We present preliminary results for BK from the MILC ultrafine lattices, based on a partial ensemble of 305 configurations. We use HYP-smeared improved staggered valence quarks. The analysis is done using fitting forms based on both SU(2) and SU(3) staggered chiral perturbation thery. For the SU(2) analysis, we find that the result using the NLO fit function is consistent with that from a partial NNLO fit. For the SU(3) analysis, where we have to use partially constrained fits due to the number of fit parameters, we find that our two preferred fits ("N-BB1" and "N-BB2") are also consistent, both with each other and with the results of the SU(2) fits. These results are used in companion proceedings to improve the control over the continuum extrapolation.
@article{arxiv.1010.4781,
title = {First results for $B_K$ on the ultrafine ($a=0.045$ fm) ensemble},
author = {Taegil Bae and Yong-Chull Jang and Hyung-Jin Kim and Jangho Kim and Jongjeong Kim and Kwangwoo Kim and Boram Yoon and Weonjong Lee and Chulwoo Jung and Stephen R. Sharpe},
journal= {arXiv preprint arXiv:1010.4781},
year = {2011}
}