Chiral-symmetry breaking in a composite model with scalars based on lattice gauge theory

In a composite model, based on the SO(3) gauge group, in which there are both fermion and scalar fundamental fields, we determine whether there is spontaneous breaking of chiral symmetry and look for the mass gap between the ground state and the one composite-fermion state. The chiral symmetry is realized in the strong-coupling lattice Hamiltonian with the fundamental fermions being massless and fundamental scalars being massive. This calculation is based on the mean-field approximation to the state wave functions. Similar to the calculations of Quinn, Drell, and Gupta in models without scalars, we also find that the chiral symmetry is spontaneously broken, and the composite fermions are massive. The extension of our calculation to SO(N) cases is shown to be straightforward