$B_c^{\pm }$ decays into tetraquarks

The recent observation by the D0 collaboration of a narrow structure $X(5568)$ consisting of four different quark flavors $bdus$, has not been confirmed by LHCb. In the tightly bound diquark model, we estimate the lightest $bdus$, $0^{+}$ tetraquark at a mass of about 5770 MeV, approximately 200 MeV above the reported $X(5568)$, and just 7 MeV below the $B\overline{K}$ threshold. The charged tetraquark is accompanied by $I=1$ and $I=0$ neutral partners almost degenerate in mass. A $bdus$, $S$-wave, $1^{+}$ quartet at 5820 MeV is implied as well. In the charm sector, $cdus$, $0^{+}$ and $1^{+}$ tetraquarks are predicted at 2365 and 2501 MeV, about 40–50 MeV heavier than $D_{s0}(2317)$ and $D_{s1}(2460)$. The $bdus$ tetraquarks can be searched in the hadronic debris of a jet initiated by a $b$. However, some of them may also be produced in $B_c$ decays, $B_c\to X_{b0}+\pi$ with the subsequent decays $X_{b0}\to B_s+\pi$, giving rise to final states such as $B_s{\pi }^{+}{\pi }^0$. We also emphasize the importance of $B_c$ decays as a source of bound hidden charm tetraquarks, such as $B_c\to X(3872)+\pi$.

Figure 1

(a) Leading order Feynman diagram for the decay $B_c^{+}\to B_s^0{\pi }^{+}$, (b) $B_c^{+}\to X_{b0}^{(I=0)}+{\pi }^{+}$, and (c) the corresponding diagram for the decays $B_c^{+}\to X_{b0}(5570{)}^{(I=1)+,0}+{\pi }^{0,+}$.