Exotic tetraquark states with the $$qq\bar{Q}\bar{Q}$$ q q Q ¯ Q ¯ configuration

In this work, we study systematically the mass splittings of the $$qq\bar{Q}\bar{Q}$$ ( $$q=u$$ , d, s and $$Q=c$$ , b) tetraquark states with the color-magnetic interaction by considering color mixing effects and estimate roughly their masses. We find that the color mixing effect is relatively important for the $$J^P=0^+$$ states and possible stable tetraquarks exist in the $$nn\bar{Q}\bar{Q}$$ ( $$n=u$$ , d) and $$ns\bar{Q}\bar{Q}$$ systems either with $$J=0$$ or with $$J=1$$ . Possible decay patterns of the tetraquarks are briefly discussed.