$B_K$ using HYP-smeared staggered fermions in $N_f=2+1$ unquenched QCD

Abstract

We present results for kaon mixing parameter $B_K$ calculated using HYP-smeared improved staggered fermions on the MILC asqtad lattices. We use three lattice spacings ($a\approx 0.12$, $0.09$ and $0.06$fm), ten different valence quark masses ($m\approx m_s/10-m_s$), 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 (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 $B_K(\text{NDR},\mu =2\text{GeV})=0.529\pm 0.009\pm 0.032$ and ${\hat{B}}_K=B_K(\text{RGI})=0.724\pm 0.012\pm 0.043$, 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.

37 pages, 31 figures, most updated version

References in corpus (8)

• Correlations among new CP violating effects in Delta F = 2 observables
• Staggered Chiral Perturbation Theory and the Fourth-Root Trick
• Renormalization-group analysis of the validity of staggered-fermion QCD with the fourth-root recipe
• Neutral kaon mixing from 2+1 flavor Domain Wall QCD
• Effective field theories for QCD with rooted staggered fermions
• Unquenched determination of the kaon parameter B_K from improved staggered fermions
• Mixed Action Effective Field Theory: an Addendum
• Taste symmetry breaking with HYP-smeared staggered fermions

Cited by in corpus (13)

• Continuum Limit of $B_K$ from 2+1 Flavor Domain Wall QCD
• BK-parameter from Nf = 2 twisted mass lattice QCD
• Constraining the mixing matrix for Standard Model with four generations: time dependent and semi-leptonic CP asymmetries in $B_d^0$, $B_s$ and $D^0$
• Finite volume effects in $B_K$ with improved staggered fermions
• Footprints of SUSY GUTs in Flavour Physics
• One-loop matching of improved four-fermion staggered operators with an improved gluon action
• Multi GPU Performance of Conjugate Gradient Algorithm with Staggered Fermions
• $B_K$ with improved staggered fermions: analysis using SU(2) staggered chiral perturbation theory
• Phenomenology from the Lattice
• Flavour Theory and the LHC Era
• First results for $B_K$ on the ultrafine ($a=0.045$ fm) ensemble
• Progress in Lattice QCD Relevant for Flavor Physics
• One loop matching factors for improved staggered four-fermion operators with improved glue