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Register a new userThe analysis of the charmonium-like states $X^{*}(3860)$,$X(3872)$, $X(3915)$, $X(3930)$ and $X(3940)$ according to its strong decay behaviors
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Inspired by the newly observed state $X^{*}(3860)$, we analyze the strong decay behaviors of some charmonium-like states $X^{*}(3860)$,$X(3872)$, $X(3915)$, $X(3930)$ and $X(3940)$ by the $^{3}P_{0}$ model. We carry out our work based on the hypothesis that these states are all being the charmonium systems. Our analysis indicates that $0^{++}$ charmonium state can be a good candidate for $X^{*}(3860)$ and $1^{++}$ state is the possible assignment for $X(3872)$. Considering as the $3^{1}S_{0}$ state, the decay behavior of $X(3940)$ is inconsistent with the experimental data. So, we can not assign $X(3940)$ as the $3^{1}S_{0}$ charmonium state by present work. Besides, our analysis imply that it is reasonable to assign $X(3915)$ and $X(3930)$ to be the same state, $2^{++}$. However, combining our analysis with that of Zhou~cite{ZhouZY}, we speculate that $X(3915)$/$X(3930)$ might not be a pure $coverline{c}$ systems.
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The new mesons $X(3940)$ and $X(4160)$ have been found by Belle Collaboration in the processes $e^+e^-to J/psi D^{(*)}bar D^{(*)}$. Considering $X(3940)$ and $X(4160)$ as $eta_c(3S)$ and $eta_c(4S)$ states, the two-body open charm OZI-allowed strong decay of $eta_c(3S)$ and $eta_c(4S)$ are studied by the improved Bethe-Salpeter method combine with the $^3P_0$ model. The strong decay width of $eta_c(3S)$ is $Gamma_{eta_c(3S)}=(33.5^{+18.4}_{-15.3})$ MeV, which is closed to the result of $X(3940)$, therefore, $eta_c(3S)$ is a good candidate of $X(3940)$. The strong decay width of $eta_c(4S)$ is $Gamma_{eta_c(4S)}=(69.9^{+22.4}_{-21.1})$ MeV, considering the errors of the results, its closed to the lower limit of $X(4160)$. But the ratio of the decay width $frac{Gamma(Dbar D^*)}{Gamma (D^*bar D^*)}$ of $eta_c(4S)$ is larger than the experimental data of $X(4160)$. According to the above analysis, $eta_c(4S)$ is not the candidate of $X(4160)$, and more investigations of $X(4160)$ is needed.
It has been proposed recently (Phys. Rev. Lett. 115 (2015), 022001) that the charmoniumlike state named X(3915) and suggested to be a $0^{++}$ scalar, is just the helicity-0 realisation of the $2^{++}$ tensor state $chi_{c2}(3930)$. This scenario would call for a helicity-0 dominance, which were at odds with the properties of a conventional tensor charmonium, but might be compatible with some exotic structure of the $chi_{c2}(3930)$. In this paper, we investigate, if such a scenario is compatible with the assumption that the $chi_{c2}(3930)$ is a $D^*bar D^*$ molecular state - a spin partner of the $X(3872)$ treated as a shallow bound state. We demonstrate that for a tensor molecule the helicity-0 component vanishes for vanishing binding energy and accordingly for a shallow bound state a helicity-2 dominance would be natural. However, for the $chi_{c2}(3930)$, residing about 100 MeV below the $D^*bar D^*$ threshold, there is no a priori reason for a helicity-2 dominance and thus the proposal formulated in the above mentioned reference might indeed point at a molecular structure of the tensor state. Nevertheless, we find that the experimental data currently available favour a dominant contribution of the helicity-2 amplitude also in this scenario, if spin symmetry arguments are employed to relate properties of the molecular state to those of the X(3872). We also discuss what research is necessary to further constrain the analysis.
In this paper we consider all possible 1D and 2P ccbar assignments for the recently discovered X(3872). Taking the experimental mass as input, we give numerical results for the E1 radiative widths as well as the three principal types of strong decays; open-charm, ccbar annihilation and closed-charm hadronic transitions. We find that many assignments may be immediately eliminated due to the small observed total width. The remaining viable ccbar assignments are 3D3, 3D2, 1D2, 2 3P1 and 2 1P1. A search for the mode J/psi pi0 pi0 can establish the C-parity of the X(3872), which will eliminate many of these possibilities. Radiative transitions can then be used to test the remaining assignments, as they populate characteristic final states. The 3D2 and 1D2 states are predicted to have large (ca.50%) radiative branching fractions to chi_1 gamma and h_c gamma respectively. We predict that the 3D3 will also be relatively narrow and will have a significant (ca.10%) branching fraction to chi_2 gamma, and should also be observable in B decay. Tests for non-ccbar X(3872) assignments are also discussed.
Considering $X(3940)$ and $X(4160)$ as $eta_c(3S)$ and $eta_c(4S)$, we study the productions of $X(3940)$ and $X(4160)$ in exclusive weak decays of $B_c$ meson by the improved Bethe-Salpeter(B-S) Method. Using the relativistic B-S equation and Mandelstam formalism, we calculate the corresponding decay form factors. The predictions of the corresponding branching ratios are: $Br(B_c^+to X(3940)e^+ u_e)$$=1.0times10^{-4}$ and $Br(B_c^+to X(4160)e^+ u_e)=2.4times10^{-5}$. That will provide us a new way to observe the $X(3940)$ and $X(4160)$ in the future, as well as to improve the knowledge of $B_c$ meson decay.
We report a search for $X(3872)$ and $X(3915)$ in $B^+ to chi_{c1} pi^0 K^+$ decays. We set an upper limit of $mathcal{B}(B^+ to X(3872) K^+) times mathcal{B}(X(3872) to chi_{c1} pi^0)$ $ < 8.1 times 10^{-6}$ and $mathcal{B}(B^+ to X(3915) K^+) times mathcal{B}(X(3915) to chi_{c1} pi^0)$ $ < 3.8 times 10^{-5}$ at 90% confidence level. We also measure $mathcal{B}(X(3872) to chi_{c1} pi^0)/mathcal{B}(X(3872) to J/psi pi^+ pi^-) < 0.97$ at 90% confidence level. The results reported here are obtained from $772 times 10^{6}$ $Boverline{B}$ events collected at the $Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider.
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