Determination of $B_K$ using improved staggered fermions (III) Finite volume effects

Details Determination of $B_K$ using improved staggered fermions (III) Finite volume effects Determination of $B_K$ using improved staggered fermions (III) Finite volume effects

2009-10-29

arxiv.org/abs/0910.5581v1

PoS LAT2009:263,2009

Physics

High Energy Physics

High Energy Physics - Lattice

7 pages, 10 figures, Lattice 2009 proceeding

Scientific paper

We study the finite-volume effects in our calculation of $B_K$ using HYP-smeared improved staggered valence fermions. We calculate the predictions of both SU(3) and SU(2) staggered chiral perturbation theory at one-loop order. We compare these to the results of a direct calculation, using MILC coarse lattices with two different volumes: $20^3$ and $28^3$. From the direct calculation, we find that the finite volume effect is $\approx 2%$ for the SU(3) analysis and $\approx 0.9%$ for the SU(2) analysis. We also show how the statistical error depends on the number of measurements made per configuration, and make a first study of autocorrelations.

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