We discuss a recent lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $bar ccbar du$, $bar cc(bar uu + bar dd)$ and $bar ccbar ss$, where the latter two can mix with $bar cc$. In this quantum channel, the long known exotic candidate, X(3872), resides. This simulation employs $N_f=2$, $m_pi=266~$MeV and a large basis of $bar cc$, 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 diquark-antidiquark operators and the two-meson operators via the Fierz transformations.
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