Estimated Errors in |Vcd|/|Vcs| from semileptonic D decays Page: 4 of 5
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2
1.5 ---
Decay Rates g=5.7
- 0 D -> T ev ---- -
1.0 -o D, -> >rgev - _
0.5
0.00.0 0.2 0.4 0.6
lpl, (GeV)1.5
o 1.0
0.50.0
0.8 1.0
Figure 1. Decay rates (with statistical errors) ver-
sus daughter recoil momentum.
3. MATRIX ELEMENTS
We use the tadpole-improved Sheikholeslami-
Wohlert quark action with the plaquette-
determined mean field coefficient zo. We obtain
0(a)-improved matrix elements using the Fermi-
lab interpretation for heavy quarks and tree-level
0(a)-improved currents[5]. Note that the vec-
tor current renormalization factor cancels in ratio
Tnr/K.
We have computed three-point correlators at
= 5.7. 5.9 and 6.1. We determine the lattice
spacing. a. using the charmonium 1P-1S splitting
and the bare charm mass using the spin-averaged
1S charmonium kinetic mass. The same gauge-
field ensembles and procedures were used to study
B and D meson decay constants[6]. Reference [7]
describes our B - rev results on these lattices
and provides more details on our three-point func-
tion calculations.
For illustration. and to reduce some known sys-
tematic errors. we take lpI"' =0.7 GeV. For this
preliminary study we take our best estimate for
matrix elements from 4 = 5.7. We approximate
the D - Kev decay by D, - wrev where a
pseudoscalar "7,7" meson consists of s and s va-
lence quarks. We denote the ratio in Eq. 3 for the
D, decay by T,/,7. The analysis for D - Kev is
underway.
In Fig. 1 we show differential decay rates for
= 5.7. The ratio of areas for Ipl"' = 0.7 GeV0.0 0.2 0.4
1/Mmeson (1/GeV)0.6 0.8
Figure 2. Comparison of M (p,7. 0) for the de-
cay of B, and D, mesons at = 5.7.
gives T,/,7 = 1.53 0.27 where the error is sta-
tistical. Systematic errors are the subject of the
rest of the paper.
We use all three lattices to study the cutoff de-
pendence of D, - wev matrix elements. We
compare partial widths at _ = 5.7 to partial
widths computed from MS, extrapolated to the
continuum linearly with the lattice spacing. Ma-
trix elements MS(p. 0) for a given p on each
lattice were found by interpolating among MS
values calculated for discrete values of p. Dis-
cretization errors in the width increase with p. as
expected. reaching 21% for lpl = 0.7GeV. Mo-
mentum dependent errors of this magnitude were
anticipated by errors estimates for free-field tree-
level quark matrix elements[4]. Errors for the
pion width are expected to be similar to those
for the ss width. These errors. however, will tend
to cancel in ratios. Hence we estimate residual
cutoff errors are below 10% for T,/,7(0.7).
Our bare charm masses were determined in
quarkonia. Charm masses determined using
heavy-light mesons differ due to discretization er-
rors and the quenched approximation. We find
at most a 10% difference in bare m, compar-
ing the two methods. Figure 2. which com-
pares MS(p. 0) calculated for D, and B, mesons.
shows that 1/mQ corrections are small in this
case[4]. Numerical results and pole dominance
arguments indicate that M.4 has somewhat morec,
C
-'-
c.1/mg Dependence
-------------- 0.100
=-4 --------------ED 0.400 -
----- 0.700 -
= 1 -- --0.400
- 0.100
- - - - I I
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J.N.Simone, A.X.El-Khadra, S.Hashimoto, A.S.Kronfeld, P.B.Mackenzie, and S.M.Ryan. Estimated Errors in |Vcd|/|Vcs| from semileptonic D decays, article, November 1, 1998; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc667429/m1/4/: accessed April 19, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.