A bound state model for a light scalar

Abstract: Recent lattice studies of near-conformal strong dynamics suggest the existence of a light scalar. This provides motivation to consider a simple Hamiltonian-based bound-state model where the pseudoscalar, scalar, vector and axial-vector states are treated on an equal footing. The model interpolates between the non-relativistic limit and the highly relativistic chiral limit, where the pseudoscalar mass drops to zero. The fermion mass becomes purely dynamical at this point. When the gauge coupling is constant over a moderate range of scales the scalar becomes significantly lighter than the spin 1 states as the chiral limit is approached. We relate this result to the behavior of the form factors of the respective states and their decay constants. In the conformal limit of the model all masses vanish and the theory is characterized by scaling dimensions.