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XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Lesson #3
Higgs boson searches at LEP1, LEP2
Standard Model
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Higgs searches at LEP
Z Z*
H
H
Z* Z
ECM=206 GeV
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 ofit’s mass are predicted by the theory
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Higgs-strahlung WW fusion
Dominant modem(H) s-m(Z)
+interference
MH(GeV/c2)
ECM=206 GeV
The dominating Higgs production mechanism at LEP1 and LEP2 is the “Higgs-strahlung”
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Higgs decay channels
For mH 120 GeV, the most important decay chanel is H bb
“b-tagging” is relevant !
4 jets 2 jets &
missing energy
19%60%
Or a instead of the b
2 jet &
2 lepton
6%
Hbb 85%
H 8%
Reaserch topology:
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014Padova 12 Aprile 2011 Ezio Torassa
Neutrino decay channel
2 jets &
missing energy
The signature is one unbalanced hadronic event.
The background is due to Z decay into b quarks
Background reduction:
• invariant mass of the two jets MZ
• jets not in collinear directions
• b-tagging
Leptons transverse momentum
bc
uds
Tracks impact parameters
udsc b
Higgs searches at LEP1
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
(1) Preselection:
Acollinearity > 8 0
20 GeV < Minvariant < 70 GeV
Zqq Z H (55GeV)X
Eff. ( Z HX) = 81.2%
Eff. (Zqq) = 1.5 %
(2) Neural network:
Neural network with 15 input variables. The output is a single quality variables: Q takes values between 0 and 1
Data analysis example (1991-1992)
Q ( )
Z HXZqq
Eff. ( Z HX) = 65.8%
Eff. (Zqq) = 0.23 %
Q > 0.95
( to be multiplied with the previous Eff. )
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Results
MH (GeV) 50 55 60 65
Eventi (simulati HZ) 7.90.4 3.60.2 1.40.1
0.410.05
# expected signal events
# observed events: 0 # expected background events : 0
Sum of the tree decay channels: Z Zee Z
For MH = 55.7 GeV we have 3 expected signal events events.
The expected number of event is a mean number (=3) with a Poisson distribution:
The probability to observe 0 events is 5%.
=3
!)|(
n
en
n
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
For MH larger than 55.7 GeV the probability to observe zero events il smaller than 5%.
Your confidence level is 95%.
Higgs mass limit: MH > 55.7 GeV al 95 % di C.L.
LEP1 : 1989-19954 detectors , all channels
m(Higgs) > 65 GeV /c2 at 95%CL
DELPHI 1991-1992:
1 M hadronic events
~380 k events ee
LEP1 1989-1995
17 M hadronic events
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Large number of events Gauss distribution approximation Small number of events Poisson distribution n = number of observed events m = mean number of events
Contributions to the mean value : background (b) and signal (s) :
n is the measurement;
• Exclusion (at least at 95% CL): the probability to observe n events 5%
• Discovery (5 significance): signal 5 times larger than the error
;;;!
)|(
n
n
nn
en
;;;!
)()|(
)(
sbsbnn
sbesbn n
nsb
Exclusion and discovery
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
EXCLUSIONThe 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) Luminositythe probability to reach the goal is 50%
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Significance
;;;!
)()|(
)(
sbsbnn
sbesbn n
nsb
sb
sScP
When the background b
can be precisely estimated
The inclusion of the background error b 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:
2bb
sScl
b
sScP With high statistics, for few units of significance,
the denominator is only √b
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
• 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”.
The “blind analysis”
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Higgs searches at LEP II
MH
ECM=206 GeV
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.
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
Higgs decay channels at LEP II
The most relevant decay channel is H bb like at LEP IOver 115 GeV (LHC region) other decay channels (WW e ZZ) becames relevant or dominant
4 jets 2 jets &
missing energy
19%60%
Or a instead of the b
2 jet &
2 lepton
6%
Hbb 85%
H 8%
Research topology:
LEP I
LEP II
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
e+ f’
e- f
Z
W+, Z, e+
,e
e- W-, Z,
e+ H
e- Z
Z
e+ -
e-
W+
W-
H
In addition to Zff we have also the WW , ZZ and production and decays.
e+
e-
e+
e-
e+e- → e+e-qq
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
mH=100 GeV
Invariant mass distribution
for MC and real data.
mH=115 GeV
Final LEP selections
for 115 GeV search
(Loose and Tight)
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
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)
mH rec reconstruced invariant mass
G discrimanant variable (QNN, b-tag)
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 Ls+b
- candidates coming from background Lb
mHrec
G
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
!
))(()|(
))((
n
msbesbn
nH
msb H
P
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 :
The Likelihood is the product of the probability density (k channel density)
kn
i kk
ikkHikk
kHkkk bs
BbmSsmsbnPL
1
)())(|(
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
The comparison between the two hypothesis is provided by the Likelihood ratio.
)(
)()(
|
|
Hbn
HsbnH mL
mLmQ
2))(ln(2 HmQ
We choose to describe the results with the log of the ratio because it provides the 2 difference :
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
kkHkk n
i kk
ikkHikk
k k
nHkk
msb
bs
BbmSs
n
msbeL
1
))(( )(
!
))((
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
green: 1 from the background yellow: 2 from the background
background(higher 2 for b+s)
signal+background(higher 2 for b)
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
mH > 114.4 GeV/c2 at 95% CLs
Finally we can estimate the exclusion at 95% of confidence level
(CLs = CLs+b / CLb)
Over 114 GeV/c2 the real data line (red) is closer the the s+b line (brown)
anyway the real data line is always (every mH ) within 2from the background line
LEP I mH > 65 GeV/c2 LEP II mH > 114.4 GeV/c2
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
The “window” for MHiggs
114.4 GeV
171 GeV
This exclusion window is at 95% of C.L. , masses outside this window are not forbidden, they have a smaller probability
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014
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