The branching fraction of $B_s\to K^0{\bar{K}}^0$: Three puzzles

The branching fraction of the $B_s\to K^0{\bar{K}}^0$ decay has been recently measured by the LHCb and Belle experiments. We study the consistency of the measured value with three relations to other decay rates and CP asymmetries which follow from the Standard Model, and from the approximate flavor $SU(3)$ symmetry of the strong interactions. We find that each of these relations is violated at a level of above $3\sigma$. We argue that various subleading effects – rescattering, electroweak penguins and $SU(3)$ breaking – if larger than theoretically expected, can account for some of these puzzles, but not for all of them simultaneously.