Detailed analysis of the tetraquark potential and flip-flop in SU(3) lattice QCD

Abstract

We perform the detailed study of the tetraquark (4Q) potential ${V}_{4\mathrm{Q}}$ for various $QQ\mathrm{\text{\ensuremath{-}}}\overline{Q}\overline{Q}$ systems in SU(3) lattice QCD with $\ensuremath{\beta}=6.0$ and ${16}^{3}\ifmmode\times\else\texttimes\fi{}32$ at the quenched level. For about 200 different patterns of 4Q systems, ${V}_{4\mathrm{Q}}$ is extracted from the 4Q Wilson loop in 300 gauge configurations, with the smearing method to enhance the ground-state component. We calculate ${V}_{4\mathrm{Q}}$ for planar, twisted, asymmetric, and large-size 4Q configurations, respectively. Here, the calculation for large-size 4Q configurations is done by identifying ${16}^{2}\ifmmode\times\else\texttimes\fi{}32$ as the spatial size and 16 as the temporal one, and the long-distance confinement force is particularly analyzed in terms of the flux-tube picture. When $QQ$ and $\overline{Q}\overline{Q}$ are well separated, ${V}_{4\mathrm{Q}}$ is found to be expressed as the sum of the one-gluon-exchange Coulomb term and multi-Y-type linear term based on the flux-tube picture. When the nearest quark and antiquark pair is spatially close, the system is described as a ``two-meson'' state. We observe a flux-tube recombination called a ``flip-flop'' between the connected 4Q state and the two-meson state around the level-crossing point. This leads to infrared screening of the long-range color forces between (anti)quarks belonging to different mesons, and results in the absence of the color van der Waals force between two mesons.