Insights into the nature of the $X(3872)$ through B meson decays

Abstract

We study the decays $B_{c,u,d}\to X(3872)P$ in the perturbative QCD (PQCD) approach, where the puzzling resonance $X(3872)$ is involved and $P$ represents a light pseudoscalar meson $K$ and $\pi$. Assuming the $X(3872)$ as a $1^{++}$ charmonium state, we find the following results: (a) The branching ratios for the decays $B_c^{+}\to X(3872){\pi }^{+}$ and $B_c^{+}\to X(3872)K^{+}$ agree with the results predicted by the covariant light-front approach within errors, but are larger than those given by the generalized factorization approach; (b) The branching ratio for the decay $B^{+}\to X(3872)K^{+}$ is predicted as $(3.8_{-1.0}^{+1.1})\times 10^{-4}$, which is smaller than the previous PQCD calculation result, but still slightly larger than the upper limits set by Belle and BaBar. So we suggest that the decays $B^{0,+}\to X(3872)K^{0,+}$ should be precisely measured by the running LHCb and Belle II experiments, which is very helpful to probe the inner structure of the $X(3872)$; (c) Compared with the decays $B_{u,d}\to X(3872)K$, the decays $B_{u,d}\to X(3872)\pi$ have much smaller branching ratios, which drop to as low as $10^{-6}$; (d) The direct CP violations for these considered decays are very small, only $10^{-3}\sim 10^{-2}$, because the penguin contributions are loop suppressed compared with the tree contributions. Testing the results for the branching ratios and the CP violations including the implicit $SU(3)$ and isospin symmetries in these decays by experiments is helpful to probe the nature of the $X(3872)$.

Comments: 11 pages, 2 figures