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@ARTICLE{Aoki:15718,
      author       = {Aoki, Y. and Arthur, R. and Blum, T. and Boyle, P.A. and
                      Brömmel, D. and Christ, N.H. and Dawson, C. and Izubuchi,
                      T. and Jung, C. and Kelly, C. and Kenway, R.D. and Lightman,
                      M. and Mawhinney, R.D. and Ohta, S. and Sachrajda, C.T. and
                      Scholz, E.E. and Soni, A. and Sturm, C. and Wennekers, J.
                      and Zhou, R.},
      title        = {{C}ontinuum {L}imit of ${B}_{K}$ from 2+1 {F}lavor {D}omain
                      {W}all {QCD}},
      journal      = {Physical review / D},
      volume       = {84},
      number       = {1},
      issn         = {1550-7998},
      address      = {[S.l.]},
      publisher    = {Soc.},
      reportid     = {PreJuSER-15718},
      pages        = {014503},
      year         = {2011},
      note         = {The calculations reported here were performed on the QCDOC
                      computers [65-68] at Columbia University, Edinburgh
                      University, and at Brookhaven National Laboratory (BNL), and
                      Argonne Leadership Class Facility (ALCF) BlueGene/P
                      resources at Argonne National Laboratory (ANL). At BNL, the
                      QCDOC computers of the RIKEN-BNL Research Center and the
                      USQCD Collaboration were used. The very large scale
                      capability of the ALCF was critical for carrying out the
                      challenging calculations reported here. The Edinburgh QCDOC
                      system was funded by PPARC JIF Grant No. PPA/J/S/1998/00756
                      and operated through support from the Universities of
                      Edinburgh, Southampton, and Wales Swansea, and from STFC
                      Grant No. PP/E006965/1. Computations for this work were
                      carried out in part on facilities of the USQCD
                      Collaboration, which are funded by the Office of Science of
                      the U.S. Department of Energy. We thank ANL, RIKEN, BNL, and
                      the U.S. DOE, the University of Edinburgh and STFC for
                      providing the facilities essential for the completion of
                      this work. The software used includes: the CPS QCD codes
                      (http://qcdoc.phys.columbia.edu/cps.html), supported in part
                      by the U.S. DOE SciDAC program; the BAGEL [69] assembler
                      kernel generator for many of the high-performance optimized
                      kernels; and the UKHadron codes. The work of the Edinburgh
                      authors was supported by PPARC Grants No. PP/D000238/1 and
                      No. PP/C503154/1. P. A. B. acknowledges support from RCUK.
                      T. B. and R. Z. were supported by the U.S. DOE under Grant
                      No. DE-FG02-92ER40716. T. I. was supported in part by the
                      Grant-in-Aid of the Japanese Ministry of Education (Grants
                      No. 22540301, No. 20105002, and No. 20025010). C.J., T. I.,
                      C.St., and A. S. (BNL) were partially supported by the U.S.
                      DOE under Contract No. DE-AC02-98CH10886. E. E. S is partly
                      supported by DFG SFB/TR 55 and by the Research Executive
                      Agency of the European Union under Grant No.
                      PITN-GA-2009-238353 (ITN STRONGnet). N.C. and R. M.
                      (Columbia University) were partially supported by the U.S.
                      DOE under Contract No. DE-FG02-92ER40699. D. B. and C. T. S.
                      (University of Southampton) were partially supported by U.K.
                      STFC Grant No. PP/D000211/1 and by EU Contract No.
                      MRTN-CT-2006-035482 (Flavianet). Y.A. is partially supported
                      by JSPS KAKENHI 21540289. We thank Andrzej Buras for useful
                      conversations.},
      abstract     = {We determine the neutral kaon mixing matrix element B-K in
                      the continuum limit with 2 + 1 flavors of domain wall
                      fermions, using the Iwasaki gauge action at two different
                      lattice spacings. These lattice fermions have near exact
                      chiral symmetry and therefore avoid artificial lattice
                      operator mixing. We introduce a significant improvement to
                      the conventional nonperturbative renormalization (NPR)
                      method in which the bare matrix elements are renormalized
                      nonperturbatively in the regularization invariant momentum
                      scheme (RI-MOM) and are then converted into the (MS) over
                      bar scheme using continuum perturbation theory. In addition
                      to RI-MOM, we introduce and implement four nonexceptional
                      intermediate momentum schemes that suppress infrared
                      nonperturbative uncertainties in the renormalization
                      procedure. We compute the conversion factors relating the
                      matrix elements in this family of regularization invariant
                      symmetric momentum schemes (RI-SMOM) and (MS) over bar at
                      one-loop order. Comparison of the results obtained using
                      these different intermediate schemes allows for a more
                      reliable estimate of the unknown higher-order contributions
                      and hence for a correspondingly more robust estimate of the
                      systematic error. We also apply a recently proposed approach
                      in which twisted boundary conditions are used to control the
                      Symanzik expansion for off-shell vertex functions leading to
                      a better control of the renormalization in the continuum
                      limit. We control chiral extrapolation errors by considering
                      both the next-to-leading order SU(2) chiral effective
                      theory, and an analytic mass expansion. We obtain B-K((MS)
                      over bar)(3 GeV) = 0.529(5)(stat)(15)(chi)(2)(FV)(11)(NPR).
                      This corresponds to (B) over cap ((RGI ) over bar)(K) =
                      0.749(7)(stat)(21)(chi)(3)(FV)(15)(NPR). Adding all sources
                      of error in quadrature, we obtain (B) over cap ((RGI ) over
                      bar)(K)0.749(27)(combined), with an overall combined error
                      of $3.6\%.$},
      keywords     = {J (WoSType)},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {Scientific Computing (FUEK411) / 411 - Computational
                      Science and Mathematical Methods (POF2-411)},
      pid          = {G:(DE-Juel1)FUEK411 / G:(DE-HGF)POF2-411},
      shelfmark    = {Astronomy $\&$ Astrophysics / Physics, Particles $\&$
                      Fields},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000292514400009},
      doi          = {10.1103/PhysRevD.84.014503},
      url          = {https://juser.fz-juelich.de/record/15718},
}