اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe weak decay $B_c$ to $Z(3930)$ and $X(4160)$ by Bethe-Salpeter method
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Considering $Z(3930)$ and $X(4160)$ as $chi_{c2}(2P)$ and $chi_{c2}(3P)$ states, the semileptonic and nonleptonic of $B_c$ decays to $Z(3930)$ and $X(4160)$ are studied by the improved Bethe-Salpeter(B-S) Method. The form factors of decay are calculated through the overlap integrals of the meson wave functions in the whole accessible kinematical range. The influence of relativistic corrections are considered in the exclusive decays. Branching ratios of $B_c$ weak decays to $Z(3930)$ and $X(4160)$ are predicted. Some of the branching ratios are: $Br(B_c^+to Z(3930)e^+ u_e)$$=(3.03^{+0.09}_{-0.16})times 10^{-4}$ and $Br(B_c^+to X(4160)e^+ u_e)$$=(3.55^{+0.83}_{-0.35})times 10^{-6}$. These results may provide useful information to discover $Z(3930)$ and $X(4160)$ and the necessary information for the phenomenological study of $B_c$ physics.
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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 Mandel
stam 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.
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is 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.
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
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