The dominant systematic error is that due to the uncertainty in the
jet energy scale, including the out-of-cone corrections. As explained
in Section 6.2.1, an upper limit on the jet
scale error is about 10%. For the analysis in [1],
the error in the final top mass due to this uncertainty was estimated
as follows. In a 
Monte Carlo sample
with 
= 160 GeV/
, the energies of
all the jets were varied up and down by
10%. This resulted in a 7.7% shift
in the mean fitted mass (using a slightly different fitting program
than that described here) [137]. This number was then divided by
0.62, the slope of the relation between input mass and average
fitted mass (see Figure 6.22). This yielded an error
of 10.8%.
A further uncertainty of about 
5 GeV/ for the difference
in event generators was then folded in, giving the quoted error
of 22 GeV/ for a central value of 199 GeV/.
Figure: Fitted mass distributions for
and 
W + jets Monte Carlos, with
= 200 GeV/, for different jet scalings. All channels are summed together.
(a), (b) Jet energies scaled by 90%.
(c), (d) Jet energies unscaled.
(e), (f) Jet energies scaled by 110%.
However, a better estimate of the jet scale systematic error can be
made by redoing the ensemble likelihood fits
(see Section 7.3) using both the = 200 GeV/
signal sample (which is much closer to the experimental value)
and the background sample with the jet energies scaled up and
down by 10%. The resulting fitted mass distributions for the
signal and background are shown in Figure 8.3.
Here, the 10% change in jet scale changes the mean fitted mass by
about 5%. These samples were then gathered together in groups
of 24, with a 1:1 signal/background ratio, and passed through the
likelihood fit as in Section 7.3. The results are
shown in Figure 8.4; they should be compared with
Figure 7.3(b). The resulting error estimate is
asymmetrical, and is about 
.
Figure 8.4: Results from Monte Carlo ensemble tests with differing
jet scales. For N = 24 and = 200 GeV/ ().
(a) Jets scaled by 90%.
(b) Jets scaled by 110%.
There are several factors which contribute to the asymmetry in this
error. First, a careful examination of Figure 8.3
shows that the fitted mass shifts slightly more for the 90% jet
scaling than for the 110% scaling (about 1 GeV/ more).
Second, the relation between true mass and fitted mass produced by the
interpolation procedure does not necessarily have a constant slope.
In fact, for the resolution functions used, it is somewhat steeper in
the range of true masses from 180 to 200 GeV/ than it is in range
from 200 to 240 GeV/. For a true mass around 200 GeV/, this
tends to make the errors on the low side larger than on the high side.
This is exacerbated by the fact that the mean fitted mass for the
= 200 GeV/ Monte Carlo sample lies somewhat
below the trend averaged over all the Monte Carlo samples
(see Figure 6.22). Note that the statistical error
shows a similar asymmetry when the one event with an unusually large
fitted mass is removed (see previous section). This effect should be
reduced in the future with better Monte Carlo statistics.
If this calculation is redone using resolution functions derived from
instead of , the result is
a systematic error of about 
.