Can $X(5568)$ be a tetraquark state?

Abstract: Very recently, the D0 collaboration has reported the observation of a narrow structure, $X(5568)$, in the decay process $X(5568)\to B^0_s\pi^\pm$ using the 10.4${\rm fb}^{-1}$ data of $p\bar p$ collision at $\sqrt s= 1.96$ TeV. This structure is of great interest since it is the first hadronic state with four different valence quark flavors, $b,s,u,d$. In this work, we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor $[su][\bar b\bar d ]$ and the spin-parity $J^P=0^+$, is about 150 MeV higher than the $X(5568)$. Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors in the future are severely needed towards a better understanding its nature and the classification of hadron exotic states.