center for Rare isotopes, Lanzhou University, 730000, Lanzhou, China
⁴ School of Physics, Beihang University, 102206, Beijing, China
⁵ Peng Huanwu Collaborative Center for Research and Education, Beihang University, 100191, Beijing, China
⁶ Beijing Key Laboratory of Advanced Nuclear Materials and Physics, Beihang University, 102206, Beijing, China
⁷ Southern Center for Nuclear-Science Theory (SCNT), Institute of Modern Physics, Chinese Academy of Sciences, 516000, Huizhou, China

^b zhengmz11@buaa.edu.cn

Received: 14 December 2023
Accepted: 29 January 2024
Published online: 10 February 2024

Abstract

The exotic states X(3872) and $Z_c(3900)$ have long been conjectured as isoscalar and isovector ${\overline{D}}^{\ast }D$ molecules. In this work, we first propose the triangle diagram mechanism to investigate their productions in B decays as well as their heavy quark spin symmetry partners, $X_2(4013)$ and $Z_c(4020)$. We show that the large isospin breaking of the ratio $\mathcal{B}[B^{+}\to X(3872)K^{+}]/\mathcal{B}[B^0\to X(3872)K^0]$ can be attributed to the isospin breaking of the neutral and charged ${\overline{D}}^{\ast }D$ components in their wave functions. For the same reason, the branching fractions of $Z_c(3900)$ in B decays are smaller than the corresponding ones of X(3872) by at least one order of magnitude, which naturally explains its non-observation. A hierarchy for the production fractions of X(3872), $Z_c(3900)$, $X_2(4013)$, and $Z_c(4020)$ in B decays, consistent with all existing data, is predicted. Furthermore, with the factorization ansatz we extract the decay constants of X(3872), $Z_c(3900)$, and $Z_c(4020)$ as ${\overline{D}}^{\ast }{D}^{(\ast )}$ molecules via the B decays, and then calculate their branching fractions in the relevant $B_{(s)}$ decays, which turn out to agree with all existing experimental data. The mechanism we proposed is useful to elucidate the internal structure of the many exotic hadrons discovered so far and to extract the decay constants of hadronic molecules, which can be used to predict their production in related processes.