  We continue our earlier study of the phase structure of a SU(2) gauge theory
whose action contains additional chirally invariant four fermion interactions.
Our lattice theory uses a reduced staggered fermion formalism to generate two
Dirac flavors in the continuum limit. In the current study we have tried to
reduce lattice spacing and taste breaking effects by using an improved fermion
action incorporating stout smeared links. As in our earlier study we observe
two regimes; for weak gauge coupling the chiral condensate behaves as an order
parameter differentiating a phase at small four fermi coupling where the
condensate vanishes from a phase at strong four fermi coupling in which chiral
symmetry is spontaneously broken. This picture changes qualitatively when the
gauge coupling is strong enough to cause confinement; in this case we observe a
first order phase transition for some critical value of the four fermi coupling
associated with a strong enhancement of the chiral condensate. We observe that
this critical four fermi coupling varies monotonically with bare gauge coupling
- decreasing, as expected, as the gauge coupling is increased. We have checked
that these results remain stable under differing levels of smearing. They
appear to rule out the appearance of new fixed points associated with chirally
invariant four fermion interactions in confining non abelian gauge theories.
