Taste symmetry breaking with HYP-smeared staggered fermions
  We study the impact of hypercubic (HYP) smearing on the size of taste breaking for staggered fermions, comparing to unimproved and to asqtad-improved staggered fermions. As in previous studies, we find a substantial reduction in taste-breaking compared to unimproved staggered fermions (by a factor of 4-7 on lattices with spacing $a\approx 0.1 $fm). In addition, we observe that discretization effects of next-to-leading order in the chiral expansion (${\cal O}(a^2 p^2)$) are markedly reduced by HYP smearing. Compared to asqtad valence fermions, we find that taste-breaking in the pion spectrum is reduced by a factor of 2.5-3, down to a level comparable to the expected size of generic ${\cal O}(a^2)$ effects. Our results suggest that, once one reaches a lattice spacing of $a\approx 0.09 $fm, taste-breaking will be small enough after HYP smearing that one can use a modified power counting in which ${\cal O}(a^2) \ll {\cal O}(p^2)$, simplify fitting to phenomenologically interesting quantities. 
Taegil Bae, David H. Adams, Chulwoo Jung, Hyung-Jin Kim, Jongjeong   Kim, Kwangwoo Kim, Weonjong Lee, and Stephen R. Sharpe