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

We perform the detailed study of the tetraquark (4Q) potential V4Q for various QQ-Q¯¯¯Q¯¯¯ systems in SU(3) lattice QCD with β=6.0 and 163×32 at the quenched level. For about 200 different patterns of 4Q systems, V4Q is extracted from the 4Q Wilson loop in 300 gauge configurations, with the smearing method to enhance the ground-state component. We calculate V4Q for planar, twisted, asymmetric, and large-size 4Q configurations, respectively. Here, the calculation for large-size 4Q configurations is done by identifying 162×32 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 Q¯¯¯Q¯¯¯ are well separated, V4Q 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