  We study the leading discretization errors for staggered fermions by first
constructing the continuum effective Lagrangian including terms of O(a^2), and
then constructing the corresponding effective chiral Lagrangian. The terms of
O(a^2) in the continuum effective Lagrangian completely break the SU(4) flavor
symmetry down to the discrete subgroup respected by the lattice theory. We
find, however, that the O(a^2) terms in the potential of the chiral Lagrangian
maintain an SO(4) subgroup of SU(4). It follows that the leading discretization
errors in the pion masses are SO(4) symmetric, implying three degeneracies
within the seven lattice irreducible representations. These predictions hold
also for perturbatively improved versions of the action. These degeneracies are
observed, to a surprising degree of accuracy, in existing data. We argue that
the SO(4) symmetry does not extend to the masses and interactions of other
hadrons (vector mesons, baryons, etc), nor to higher order in a^2. We show how
it is possible that, for physical quark masses of O(a^2), the new SO(4)
symmetry can be spontaneously broken, leading to a staggered analogue of the
Aoki-phase of Wilson fermions. This does not, however, appear to happen for
presently studied versions of the staggered action.
