  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.
