Abstract:
We present recent progress in our calculation of $B_K$ with improved staggered fermions using chiral extrapolations based on SU(3) staggered chiral perturbation theory. We have accumulated significantly higher statistics on the coarse, fine, and ultrafine MILC asqtad lattices. This leads to a reduction in statistical error and an improved continuum extrapolation. Our updated result is $\hat{B}_K = B_K(\text{RGI}) = 0.737 \pm 0.003(\text{stat}) \pm 0.046 (\text{sys})$. This is consistent with the result obtained using chiral extrapolations based on SU(2) staggered chiral perturbation theory, although the total error is somewhat larger with the SU(3) analysis.

Abstract:
We study the extended phase diagram for staggered quarks using chiral perturbation theory. Recent beyond-the-standard-model simulations have shown that broken phases occur for coarse enough lattice spacing, so long as the number of quark flavors in the simulation is large enough (greater than eight). One of the phases seen in these simulations can be studied in depth using chiral perturbation theory. We also show that there are only three broken phases for staggered quarks that can arise, at least for lattice spacings in the regime a^2<< Lambda^2_{QCD}.

Abstract:
The topological susceptibility of the vacuum in quantum chromodynamics has been simulated numerically using the Asqtad improved staggered fermion formalism. At nonzero lattice spacing the residual fermion doublers (fermion ``tastes'') in the staggered fermion formalism give contributions to the susceptibility that deviate from conventional continuum chiral perturbation theory. In this brief report we estimate the taste-breaking artifact and compare it with results of recent simulations, finding that it accounts for roughly half of the scaling violation.

Abstract:
We discuss how to formulate a staggered chiral perturbation theory. This amounts to a generalization of the Lee-Sharpe Lagrangian to include more than one flavor (i.e. multiple staggered fields), which turns out to be nontrivial. One loop corrections to pion and kaon masses and decay constants are computed as examples in three cases: the quenched, partially quenched, and full (unquenched) case. The results for the one loop mass and decay constant corrections have already been presented in Ref. [1].

Abstract:
We present a brief account of the developments in the description of light meson resonances using unitarized extensions of the Chiral Perturbation Theory series, both in energy and temperature. In particular, we describe how these methods have been recently shown to describe simultaneously the low energy and resonance regions of meson-meson scattering. This approach could be of relevance to understand the light scalar mesons since it provides a formalism that respects chiral symmetry and unitarity and is able to generate resonant states without any a priori theoretical bias toward their existence, classification or spectroscopic nature. We will also review how this approach is also able to describe the thermal evolution of the $\rho$ and $\sigma$ mesons. In addition we review their extensions to higher orders, the most recent determination of the resonance pole properties, as well as their behavior in the large $N_c$ limit, which could be of relevance to understand their spectroscopic nature.

Abstract:
Durr and Hoelbling recently observed that the continuum and chiral limits do not commute in the two dimensional, one flavor, Schwinger model with staggered fermions. I point out that such lack of commutativity can also be seen in four-dimensional staggered chiral perturbation theory (SChPT) in quenched or partially quenched quantities constructed to be particularly sensitive to the chiral limit. Although the physics involved in the SChPT examples is quite different from that in the Schwinger model, neither singularity seems to be connected to the trick of taking the nth root of the fermion determinant to remove unwanted degrees of freedom ("tastes"). Further, I argue that the singularities in SChPT are absent in most commonly-computed quantities in the unquenched (full) QCD case and do not imply any unexpected systematic errors in recent MILC calculations with staggered fermions.

Abstract:
Although taste violations significantly affect the results of staggered calculations of pseudoscalar and heavy-light mesonic quantities, those entering staggered calculations of baryonic quantities have not been quantified. Here I develop staggered chiral perturbation theory in the light-quark baryon sector by mapping the Symanzik action into heavy baryon chiral perturbation theory. For 2+1 dynamical quark flavors, the masses of flavor-symmetric nucleons are calculated to third order in partially quenched and fully dynamical staggered chiral perturbation theory. To this order the expansion includes the leading chiral logarithms, which come from loops with virtual decuplet-like states, as well as terms the order of the cubed pion mass, which come from loops with virtual octet-like states. Taste violations enter through the meson propagators in loops and tree-level terms the order of the squared lattice spacing. The pattern of taste symmetry breaking and the resulting degeneracies and mixings are discussed in detail. The resulting chiral forms are appropriate to lattice results obtained with operators already in use and could be used to study the restoration of taste symmetry in the continuum limit. I assume that the fourth root of the fermion determinant can be incorporated in staggered chiral perturbation theory using the replica method.

Abstract:
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, $f_{\pi^+_5}$ and $f_{K^+_5}$. We consider the partially quenched, ``full QCD'' (with three dynamical flavors), and quenched cases.

Abstract:
An unquenched calculation of the form factor for $B\to D^* l \nu$ is needed to improve the determination of $|V_{cb}|$. The MILC lattices, computed with a 2+1 improved staggered action for the light quarks, are well suited to this purpose. The relevant staggered chiral perturbation theory (SChPT) must be known in order to correctly account for the "taste" breaking discretization effects associated with the staggered quarks to NLO in $1/ m_{D^*}$. This SChPT calculation is presented.

Abstract:
To reduce errors in light-quark mass determinations, it is now necessary to consider electromagnetic contributions to light-meson masses. Calculations using staggered quarks and quenched photons are currently underway. Suitably-extended chiral perturbation theory is necessary to extrapolate the lattice data to the physical limit. Here we give (preliminary) results for light-meson masses using staggered chiral perturbation theory including electromagnetism, and discuss the extent to which quenched-photon simulations can improve quark-mass calculations.