The phase diagram for staggered fermions is discussed in the context of the staggered chiral Lagrangian, extending previous work on the subject. When the discretization errors are significant, there may be an Aoki-like phase for staggered fermions, where the remnant SO4 taste-symmetry is broken down to SO3. We solve explicitly for the mass spectrum in the 3-flavor degenerate mass case and discuss qualitatively the 2 1-flavor case. From numerical results we find that current simulations are outside the staggered-Aoki phase. As for near-future simulations with more-improved versions of the staggered action, it seems unlikely that these will be in the Aoki phase for any realistic value of the quark mass, although the evidence is not conclusive.

We show how to compute chiral logarithms that take into account both the O(a 2 ) taste-symmetry breaking of staggered fermions and the fourth-root trick that produces one taste per flavor. The calculation starts from the Lee-Sharpe Lagrangian generalized to multiple flavors. An error in a previous treatment by one of us is explained and corrected. The one loop chiral logarithm corrections to the pion and kaon masses in the full ͑unquenched͒, partially quenched, and quenched cases are computed as examples.

We have extended our program of QCD simulations with an improved Kogut-Susskind quark action to a smaller lattice spacing, approximately 0.09 fm. Also, the simulations with a 0:12 fm have been extended to smaller quark masses. In this paper we describe the new simulations and computations of the static quark potential and light hadron spectrum. These results give information about the remaining dependences on the lattice spacing. We examine the dependence of computed quantities on the spatial size of the lattice, on the numerical precision in the computations, and on the step size used in the numerical integrations. We examine the effects of autocorrelations in ''simulation time'' on the potential and spectrum. We see possible effects of decays, or coupling to two-meson states in the 0 and 1 meson propagators. A state consistent with K is seen as a ''parity partner'' in the Goldstone kaon propagator, and we make a preliminary mass computation for a radially excited 0 ÿ meson.

We incorporate heavy-light mesons into staggered chiral perturbation theory (SPT), working to leading order in 1=m Q , where m Q is the heavy-quark mass. At first nontrivial order in the chiral expansion, staggered taste violations affect the chiral logarithms for heavy-light quantities only through the lightmeson propagators in loops. There are also new analytic contributions coming from additional terms in the Lagrangian involving heavy-light and light mesons. Using this heavy-light SPT, we perform the oneloop calculation of the B (or D) meson leptonic decay constant in the partially quenched and full QCD cases. In our treatment, we assume the validity both of the ''fourth root trick'' to reduce four staggered tastes to one, and of the SPT prescription to represent this trick by insertions of factors of 1=4 for each sea-quark loop.

The recently developed Symanzik-improved staggered-quark discretization allows unquenched lattice-QCD simulations with much smaller (and more realistic) quark masses than previously possible. To test this formalism, we compare experiment with a variety of nonperturbative calculations in QCD drawn from a restricted set of "gold-plated" quantities. We find agreement to within statistical and systematic errors of 3% or less. We discuss the implications for phenomenology and, in particular, for heavy-quark physics.

In a continuation of an ongoing program, we use staggered chiral perturbation theory to calculate the one-loop chiral logarithms and analytic terms in the pseudoscalar meson leptonic decay constants f 5 ϩ and f K 5 ϩ.We consider the partially quenched, ''full QCD'' ͑with three dynamical flavors͒, and quenched cases. 1 We use ͓7,8͔ the term ''taste'' to denote the different KS species resulting from doubling, and ''flavor'' for the physical u-d-s quantum number. 2 Here n refers to the number of sea quarks.PHYSICAL REVIEW D 68, 074011 ͑2003͒

We present a lattice calculation of the hadronic vacuum polarization and the lowest-order hadronic contribution (HLO) to the muon anomalous magnetic moment, a µ = (g − 2)/2, using 2 + 1 flavors of improved staggered fermions. A precise fit to the low-q 2 region of the vacuum polarization is necessary to accurately extract the muon g−2. To obtain this fit, we use staggered chiral perturbation theory, including a model to incorporate the vector particles as resonances, and compare these to polynomial fits to the lattice data. We discuss the fit results and associated systematic uncertainties, paying particular attention to the relative contributions of the pions and vector mesons. Using a single lattice spacing ensemble generated by the MILC Collaboration (a = 0.086 fm), light quark masses as small as roughly one-tenth the strange quark mass, and volumes as large as (3.4 fm) 3 , we find a HLO µ = (713 ± 15) × 10 −10 and (748 ± 21) × 10 −10 where the error is statistical only and the two values correspond to linear and quadratic extrapolations in the light quark mass, respectively. Considering various systematic uncertainties not eliminated in this study (including a model of vector resonances used to fit the lattice data and the omission of disconnected quark contractions in the vector-vector correlation function), we view this as agreement with the current best calculations using the experimental cross section for e + e − annihilation to hadrons, 692.4 (5.9) (2.4)×10 −10 , and including the experimental decay rate of the tau lepton to hadrons, 711.0 (5.0) (0.8)(2.8)×10 −10 . We discuss several ways to improve the current lattice calculation.

We report on the computation of the connected light quark vacuum polarization with 2+1+1 flavors of HISQ fermions at the physical point and its contribution to the muon anomalous magnetic moment. Three ensembles, generated by the MILC collaboration, are used to take the continuum limit. The finite volume correction to this result is computed in the (Euclidean) time-momentum representation to NNLO in chiral perturbation theory. We find a ll µ (HVP) = (659 ± 20 ± 5 ± 5 ± 4) × 10 −10 , where the errors are statistical and estimates of residual uncertainties from taking the continuum limit, scale setting, and truncation of chiral perturbation theory at NNLO. We compare our results with recent ones in the literature.