Rare B meson decays - mathieu trocmé

III- Analysis Method 37
III.4- Optimisation of the cuts:
III.4.1- Significance calculation:
All the cuts values, except for ∆E and m ES , are optimised by maximising an
approximation of the statistical significance of the branching ratio σ defined by:
σ =
s
s + b
where b is the number of background in the signal region (by analogy from above, it
corresponds to nbg _ SR )
b = R × ntot
_ GSB
and s is the estimated final number of events in the signal region (by analogy from above, it
real
corresponds to N sig )
real '
= N × BR × ε
s 0
B
MC,
corr
(since still by analogy
s × 1
' ε
BR = )
N
MC,
corr
real
0
B
s is said estimated since the branching ratio BR’ used to calculate it must be assumed (for
reason given later – Cf III.5, p.42) Although this may not completely reflect the true
branching ratio for the channel under study, the optimisation is usually not heavily affected. A
sensible value for it is usually the previous value found by someone else. The last person
having studied this decay being N. Chevalier, the BR she found was used.
Practically, each time a cut varies, 2 values change: the MC Efficiency appearing in s
first, the number of events in the GSB leading to b secondly. Thus, by recalculating the
corrected MC Efficiency and recounting the number of events in the GSB for each different
value of one cut, the significance can be plotted versus these changing values and the
maximum then found.