Effect of four-fermion operators on the mass of the composite particles

We propose a theoretical framework for evaluating the effect of four-fermion operators on the mass of composite particles in confining strongly-coupled gauge theories. The confining sector is modelled by a non-local Nambu-Jona Lasinio action, whereas the four-fermion operators, arising from a different sector, are local. In order to illustrate the method, we investigate a simple toy model with a global $SU(2)_L\times SU(2)_R\to SU(2)_V$ symmetry breaking, and a four-fermion operator breaking $SU(2)_L\times SU(2)_R$ but preserving $SU(2)_V$. In the particle spectrum we only include the pseudoscalar isospin triplet, that is the pseudo-Nambu-Goldstone bosons associated with chiral symmetry breaking, and the lightest scalar singlet. After checking that the nonlocal model successfully accounts for the experimental results in two-flavour QCD, we investigate the mass spectrum as a function of the four-fermion coupling. For our specific choice of four-fermion operator, we find that the mass of the pseudoscalar triplet grows, whereas the mass of the lightest scalar singlet is approximately unaffected, as the four-fermion coupling grows. We argue that these results can be directly tested on the lattice, and briefly discuss possible applications of this technique to models of dynamical electroweak symmetry breaking.