Etude et impact du bruit de fond corrélé pour la mesure de l'angle ...

114 5. Correlated background
tel-00821629, version 1 - 11 May 2013
prompt and delayed. The time correlation obtained from the pure sample of
correlated background selected in [12, 30] MeV is shown in Fig. 5.3, where
the expected fast and slow components, respectively due to SM and FN,
appear evident. The SM time correlation has an exponential distribution,
proportional to the muon live time of ⌧ µ ' 2.2 µs. The FN time correlation
is driven by the neutron capture on Gd, exactly like the prompt-delayed
time correlation of ¯⌫ e candidates shown in Fig. 4.6 (left), with an increasing
components at short t, due to the neutron thermalization process, and a
decreasing component with a time constant ⌧ Gd ' 30 µs, due to the neutron
capture on Gd. The increasing component of the FN distribution is not
evident since the lower part of the t distribution is dominated by SM.
The e ciency and the purity of the FN/SM separation by the t cut are estimated
by approximating the time distribution with two exponential terms,
as shown in Eq. 5.1:
f(t) =f SM (t)+f FN (t) =c SM
!
!
e t/⌧ SM
e t/⌧ FN
+ c FN
⌧ SM ⌧ FN
(5.1)
Such approximation neglect the neutron thermalization process at short t,
which require a third positive exponential as shown in [64]. This approximation
is necessary since the low statistics of the pure correlated background
sample do not allow to obtain good fit result with a third exponential term
in Eq. 5.1. Since the shape of the time distribution of neutron capture on
Gd is well known from MC, ¯⌫ e candidates and 252 Cf source, it is possible
to correct for such approximation. The model fitted to the data is shown
by the black curve in Fig. 5.3, while the red and the blue dashed curves
represent the FN and the SM component respectively. Defining t cut as the
cut value, the FN sample is defined such as t>t cut while the SM sample is
defined such as tt cut ) =
R 1
t cut
f FN (t)dt
R 1
0
f FN (t)dt
(5.2)
⇢ FN (t>t cut ) =
R 1
t cut
f SM (t)dt
R 1
t cut
f SM + f FN (t)dt
(5.3)
✏ SM (t