Quantum Monte Carlo calculations of six-quark states

Abstract

The variational Monte Carlo method is used to find the ground state of six quarks confined to a cavity of diameter ${R}_{c},$ interacting via an assumed nonrelativistic constituent quark model Hamiltonian. We use a flux-tube model augmented with one-gluon and one-pion exchange interactions, which has been successful in describing single hadron spectra. The variational wave function is written as a product of three-quark nucleon states with correlations between quarks in different nucleons. We study the role of quark exchange effects by allowing flux-tube configuration mixing. An accurate six-body variational wave function is obtained. It has only \ensuremath{\sim}13% rms fluctuation in the total energy and yields a standard deviation of \ensuremath{\lesssim}0.1%; small enough to be useful in discerning nuclear interaction effects from the large rest mass of the two nucleons. Results are presented for three values of the cavity diameter, ${R}_{c}=2,$ 4, and 6 fm. They indicate that the flux-tube model Hamiltonian with gluon and pion exchange requires revisions in order to obtain agreement with the energies estimated from realistic two-nucleon interactions. We calculate the two-quark probability distribution functions and show how they may be used to study and adjust the model Hamiltonian.