Chiral perturbation theory for lattice QCD at O(a)

Chiral perturbation theory (χPT) is widely used in analyzing lattice QCD data. Since χPT describes continuum QCD one has to take the continuum limit first before fitting the lattice data to the analytic predictions of χPT. Unfortunately, lattice data for various lattice spacings is often not available in order to perform a reliable continuum extrapolation. Nevertheless, it is common practice to directly fit lattice data obtained for non-vanishing lattice spacing to continuum χPT, thus introducing a systematic error. This uncertainty can be analytically controlled by including the discretization effects stemming from a non-zero lattice spacing in χPT. For example, the O(a) taste violations in staggered fermion simulations have been systematically accounted for that way [1]. Fits of MILC simulation data to χPT including O(a) taste violating terms show a significantly improved χ [2]. In fact, good fits are not possible without these terms. Similarly, the leading effects linear in a for simulations with Wilson fermions have been included in χPT [3] and the resulting expressions for the pseudo scalar mass and decay constant have already been used in fits to simulation data [4]. However, since the lattice spacings in current unquenched simulations with Wilson fermions are