Axially symmetricB=2solution in the chiral quark soliton model

Abstract

The baryon-number-two $(B=2)$ solution based on the SU(2) chiral quark soliton model (\ensuremath{\chi}QSM) is solved numerically, including fully the sea quark degrees of freedom. We confirm that the axially symmetric meson configurations yield the energy minimum for the $B=2$ state in the \ensuremath{\chi}QSM when taking into account quark dynamics. Due to the axially symmetric meson fields, six valence quarks occupy the lowest energy level, consistent with the Pauli exclusion principle. The minimal-energy of the entire system is obtained within the framework of a symmetric ansatz. The fermion determinant with axially symmetric meson fields is calculated by diagonalizing the corresponding Dirac Hamiltonian in a nonperturbative way, using a cylindrical Dirac basis. The baryon number density, calculated with quark fields corresponding to a soliton, is toroidal in shape. We also calculate the mean radius of the toroid from the quark fields. These results are closely related to Skyrme model calculations based upon pion degrees of freedom. Our model calculations clarify the underlying dynamical structure of the baryons at the quark level.