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Fig. 1(a) shows the heavy-quark mass dependence from Ref. [3]. As expected, tV is the
largest of the 1/mQ matrix elements. Because of the fit, the value of tV is highly correlated
with that of (3, but the physical combination is better determined.
We have also studied the dependence of the calculation on the mass of the light spectator
quark, over the range 0.4 < mq/ms < 1. As seen in Fig. 1(b), there is a slight linear dependence
on m!, which is proportional to mq. The points are correlated, so the trend is significant. The
main effect of extrapolating in m2 is to increase the statistical error. In addition, there must
be a pion loop contribution [16], which is mistreated in the quenched approximation. We treat
the omission of this effect as a systematic error.
After putting everything back together again, we find [3]
.7B-,*D* (1) = 0.913+004 +i 0.016+0.003 +0.000+0.006
(10)
where the uncertainties stem, respectively, from statistics and fitting, HQET matching, lattice
0.06
d0.04
0.02
0.00
-0.02
0.96
.0.92
* h
- M h
A hA
--------------------
1/am2c + 1am2b
2c 2b
0.88-
0.04
0.08
(m a)2
0.12
0.16
Figure 1: (a) Heavy-quark mass dependence of the double ratios. (b) Chiral extrapolation of
ha (1).
3
4 ' ' ' I
.0
0
