Weak Decays of Stable Open-bottom Tetraquark by SU(3) Symmetry Analysis

The exotic state $X(5568)$ which was observed by D0 Collaboration is very likely to be a tetraquark state with four different valence quark flavors, though the existence was not confirmed by other collaborations. The possibility of such state still generate lots of interests in theory. In the paper, we will study the properties of the state under the SU(3) flavor symmetry. This four quark state with a heavy bottom quark and three light quarks(anti-quark) can form a $6$ or $\overline {15}$ representation. The weak decays can be dominant and should be discussed carefully while such state is stable against the strong interaction. Therefor we will study the multi-body semileptonic and nonleptonic weak decays systematically. With the help of SU(3) flavor symmetry, we can give the Hamiltonian in the hadronic level, then obtain the parameterized irreducible amplitudes and the relations of different channels. At the end of the article, we collect some Cabibbo allowed two-body and three-body weak decay channels which can be used to reconstruct $X_{b6}$ states at the branching fraction up to be $10^{-5}$.