X ( 3872 ) and Y ( 4140 ) using diquark - antidiquark operators with lattice QCD

We discuss a recent lattice study of charmonium-like mesons with JPC = 1++ and three quark contents c̄cd̄u, c̄c(ūu+ d̄d) and c̄cs̄s, where the latter two can mix with c̄c. In this quantum channel, the long known exotic candidate, X(3872), resides. This simulation employs N f = 2, mπ = 266 MeV and a large basis of c̄c, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. It aims at the possible signatures of four-quark exotic states. Along the way, we discuss the relations between the diquarkantidiquark operators and the two-meson operators via the Fierz transformations.