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We present a new determination of the $B_s$ leptonic decay constant from lattice QCD simulations that use gluon configurations from MILC and a highly improved discretization of the relativistic quark action for both valence quarks.
For a review of HQET and its application to f B s f_{B_{s}} see G. Buchalla, arXiv:hep-ph/0202092, in the Proceedings of the 55th Scottish Universities Summer School in Physics, edited by C. T. H. Davies and S. M. Playfer (Bristol, IOP, 2002)
2002
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R. G. Edwards and B. Joo, Nucl. Phys. B Proc. Suppl. 140, 832 (2005)
2005
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E. Follana et al
2007
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2008
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2008
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2009
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2010
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2010
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2010
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2010
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2010
2010
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See talk by J. Shigemitsu (HPQCD) and poster by E. Neil (Fermilab/MILC) at Lattice 2011 (Squaw Valley, Ca., July 2011)
2011
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2011
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2011
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K. Nakamura et al. (Particle Data Group), Journal of Physics G37, 075021 (2010) and 2011 partial update for the 2012 edition
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A. Bazavov, D. Toussaint, C. Bernard, J. Laiho, C. DeTar, L. Levkova, M. B. Oktay, S. Gottlieb et al
2010
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We include only the leading-order anomalous dimension because of the limited precision of our data. Our results are essentially unchanged if we omit leading-order as well
Cited in the paper.
Parameter c s c_{s} depends upon M H s M_{H_{s}} but we have verified that such variation has negligible impact on our analysis given our statistical errors. Our value for c s c_{s} agrees with the f D s f_{D_{s}} slope given in [ 6 ]
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Naively one expects c i j k l ≈ O ( 1 ) c_{ijkl}\!\approx\!O(1) . Making the prior 50% wider is conservative and increases our final error estimates. The empirical Bayes criterion, for example, indicates that a prior of 0 ± 1 0\pm 1 is optimal. The empirical Bayes criterion is discussed in: G. P. Lepage et al. , Nucl. Phys. Proc. Suppl. 106
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Our value for slope d s d_{s} agrees reasonably well with the value 0.20(1) found for m D s m_{D_{s}} in [ 6 ]
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HPQCD collaboration, in preparation
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2012
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