Ground state baryons in the flux-tube three-body confinement model using Diffusion Monte Carlo

TL;DR

This paper uses diffusion Monte Carlo to study ground state baryons under different confinement models, providing detailed mass and structural data, and demonstrating the method's effectiveness in multiquark state analysis.

Contribution

It introduces a systematic DMC approach for baryons with pairwise and flux-tube confinement, extending to multiquark states and highlighting the importance of channel pre-assignment.

Findings

Both confinement models fit experimental data with proper parameters.

Flux-tube confinement requires different tension parameters for baryons and mesons.

Successfully identified the ground state of the $cc\bar{c}\bar{c}$ system in a challenging configuration.

Abstract

We make a systematical diffusion Monte Carlo (DMC) calculation for all ground state baryons in two confinement scenarios, the pairwise confinement and the three-body flux-tube confinement. With the baryons as an example, we illustrate a feasible procedure to investigate the few-quark states with possible few-body confinement mechanisms, which can be extended to the multiquark states easily. For each baryon, we extract the mass, mean-square radius, charge radius, and the quark distributions. We use the Jackknife resampling method to estimate the statistical uncertainties of masses to be less than 1 MeV. To determine the baryon charge radii, we include the constituent quark size effect, which is fixed by the experimental and lattice QCD results. Our results show that both two-body and three-body confinement mechanisms can give a good description of the experimental data if the parameters are chosen properly. In the flux-tube confinement, introducing different tension parameters for the baryons and mesons are necessary, specifically, $\sigma_Y= 0.9204 \sigma_{Q\bar{Q}}$. The lesson from the calculation of the nucleon mass with the DMC method is that the improper pre-assignment of the channels may prevent us from obtaining the real ground state. With this experience, we obtain the real ground state (the $\eta_c \eta_c$ threshold with the di-meson configuration) of the $cc\bar{c}\bar{c}$ system with $J^{PC}=0^{++}$ starting from the diquark-antidiquark spin-color channels alone, which is hard to achieve in the variational method and was not obtained in the previous DMC calculations.