Continuum Limit of B_K from 2+1 Flavor Domain Wall QCD

Aoki, Y.; Soni, A.; Lightman, M.; Arthur, R.; Ohta, S.; Jung, C.; Kenway, R.D.; Kelly, C.; Brömmel, D.; Scholz, E.E.; Mawhinney, R.D.; Blum, T.; Boyle, P.A.; Dawson, C.; Sturm, C.; Izubuchi, T.; Sachrajda, C.T.; Wennekers, J.; Zhou, R.; Christ, N.H.

doi:10.1103/PhysRevD.84.014503

Journal Article

Continuum Limit of B_K from 2+1 Flavor Domain Wall QCD

Aoki, Y. ; Arthur, R. ; Blum, T. ; Boyle, P. A. ; Brömmel, D.FZJ* ; Christ, N. H. ; Dawson, C. ; Izubuchi, T. ; Jung, C. ; Kelly, C. ; Kenway, R. D. ; Lightman, M. ; Mawhinney, R. D. ; Ohta, S. ; Sachrajda, C. T. ; Scholz, E. E. ; Soni, A. ; Sturm, C. ; Wennekers, J. ; Zhou, R.

2011
Soc. [S.l.]

Physical review / D 84(1), 014503 (2011) [10.1103/PhysRevD.84.014503]

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Please use a persistent id in citations: http://hdl.handle.net/2128/11142 doi:10.1103/PhysRevD.84.014503

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%.

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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.

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