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Beauty tetraquark states $X(\bar b q'q'' \bar q )$ composed of $ \bar b s u\bar d$, $\bar b d s \bar u$, and $\bar b u d \bar s$, are unique that all thefour valence quarks are different. Although the claim of existence of the firsttwo states by D0 was not confirmed by data from LHCb, the possibility of suchstates still generated a lot of interests and should be pursued further.Non-observation of $X(\bar b q'q'' \bar q )$ states by LHCb may be just due toa still lower production rate than the limit of LHCb or at some different massranges. In this work we use light quark $SU(3)$ flavor symmetry as guideline toclassify symmetry properties of beauty tetraquark states. The multiplets whichcontain states with three different light quarks must be one of ${\bf \bar 6}$or ${\bf 15}$ of $SU(3)$ representations. We study possible decays of such atetraquark state into a $B$ meson and a light pesudoscalar octet meson byconstructing a leading order chiral Lagrangian, and also provide searchstrategies to determine whether a given tetraquark state of this type belongsto ${\bf \bar 6}$ or ${\bf 15}$. If $X(\bar b q'q''\bar q )$ belongs to ${\bf15}$, there are new doubly charged tetraquark states $\bar b u u \bar d$ and$\bar b u u \bar s$.

Flavor $SU(3)$ properties of beauty tetraquark states with three different light quarks