XXIX Ph.D in Physics Ezio TorassaPadova, May 9th 2014 Lesson #3 Higgs boson searches at LEP1, LEP2 Standard Model.

XXIX Ph.D in PhysicsEzio TorassaPadova, May 9th 2014

Lesson #3

Higgs boson searches at LEP1, LEP2

Standard Model


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


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”


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


(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. )


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


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


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


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%


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


• 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”


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.


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


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-

qq

e+e- → e+e-qq


mH=100 GeV

Invariant mass distribution

for MC and real data.

mH=115 GeV

Final LEP selections

for 115 GeV search

(Loose and Tight)


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


!

))(()|(

))((

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

)())(|(


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

))(( )(

!

))((


green: 1 from the background yellow: 2 from the background

background(higher 2 for b+s)

signal+background(higher 2 for b)


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


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



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

XXIX Ph.D in Physics Ezio TorassaPadova, May 9th 2014 Lesson #3 Higgs boson searches at LEP1, LEP2 Standard Model.

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