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

We discuss a recent lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $\bar{c}c\bar{d}u$, $\bar cc(\bar uu + \bar dd)$and$\bar cc\bar ss$,wherethelattertwocanmixwith$\bar cc$. 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 $\bar{c}c$, 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.