The decay constants f(B) and f(D+) from three-flavor lattice QCD Page: 3 of 7
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The decay constants fB and fD from three-flavor lattice QCD
Factors ZV4 are fixed nonperturbatively from scattering 3-pt functions and the known normalization
of the vector current. Factors p4 are known to one-loop order and are close to unity .
3. Staggered Chiral Perturbation Theory (SxPT)
With staggered quarks the (squared) taste-nonsinglet pseudoscalar meson masses are split:
Ma = (ma --mb)p --a2A (3.1)
where ma, mb are quark masses and the (sixteen) mesons are labeled by their taste representation
S= PA, T, V, I with Ap = 0.
At next-to-leading order (NLO) in XPT the expression for the decay constants is
OPH9 = (PH [1 +-AfH (mq, mImh) +-PH (mq, mImh)] (3.2)
where AfH denotes the "chiral logs" and pH denotes terms analytic in the meson masses.
With staggered quarks
AfH _ *+Hw2_ I +[hq +a2( (Ah + w(hq) ] . (3.3)
Taste-breaking effects arise at finite a from the meson mass splittings and the 3A and 3(, hair-pin
terms . Finite a effects reduce the chiral logarithm curvature, however, the expected QCD chiral
logarithm is recovered in the continuum limit.
The NLO analytic terms are
PH [P24 2 P1(mI,mh) --P2(mq)] (3.4)
Pi = fi(AX) 9p(2m,+mh)-a2 A--A) (3.5)
P2 = f2(Ax) 5 3mq+a2 ( A ,AI) (3.6)
where A is the weighted average of taste splittings. The 0(a2) terms ensure that dependence upon
the chiral logarithm scale, Ax, in fi and f2 cancels that of Afq.
Equation (3.2) with the addition of four NNLO analytic terms parameterizes our chiral ex-
trapolations. We fit OHq to determine the parameters. Constraints (value and width) for p, A ,
f1, 3A and come from XPT for lattice pions and kaons . The coupling g *Dz = 0.35 0.14
is likewise constrained by the CLEO measurement . From heavy quark symmetry we expect
gB*Bi *Dir. The remaining parameters (PH, fi and f2 and the NNLO analytic parameters are
determined in the fit.
In order to extrapolate to the physical results we set A = 3A = 0, mh -* ms and m,
(mu +md)/2. Then OH, (OHS) is found in the limit mq mad (ms).
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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/m1/3/: accessed December 16, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.