The decay constants f(B) and f(D+) from three-flavor lattice QCD Page: 2 of 7
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The decay constants fB and fD from three-flavor lattice QCD
The D meson decay constants, when compared to precise experimental results, are a critical
check of the lattice methods needed for fB. In Ref.  we predicted fD+ = 201 3 17 MeV in
good agreement with the CLEO-c measurement fD+ = 223 17 3 MeV revealed days later .
In this work we present new results for the D and B meson decay constants. Precise determi-
nations of fB, fB, and the ratio fBfB are needed to study the Standard Model picture of B-B and
Bs-Bs mixing. A progress report for the mixing matrix element study is presented in Ref. .
2. Simulation details
We use the MILC Collaboration three-flavor asqtad ensembles . Details are tabulated in
Table 1. For these ensembles, ml denotes the mass of the two degenerate lighter sea quarks. A 1
single heavier sea quark has a mass mh near the strange quark mass. Upsilon spectroscopy tells us
the heavy quark potential scale ri = 0.318(7) fm . The number of valence quark masses, #mq, -
used in this study is listed in the last column of the table.
The leptonic decay constant fHq for a meson Hq is defined by
0 1 A Hq(p) = ifHq p . (2.1)
The combination pHq = fHq mHq emerges from a combined fit to lattice 2-pt functions:
Co (t) = (OHi(t) OH(0)) (2.2)
CA,(t) = (A4(t) OHq(0)) , (2.3)
where OHq can be either a smeared or local operator.
The axial current renormalization is taken to be
ZQj = pfQ 'Z Z . (2.4)
a [fm] amh am f ri/a configs # mq
0.09 0.031 0.0031 7.08 3.69 435 11
0.0062 7.09 3.70 557 10
0.0124 7.11 3.72 518 8
0.12 0.05 0.005 6.76 2.64 529 12
0.007 6.76 2.63 833 12
0.01 6.76 2.62 592 12
0.02 6.79 2.65 460 12
0.03 6.81 2.66 549 12
0.15 0.0484 0.0097 6.572 2.13 631 9
0.0194 6.586 2.13 631 9
0.029 6.600 2.13 440 9
Table 1: MILC three-flavor lattice parameters. The last column lists the number of valence light quarks
used in this study.
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Bernard, C.; DeTar, C.; Di Pierro, M.; El-Khadra, A. X.; Evans, R. T.; Freeland, E. et al. The decay constants f(B) and f(D+) from three-flavor lattice QCD, article, January 1, 2007; Batavia, Illinois. (digital.library.unt.edu/ark:/67531/metadc897981/m1/2/: accessed June 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.