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# Scaling behavior and sea quark dependence of pion spectrum with HYP-smeared staggered fermions

09/2008;

Source: arXiv

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**ABSTRACT:**We present results for the kaon mixing parameter BK calculated using HYP (hypercubic fat link)-smeared improved staggered fermions on the asqtad lattices generated by the MILC collaboration. We use three lattice spacings (a≈0.12, 0.09 and 0.06 fm), ten different valence-quark masses (m≈ms/10-ms), and several light sea-quark masses in order to control the continuum and chiral extrapolations. We derive the next-to-leading order staggered chiral perturbation theory (SChPT) results necessary to fit our data, and use these results to do extrapolations based both on SU(2) and SU(3) SChPT. The SU(2) fitting is particularly straightforward because parameters related to taste breaking and matching errors appear only at next-to-next-to-leading order. We match to the continuum renormalization scheme [naïve dimensional regularization (NDR)] using one-loop perturbation theory. Our final result is from the SU(2) analysis, with the SU(3) result providing a (less accurate) cross check. We find BK(NDR,μ=2 GeV)=0.529±0.009±0.032 and B̂K=BK(RGI)=0.724±0.012±0.043, where the first error is statistical and the second systematic. The error is dominated by the truncation error in the matching factor. Our results are consistent with those obtained using valence domain-wall fermions on lattices generated with asqtad or domain-wall sea quarks.Physical Review D 12/2010; 82(11). · 4.86 Impact Factor -
##### Article: Determination of $B_K$ using improved staggered fermions (II) SU(2) chiral perturbation theory fit

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**ABSTRACT:**We present results for $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. In this report, the data is analyzed using the results of SU(2) staggered chiral perturbation theory (SChPT). We outline the derivation of the NLO SU(2) SChPT result, explain our fitting procedure, and outline how we estimate systematic errors. We also show the light sea-quark mass and lattice spacing dependence for both SU(2) and SU(3)-based analyses. Our preliminary result from the SU(2) analysis is $B_K(\text{NDR}, \mu = 2 \text{GeV}) = 0.512 \pm 0.014 \pm 0.034$ and $\hat{B}_K = B_K(\text{RGI})= 0.701 \pm 0.019 \pm 0.047$. This is somewhat more accurate than our result from the SU(3) analysis. It is consistent with results obtained using valence domain-wall fermions Comment: 7 pages, 6 figures, Lattice 2009 proceeding10/2009; - [Show abstract] [Hide abstract]

**ABSTRACT:**We calculate the masses of taste non-Goldstone pions and kaons in staggered chiral perturbation theory through next-to-leading order in the standard power counting. The results can be used to quantitatively understand taste violations in existing lattice data generated with staggered fermions and to extract the $u$, $d$, and $s$ quark masses and Gasser-Leutwyler parameters from the experimentally observed spectrum. The expressions for the non-Goldstone masses contain low-energy couplings unique to the non-Goldstone sector. With two exceptions these enter as coefficients of analytic terms; all the new couplings can be fixed by performing spectrum calculations. We report one-loop results for the quenched case and the fully dynamical and partially quenched 1+1+1 and 2+1 flavor cases in the chiral SU(3) and SU(2) theories.Physical review D: Particles and fields 12/2011; 85(9).

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