Simulations with different lattice Dirac operators for valence and sea quarks

We discuss simulations with different lattice Dirac operators for sea and valence quarks. A goal of such a “mixed” action approach is to probe deeper the chiral regime of QCD by enabling simulations with light valence quarks. This is achieved by using chiral fermions as valence quarks while computationally inexpensive fermions are used in the sea sector. Specifically, we consider Wilson sea quarks and Ginsparg-Wilson valence quarks. The local Symanzik action for this mixed theory is derived to $\mathcal{O}\mathrm{}\left(a\right),$ and the appropriate low energy chiral effective Lagrangian is constructed, including the leading $\mathcal{O}\mathrm{}\left(a\right)\mathrm{}$ contributions. Using this Lagrangian one can calculate expressions for physical observables and determine the Gasser-Leutwyler coefficients by fitting them to the lattice data.