Fourth root prescription for dynamical staggered fermions

With the aim of resolving theoretical issues associated with the fourth root prescription for dynamical staggered fermions in lattice QCD simulations, we consider the problem of finding a viable lattice Dirac operator $D$ such that $(\det D_{\mathrm{staggered}}{)}^{1/4}=\det D$. Working in the flavor field representation we show that in the free field case there is a simple and natural candidate $D$ satisfying this relation, and we show that it has acceptable locality behavior: exponentially local with a localization range vanishing $\sim \sqrt{a/m}$ for lattice spacing $a\to 0$. Prospects for the interacting case are also discussed, although we do not solve this case here.