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

TL;DR

This lattice QCD study investigates charmonium-like mesons with specific quantum numbers and quark contents, identifying potential signatures of the X(3872) state only when certain operators are included, and finding no evidence for Y(4140).

Contribution

The paper introduces a comprehensive lattice QCD approach using a large basis of operators, including diquark-antidiquark configurations, to study exotic charmonium-like states and their signatures.

Findings

Candidate for X(3872) observed with combined $ar cc$ and $Dar D^*$ operators.

No evidence found for Y(4140) or other exotic states below 4.3 GeV.

Exotic states are sensitive to the choice of interpolating operators.

Abstract

We perform a lattice study of charmonium-like mesons with $J^{PC}=1^{++}$ and three quark contents $\bar cc \bar du$, $\bar cc(\bar uu+\bar dd)$ and $\bar cc \bar ss$, where the later two can mix with $\bar cc$. This simulation with $N_f=2$ and $m_\pi=266$ MeV aims at the possible signatures of four-quark exotic states. We utilize a large basis of $\bar cc$, 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 $\bar cc$ and $D\bar D^*$ interpolators are included; the candidate is not found if diquark-antidiquark and $D\bar D^*$ are used in the absence of $\bar cc$. 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.