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 $V_{\rm 4Q}$ for various QQ-$\rm \bar{Q}\bar{Q}$ systems in SU(3) lattice QCD with $β=6.0$ and $16^3 \times 32$ at the quenched level. For about 200 different patterns of 4Q systems, $V_{\rm 4Q}$ is extracted from the 4Q Wilson loop in 300 gauge configurations, with the smearing method to enhance the ground-state component. We calculate $V_{\rm 4Q}$ for planar, twisted, asymmetric, and large-size 4Q configurations, respectively. Here, the calculation for large-size 4Q configurations is done by identifying $16^2 \times 32$ 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 $\rm \bar{Q}\bar{Q}$ are well separated, $V_{\rm 4Q}$ 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 as "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.