Rare B meson decays - mathieu trocmé

III- Analysis Method 39
Hence,
σ σ
real '
With, 1 s = N 0 × BR × ε MC,
corr
σ
σ
stat
s
syst
s
B
= s ×
= s ×
⎛σ
⎜
⎜
⎜ N
⎝
stat
real
N
B
0
real
0
B
⎛σ
⎜ N
⎜
⎜ N B
⎝
And where
And, 2 b = R × ntot
_ GSB
σ
stat
b
= b ×
syst
real
B
0
real
0
⎛σ
⎜
⎝ R
1
=
( s + b)
2
⎞
⎟
⎟
⎟
⎠
2
⎞
⎟
⎟
⎟
⎠
ε
stat
R
⎛σ
+
⎜
⎜ BR
⎝
stat
'
BR
'
3 / 2
⎞
⎟
⎟
⎠
2
2
⎛ s ⎞ 2 ⎛ s ⎞
⎜ + b⎟σ
s + ⎜ ⎟σ ⎝ 2 ⎠ ⎝ 2 ⎠
⎛ σ
+
⎜
⎜ ε
⎝
syst ⎛σ
' ⎞ ⎛ σ
⎜ BR ⎟
+
⎜ ε
+
⎜ '
BR ⎟ ⎜ ε
⎝ ⎠ ⎝
MC,
corr
⎞
⎟
⎠
2
⎛ σ
+
⎜
⎜ n
⎝
syst
ε MC , corr
MC,
corr
syst
MC , corr
MC,
corr
⎞
⎟
⎟
⎠
⎞
⎟
⎟
⎠
2
2
= s ×
MC ⎛ N ⎞ sig
= k = ⎜ ⎟
corrε
MC kcorr
⎜ MC ⎟
⎝ N 0
B ⎠
stat
n
tot _ GSB
tot _ GSB
⎞
⎟
⎟
⎠
2
=
n
b
tot _ GSB
= R
2
b
⎛σ
⎜
⎜ BR
⎝
n
stat
'
BR
'
⎞
⎟
⎟
⎠
2
tot _ GSB
syst
2
syst
2
syst
syst ⎛σ
⎞
⎛ σ ⎞
R
n
R
b b
⎜
⎛
tot GSB σ ⎞
_
= ×
⎟
⎜
= b × = ntot
GSB
R ⎟ +
n
⎜
tot GSB R ⎟
⎜ ⎟
_
_
σ × σ
⎝ ⎠
⎝ ⎠
⎝ ⎠
⎛ σ
+
⎜
⎜ ε
⎝
syst
R
stat
ε MC , corr
MC,
corr
This gives the exact error on the statistical significance σ. Nonetheless, the interest of
the optimisation process is not to accurately calculate this value. Its interest is, via this σ
calculation, to be able to say which of 2 following values is the best if any differences
between them. Thus, the error must be taken into account and especially the variation of error
between these 2 points instead of the total error itself in which this variation may be (is)
drowned.
⎞
⎟
⎟
⎠
( See previous parts
for errors calculation )
2