Open charm-bottom scalar tetraquarks and their strong decays

Abstract

The mass and meson-current coupling of the diquark-antidiquark states with the quantum numbers $J^{P}=0^{+}$ and quark contents $Z_{q}=[cq][\bar {b} \bar q ]$ and $Z_{s}=[cs][\bar {b} \bar s]$ are calculated using two-point QCD sum rule approach. In calculations the quark, gluon and mixing condensates up to eight dimensions are taken into account. The parameters of the scalar tetraquarks extracted from this analysis are employed to explore the strong vertices $Z_q B_c \pi $, $Z_q B_c \eta $ and $Z_s B_c \eta $ and compute the couplings $g_{Z_qB_c \pi }$, $g_{Z_qB_c \eta }$ and $g_{Z_sB_c \eta }$. The strong couplings are obtained within the soft-meson approximation of QCD light-cone sum rule method: they form, alongside with other parameters, the basis for evaluating the widths of $Z_q \to B_c \pi$, $% Z_q \to B_c \eta$ and $Z_s \to B_c \eta$ decays. Obtained in this work results for the mass of the tetraquarks $Z_{q}$ and $Z_{s}$ are compared with available predictions presented in the literature.