Status of B[sub K] from lattice QCD Page: 4 of 7
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Ratio of correlation functions needed to calculate BK
Collaboration year BK(2GeV) Formulation Renormalization a-1 (GeV)
Staggered  1997 0.62(2)(2) staggered 1-loop oo
JLQCD  1997 0.63(4) staggered 1-loop o
Rome  2002 0.63(10) Improved Wilson NP oo
Rome  2002 0.70(12) Improved Wilson NP 00
CP-PACS  2001 0.58(1) Domain Wall 1-loop 1.8 GeV
CP-PACS  2001 0.57(1) Domain Wall 1-loop 2.8 GeV
RBC  2002 0.53(1) Domain Wall NP 1.9 GeV
DeGrand  2002 0.66(3) Overlap 1-loop 1.6 GeV
DeGrand  2002 0.66(4) Overlap 1-loop 2.2 GeV
GGHLR  2002 0.61(7) Overlap NP 2.1 GeV
TABLE I: Quenched estimates for BK evaluated in the NDR scheme at 2GeV. The fermion
formulation used in the calculation, the method used for renormalizing the operators, and the
lattice scale at which the calculation was done are also given. NP indicates non-perturbative
renormalization using the RI/MOM scheme and a-1 = oo implies that the quoted result is after a
continuum extrapolation. -
BK(2GeV) = 0.63(10) and 0.70(12) . These, while demonstrating the efficacy of
this method, do not supplant the staggered result, as the continuum extrapolation is
based on only three points and the data have larger errors. The discretization errors
can be characterized as BK(a) = BK(1 + aA) with A ~ 400 MeV and are similar in
magnitude to those with staggered fermions at 1/a = 2 GeV, as are the differences in
estimates with using different operators. In the staggered formulation, the artifacts
are, however, 0(a2A2) and 0(a) and the data suggest an unexpectedly large A ~ 900
" Four collaborations have new results using domain wall and overlap fermions as shown
in Table I [10-14]. Both formulations have built in chiral symmetry at finite a and 0(a)
improvement. Each of these collaborations have used slightly different methodology,
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Gupta, R. (Rajan). Status of B[sub K] from lattice QCD, article, January 1, 2002; United States. (https://digital.library.unt.edu/ark:/67531/metadc933463/m1/4/: accessed April 20, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.