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

We perform a lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $\bar{c}c\bar{d}u$, $\bar{c}c(\bar{u}u+\bar{d}d)$ and $\bar cc \bar ss$,wherethelatertwocanmixwith$\bar cc$\mathrm{.}Thissimulationwith$N_f=2$and$m_\pi=266$ MeV aims at the possible signatures of four-quark exotic states. We utilize a large basis of $\bar{c}c$, two-meson and diquark-antidiquark interpolating fields, with diquarks in both anti-triplet and sextet color representations. A lattice candidate for X(3872) with I=0 is observed very close to the experimental state only if both $\bar{c}c$ and $D\bar D^*$ interpolators are included; the candidate is not found if diquark-antidiquark and $D{\bar{D}}^{\ast }$ are used in the absence of $\bar{c}c$. No candidate for neutral or charged X(3872), or any other exotic candidates are found in the I=1 channel. We also do not find signatures of exotic $\bar cc\bar ss$ candidates below 4.3 GeV, such as Y(4140). Possible physics and methodology related reasons for that are discussed. Along the way, we present the diquark-antidiquark operators as linear combinations of the two-meson operators via the Fierz transformations.