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Standard Model
Lesson #3
Higgs boson searches at LEP1, LEP2
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Higgs searches at LEP
The coupling of the Higgs field to the vectorial bosons and fermions it’s
fully defined in the Standard Model
The cross section of the Higgs production and the decay modes as a function of
it’s mass are predicted by the theory
Z
Z*
H
Z*
Z
H
Padova, May 6th 2013
Ezio Torassa
ECM=206 GeV
XXVIII Ph.D in Physics
ECM=206 GeV
The dominating Higgs production mechanism
at LEP1 and LEP2 is the “Higgs-strahlung”
MH(GeV/c2)
Higgs-strahlung
WW fusion
+
interference
Dominant mode
m(H)  s-m(Z)
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Higgs decay channels
For mH 120 GeV, the most important decay chanel is H bb
Hbb 85%
“b-tagging” is relevant !
Reaserch topology:
4 jets
2 jets &
missing energy
19%
60%
Htt 8%
2 jet &
2 lepton
6%
Padova, May 6th 2013
Ezio Torassa
XXVIII
in Physics
Or a tPh.D
instead
of the b
Higgs searches at LEP1
Neutrino decay channel
The signature is one unbalanced hadronic event.
2 jets &
The background is due to Z decay into b quarks
missing energy
Background reduction:
• invariant mass of the two jets  MZ
• jets not in collinear directions
• b-tagging
b
c
uds
c
uds
b
Tracks impact parameters
Padova,
6th 2013
Padova May
12 Aprile
2011
Ezio Torassa
Ezio Torassa
Leptons transverse momentum
XXVIII Ph.D in Physics
Data analysis example (1991-1992)
Zqq
Z H (55GeV)X
(1) Preselection:
Acollinearity > 8 0
Eff. ( Z HX) = 81.2%
Eff. (Zqq) = 1.5 %
20 GeV < Minvariant < 70 GeV
(2) Neural network:
Z HX
Zqq
Neural network with 15 input variables. The output is a
single quality variables: Q takes values between 0 and 1
Q > 0.95
Eff. ( Z HX) = 65.8%
Eff. (Zqq) = 0.23 %
( to be multiplied with the previous Eff. )
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Q(
)
Results
Sum of the tree decay channels:
# observed events: 0
Z
Zee
Z
# expected background events : 0
# expected signal events M (GeV)
H
Eventi (simulati HZ)
50
55
7.90.4
3.60.2
60
65
1.40.1 0.410.05
For MH = 55.7 GeV we have 3 expected signal events events.
The expected number of event is a mean number (l=3) with a Poisson distribution:
The probability to observe 0 events is 5%.
l=3
e  l ln
(n | l ) 
n!
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
For MH larger than 55.7 GeV the probability to observe zero events il smaller than 5%.
Your confidence level is 95%.
DELPHI 1991-1992:
Higgs mass limit:
MH > 55.7 GeV al 95 % di C.L.
1 M hadronic events
~380 k events  ee 
LEP1 : 1989-1995
4 detectors , all channels
m(Higgs) > 65 GeV
Padova, May 6th 2013
/c2
Ezio Torassa
LEP1 1989-1995
at 95%CL
17 M hadronic events
XXVIII Ph.D in Physics
Exclusion and discovery
Large number of events  Gauss distribution approximation
Small number of events  Poisson distribution
n = number of observed events
e  l ln
(n | l ) 
;  n  l ;  n  l ;
m = mean number of events
n!
Contributions to the mean value l: background (b) and signal (s) :
e  (b  s ) (b  s) n
(n | b  s) 
;  n  b  s;  n  b  s;
n!
n is the measurement;
• Exclusion (at least at 95% CL): the probability to observe n events  5%
• Discovery (5  significance):
Padova, May 6th 2013
signal 5 times larger than the error
Ezio Torassa
XXVIII Ph.D in Physics
EXCLUSION
The observed small number of events could be due to
a statistical fluctuation with prob.  5×10-2
DISCOVERY
The observed large number of events could be due to
a statistical fluctuation with prob.  5.7×10-5
Lexclusion
Increasing the Integrated luminosity the background
uncertainty decreases. When the difference
between background and background+signal is 2
the Luminosity for the exclusion is reached.
Ldiscovery
Similar definition for the discovery
Really observe n events and expect to observe n
events at a given luminosity is not the same.
At the exclusion (or discovery) Luminosity
the
probability
to 2013
reach the goal is 50% Ezio Torassa
Padova,
May 6th
XXVIII Ph.D in Physics
Significance
e ( b  s ) ( b  s ) n
(n | b  s ) 
; n  b  s;  n  b  s;
n!

S cP 
ScP 
s
bs
s
b
When the background b
can be precisely estimated
With high statistics, for few units of significance,
the denominator is only √b
The inclusion of the background error Db with a Gaussian distribution needs a
specific calculation, with the Gaussian approximation for the number of events n the
significance can be expressed with the following relation:
S cl 
s
b  Db 2
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
The “blind analysis”
• With a large number of observed events (n>>n), the statistical fluctuations do not
have a big impact in the final result; for small numbers is the opposite:
small changes in the selection can produce big differences (i.e. 0 evts  2 evts)
• None is “neutral” , good arguments can be found to modify a little bit the cuts to obtain a
sensible change of the final result;
• The selection criteria must be defined a priori with the MC to optimize the signal
significance, only at the end we can open the box and look the impact on the real data.
This method is called “blind analysis”.
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Higgs searches at LEP II
The “Higgs-strahlung” is dominant production also at LEP II. At higher s
- the diboson fusion increas the relative relevance;
- higher Higgs masses can be produced.
ECM=206 GeV
Padova, May 6th 2013
MH
Ezio Torassa
XXVIII Ph.D in Physics
Higgs decay channels at LEP II
The most relevant decay channel is H bb like at LEP I
Over 115 GeV (LHC region) other decay channels (WW e ZZ) becames
relevant or dominant
Research topology:
Hbb 85%
4 jets
2 jets &
LEP I
missing energy
LEP II
19%
60%
Htt 8%
2 jet &
2 lepton
6%
Padova, May 6th 2013
Ezio Torassa
XXVIII
in Physics
Or a tPh.D
instead
of the b
In addition to Zff we have also the WW , ZZ and  production and decays.

e+
W+
We-
H
e+

e-

e+

Z
e+e- → e+e-qq
H
Z
f’
Z

ee+
f
W+, Z, 
,e
ePadova, May 6th 2013
e+
W-, Z, 
eEzio Torassa


e+
e-
q
q
XXVIII Ph.D in Physics
mH=100 GeV
mH=115 GeV
Invariant mass distribution
for MC and real data.
Final LEP selections
for 115 GeV search
(Loose and Tight)
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Statistic approach for the global combination
We need to combine the results from different channels (Hqq, H, Hll) and different
energies Ecm. They are grouped in the same two-dimensional space (mH rec , G)
G
mH rec reconstruced invariant mass
G
discrimanant variable (QNN, b-tag)
mHrec
For every k channel we obtain:
- bk estimanted background
- sk
estimated signal (related to mH)
- nk number of Higgs candidate from the real data
We build the Likelihood for two hypothesis:
- candidates coming from signal + background
- candidates coming from background
Padova, May 6th 2013
Ezio Torassa
Ls+b
Lb
XXVIII Ph.D in Physics
We want to discriminate the number of observed events
(n)
w.r.t. the mean number of expected signal plus background (b+s) or only background (b)
The following is the probability for b+s , s is a function related to mH :
e  (b  s ( mH )) (b  s(mH )) n
P( n | b  s ) 
n!
The Likelihood is the product of the probability density (k channel density)
nk
L   P(nk | bk  sk (mH ))  
i 1
k
Padova, May 6th 2013
Ezio Torassa
sk Sik (mH )  bk Bik
sk  bk
XXVIII Ph.D in Physics
 e  (bk  sk ( mH )) (bk  sk (mH )) nk
L   
nk !
k 
 nk sk Sik (mH )  bk Bik
  
sk  bk
 i 1
The comparison between the two hypothesis is provided by the Likelihood ratio.
Q ( mH ) 
Ln|b  s (mH )
Ln|b (mH )
We choose to describe the results with the log of the ratio because it provides the 2
difference :
 2 ln( Q(mH ))  D 2
We look to the function -2ln(Q(mH))
(i) For the real data
(ii) For the MC with n=b
(iii) For the MC with n=b+s
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
green: 1  from the background
yellow: 2  from the background
background
(higher 2 for b+s)
signal+background
(higher 2 for b)
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Over 114 GeV/c2 the real data line
(red) is closer the the s+b line (brown)
Finally we can estimate the exclusion
at 95% of confidence level
anyway the real data line is always
(every mH ) within 2 from the
background line
(CLs = CLs+b / CLb)
mH > 114.4 GeV/c2 at 95% CLs
LEP I mH > 65 GeV/c2
Padova, May 6th 2013
LEP II mH > 114.4 GeV/c2
Ezio Torassa
XXVIII Ph.D in Physics
The “window” for MHiggs
171 GeV
114.4 GeV
This exclusion window is at 95% of C.L. , masses outside this window are not
forbidden, they have a smaller probability
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics
Higgs searches at LEP I :
Z Physics at LEP I CERN 89-08 Vol 2 – Higgs search (pag. 58)
Search for the standard model Higgs boson in Z decays – Nucl Physics B 421 (1994) 3-37
Higgs searches at LEP II :
Search for the Standard Model Higgs Boson at LEP – CERN-EP/2003- 011
Padova, May 6th 2013
Ezio Torassa
XXVIII Ph.D in Physics