An analysis of four-quark energies in SU(2) lattice Monte Carlo using the flux-tube symmetry

Abstract

Energies of four-quark systems calculated by the static quenched SU(2) lattice Monte Carlo method are analyzed in 2 × 2 bases for square, rectangle, tilted rectangle, linear and quadrilateral geometry configurations and in 3 × 3 bases for a non-planar geometry configuration. For small interquark distances, a lattice effect is taken into account by considering perimeter dependent terms which are characterized by the cubic symmetry. It is then found that a parameter f -that can be identified as a gluon field overlap factor -is rather well described by the form, where A and P are the area and perimeter mainly defined by the positions of the four quarks, b s is the string constant in the 2-quark potentials and E, F are constants. 0 1. Fit eigen-energies of all the (r, d) sets directly.

Interquark potential model for multiquark systems

“…A fit with a potential model to some of the above four-quark binding energies was attempted earlier in Ref. [17]. However, there are several important differences compared with the present fit: 1) The model contained only 2 × 2 or 3 × 3 bases that were essentially constructed from A, B, C.…”

“…In the present work the cut-off is at two lattice links. For Squares the outcome in [17] was k f = 0.296(11) and k P = 0.080(2), compared with k f = 0.571(12) using Model Ia above in Subsection II A. The difference between the values of these area constants is because the perimeter term, which is introduced to make artefact corrections for small configurations, is still important for large configurations, where rotational symmetry is restored and their presence not needed.…”

An Analysis of 4-Quark Energies in (2) Lattice Monte Carlo

“…, where A and P are the area and the perimeter. We assume that the length of the zig-zag perimeter has the fractal dimension 2, and so it is fixed from that of the coarse lattice, use the string constant b s measured in the simulation of the 2-quark potentials and fit constants E and F ij [2]. The length P ij depends on the base but the minimal area A are chosen to be independent of the base and estimated by the analytical form derived in the regular surface approximation.…”

“…The length P ij depends on the base but the minimal area A are chosen to be independent of the base and estimated by the analytical form derived in the regular surface approximation. (The analysis of NP of [2] is revised, where the area depended on the bases.) The perimeter dependent terms contain lattice artefacts and the physical quantities are obtained by subtracting the artefacts.…”

“…The parameter E for the area term and A 0 for the self energy in the Linear configuration are fixed in the previous model [2]. In the NP case we fitted three coefficients F corresponding to the three types of the perimeter lengths and a mixing parameter between the parity eigenstates [2]. The details of the revised fitting are in [4].…”