search for the higgs boson: a numerical adventure of ...horvath/talks/2013/higgs_ccp-2013.pdf ·...

Search for the Higgs Boson:A Numerical Adventure of Exclusion

and DiscoveryCCP-2013, Moscow, 21-24 August 2013

Dezso Horváthon behalf of the CMS Collaboration

[email protected]

Wigner Research Centre for Physics,

Institute for Particle and Nuclear Physics, Budapest, Hungary

& ATOMKI, Debrecen, Hungary

Dezso Horváth: Search for for the Higgs Boson CCP-2013, Moscow, 21-24 August 2013 – p. 1

Outline

The Higgs boson of the Standard Model

Statistical Methods of the Search

Exclusion at LEP

Observation at LHC

What next?

With the support of the Hungarian OTKA Grant NK-81447


References

The CMS Collaboration: Observation of a new boson at a mass of125 GeV with the CMS experiment at the LHC,Phys. Lett. B 716 (2012) 30-61.Long version: arXiv:1303.4571 submitted to JHEP

The CMS Collaboration: Measurements of the properties of thenew boson with a mass near 125 GeVCMS Physics Analysis Summary HIG-13-005, 14 March 2013

The ATLAS Collaboration: Observation of a new particle in thesearch for the Standard Model Higgs boson with the ATLAS detectorat the LHC, Phys. Lett. B 716 (2012) 1–29

The ATLAS Collaboration: Combined coupling measurements ofthe Higgs-like boson with the ATLAS detector using up to 25 fb−1 ofproton-proton collision dataATLAS NOTE, ATLAS-CONF-2013-034


The Zoo of the Standard Model

The elementary particles

3 fermion families:1 pair of quarks and1 pair of leptons in each

3 kinds of gauge bosons:the force carriers

All identified and studied!

+ the Higgs boson (?)

Color: the charge of the strong interactioncolored quarks ⇒ colorless composite hadrons of 2 kinds

hadrons = mesons (qq) + baryons (qqq)


The Standard Model

Derive 3 interactions of local U(1), SU(2) and SU(3)symmetries

Unify and separate e-m U(1) and weak SU(2) interactionsusing spontaneous symmetry breaking:

(Anderson-Englert-Brout-Higgs-Guralnik-Hagen-Kibble mechanism, 1963-64)

Add a 4-component, symmetry breaking field to vacuum.Separate a good U(1) local symmetry from the ruined

U(1) ⊗ SU(2)

⇓electromagnetism + zero-mass photon, OK!

Turn 3 d.f. of Higgs-field to create masses for Z, W+, W−,get a correct weak interaction with 3 heavy gauge bosons.

4th degree of freedom: heavy scalar boson.Dezso Horváth: Search for for the Higgs Boson CCP-2013, Moscow, 21-24 August 2013 – p. 5

Glory Road of the Standard Model

Status in 2013

Includes hundreds ofmeasurements of all experiments

|Expt – theory|expt. uncertainty

Slightly deviating quantity usedto change

Now it is forward-backwardasymmetry of

e+e− → Z → bb

LEP Electroweak Working Group:

http://lepewwg.web.cern.ch/

Measurement Fit |Omeas−Ofit|/σmeas

0 1 2 3

0 1 2 3

∆αhad(mZ)∆α(5) 0.02750 ± 0.00033 0.02759

mZ [GeV]mZ [GeV] 91.1875 ± 0.0021 91.1874

ΓZ [GeV]ΓZ [GeV] 2.4952 ± 0.0023 2.4959

σhad [nb]σ0 41.540 ± 0.037 41.478

RlRl 20.767 ± 0.025 20.742

AfbA0,l 0.01714 ± 0.00095 0.01645

Al(Pτ)Al(Pτ) 0.1465 ± 0.0032 0.1481

RbRb 0.21629 ± 0.00066 0.21579

RcRc 0.1721 ± 0.0030 0.1723

AfbA0,b 0.0992 ± 0.0016 0.1038

AfbA0,c 0.0707 ± 0.0035 0.0742

AbAb 0.923 ± 0.020 0.935

AcAc 0.670 ± 0.027 0.668

Al(SLD)Al(SLD) 0.1513 ± 0.0021 0.1481

sin2θeffsin2θlept(Qfb) 0.2324 ± 0.0012 0.2314

mW [GeV]mW [GeV] 80.385 ± 0.015 80.377

ΓW [GeV]ΓW [GeV] 2.085 ± 0.042 2.092

mt [GeV]mt [GeV] 173.20 ± 0.90 173.26

March 2012


The Higgs boson of the Standard ModelSpontaneous symmetry breaking:

Spinless, neutral, heavy particle

The scalar particle needed for renormalisation

Does it really exist? SM: it must!

Many jokes of the Higgs boson on internet...The Higgs boson walks into a bar. The bartender says"Watch out, there were some guys looking for you."

The Higgs boson walks into a church. The priest says „Yourkind is not welcome here”. The boson replies: „But withoutme how can you have mass?”


Where is the Higgs boson?

By-product of spontaneous symmetry breaking of the SM

Most wanted particle of physics as

the only missing piece of the Standard Model.

Experimentally not observed before 2012

„It was in 1972 ...

that my life as a boson really began”

Peter Higgs:

My Life as a Boson: The Story of „The Higgs”,

Int. J. Mod. Phys. A 17 Suppl. (2002) 86-88.


Statistical Concepts of Particle Physicistsare far from those of official math statistics!

LHC Statistics for Pedestrians by Eilam Grossin PHYSTAT-LHC Workshop on Statistical Issues for LHC

Physics, CERN-2008-001, p. 205:

A pedestrians guide . . . to help the confused physicist tounderstand the jargon and methods used by HEP

Phystatisticians.

A Phystatistician is a Physicist who knows his way inStatistics and knows how Kendalls advanced theory of

statistics book looks like....

Every collaboration has phystatistician experts and they allhave quite different ideas how to analyse data...


Last 2 PHYSTAT-LHC Workshops


Statistics Committees


Likelihood

Poisson distribution (ni events in bin i):

P(ni|µi) =µ

nii e−µi

ni!

Poisson likelihood: L = ΠiP(ni|µi)

Expected < ni >: µi =∑

j Lσjǫji

L: luminosity (∼ collision rate),σj : cross section of source j,

ǫji: efficiency (Monte Carlo) of source j in bin i.


Luminosity: collision rate

Luminosity: L = fnN1N2

A

[L] = s−1cm−2 (∼ flux)

f : circulation frequency; n: nr. of bunches in ring;N1, N2 particles/bunch; A: spatial overlap

Rate of reaction with cross section σ at ǫ efficiencyR = ǫσL

Integrated luminosity:∫ t2t1

Ldt

measured in units of inverse cross-section:[pb−1, fb−1]


Exclusion and Discovery

General convention inaccelerator

experiments:

Exclusion of a givenphenomenon at

≥ 95% confidencelevel.

Observation ofsomething new:> 5σ abovebackground.

(x−x )/0 σ

ε/2ε/2

One-sided exclusion:X > X0 at 95% CL ifXobs − X0 > 1.64σ


And what is σ?The total uncertainty of the physics parameters P

according to the best honest guess of the experimentalist.

It has a statistical component(from the number of observed events)

and systematic ones from various sources:

Monte Carlo statistics and inputs, calibration factors,efficiencies, etc. (nuisance parameters Θ)

could be added up with correlations accounted for with a

final uncertainty roughly: σ =√

σ2stat + σ2

syst

However, we derive the final uncertainty via marginalizing(integrating out) the nuisance parameters in likelihood L

using the related probability distributions W:

L(P ;x) = W(x|P ) =∫

W(x|P,Θ)W(Θ|P )dΘ


Blind Analysis„A blind analysis is a measurement which is performedwithout looking at the answer. Blind analyses are the

optimal way to reduce or eliminate experimenter’s bias, theunintended biasing of a result in a particular direction.”

A. Roodman: Blind Analysis in Particle Physics,http://arxiv.org/abs/physics/0312102, SLAC, 2003

Originally coming from medicine

Basic analysis method of Higgs search at LHC:

Optimize, prove and publish your analysis technique usingsimulations and earlier data only before touching new data

in the critical regionCMS, 2012: 110 < MH < 140 GeV blinded

because of 3σ excess observed in 2011

Simultaneous unblinding for all analysis channelsDezso Horváth: Search for for the Higgs Boson CCP-2013, Moscow, 21-24 August 2013 – p. 16

The Large Electron Positron collider


Accelerators at CERN, LEP era


The LEP Collider

Year E(e+e−), GeV∫

Ldt/4, pb−1 main goal

1989–94 ∼ 91 140 Z0

1995 130–136 5

1996 161–172 20 W+W−

1997 184 60 WW, ZZ

1998 189 190 WW, ZZ

1999 192–202 220 Higgs

2000 204–209 220 Higgs


Search for the SM Higgs boson at LEP

Dominant formation:

Higgs-strahlung

e−e+→ZH

Dominant decay:

H → bb

Various analyses for different Z decays


What is observed: resonance

τ = Γ−1 lifetime ⇒ exp. decay: N(t) = N0e−Γt

Probability distribution:

|χ(E)|2 = 1(E−M)2+Γ2/4

Breit-Wigner equation

M

Γ

resonance

centre

width

(~ = 1, c = 1)Lorentz curve

New particle discovery: resonance at decay energycorresponding to the particle mass


Hunting the Higgs boson

Compose a complete SM background using MonteCarlo simulation taking all types of possible eventsnormalized to their cross-sections.

Higgs signal: simulation of all possible production anddecay processes with all possible Higgs-boson masses

Put all these through the detector simulation to getevents analogous to the measured ones.

Optimize the event selection:reduce background, enhance signal via e.g.sig/

√bgr = max or 2 · (√sig + bgr − √

bgr = max.

Calculate at experimental luminosity expected nr. ofevents for signal and background at various conditions.

SM background ∼ experiment? (YES ⇓ / NO ⇑).


Hypothesis Testing: Test StatisticLikelihood ratio: signal+background/background Q = Ls+b/Lb

Usually analysed and plotted:−2 lnQ(mH) =

2∑Nch

k=1

[

sk(mH) −∑nk

j=1 ln(

1 +sk(mH)Sk(xjk;mH)

bkBk(xjk)

)]

nk: events observed in channel k, k = 1 . . . Nch

sk(mH) and bk: signal and background events in channel k forHiggs mass mH

Sk(xjk;mH) and Bk(xjk): probability distributions for events forHiggs mass mH at test point xjk

xjk: position of event j of channel k on the plane of itsreconstructed Higgs mass and cumulative testing variableconstructed of various features of the event like b-tagging, signallikelihood, neural network output, etc.


No Higgs at LEP:MH > 114.4 GeV

10-5

10-4

10-3

10-2

10-1

1

100 102 104 106 108 110 112 114 116 118 120

mH(GeV/c2)

1-C

Lb

3σ

2σ

4σ

ALEPH

ObservedExpected signal+backgroundExpected background

10-5

10-4

10-3

10-2

10-1

1

100 102 104 106 108 110 112 114 116 118 120

mH(GeV/c2)

1-C

Lb

3σ

2σ

4σ

DLO

ObservedExpected signal+backgroundExpected background

Expected and observed signal confidence level

assuming background only

(ALEPH, DELPHI, L3 and OPAL: Phys. Lett. B 565 (2003) 61-75.)

Excess in ALEPH’s 4-jet events at 115 GeV:

ELEP2000 = 206 GeV mH(115) + mZ(91) = 206 GeV !!


LEP: exclusion by experiment


LEP: exclusion by channel


ALEPH event (e+e−→bbqq)

b quark: long lifetime ⇒ secondary vertexDezso Horváth: Search for for the Higgs Boson CCP-2013, Moscow, 21-24 August 2013 – p. 27

LEP: spaghetti diagrams

Event weightsvs. Higgs mass

for 17 selected LEPevents

The LEPCollaborations,Search for the

Standard Model HiggsBoson at LEPPhys. Lett. B

565 (2003) 61.

0

0.5

1

1.5

2

2.5

100 105 110 115 120

mH (GeV/c2)

ln(1

+s/

b)

1

2

3

5

6

8 15

11

0

0.5

1

1.5

2

2.5

100 105 110 115 120

ALEPH

0

0.5

1

1.5

2

2.5

100 105 110 115 120

mH (GeV/c2)

ln(1

+s/

b)

16

10

12

0

0.5

1

1.5

2

2.5

100 105 110 115 120

DELPHI

0

0.5

1

1.5

2

2.5

100 105 110 115 120

mH (GeV/c2)

ln(1

+s/

b)

4

9

14 17

0

0.5

1

1.5

2

2.5

100 105 110 115 120

L3

0

0.5

1

1.5

2

2.5

100 105 110 115 120

mH (GeV/c2)

ln(1

+s/

b)

7

13

0

0.5

1

1.5

2

2.5

100 105 110 115 120

OPAL


Accelerators of CERN now

LHC: Large Hadron Collider

SPS: Super Proton

Synchrotron

AD: Antiproton Decelerator

ISOLDE: Isotope Separator

On Line DEvice

PSB: Proton Synchrotron

Booster

PS: Proton Synchrotron

LINAC: LINear ACcelerator

LEIR: Low Energy Ion Ring

CNGS: Cern Neutrinos

to Gran Sasso


LHC and its main experiments


Steering magnets of LHC

1232 superconducting magnets (before installation)(L = 15 m, M = 35 t, T = 1.9 K, B = 8.3 T)


Dipole magnets of LHC in the tunnel


CMS: Compact Muon Solenoid

14000 ton digital camera:100 M pixel, 20 M pictures/sec, 1000 GB/sec data

Processes max 400 pictures/sec ⇒ intelligent filter!!Dezso Horváth: Search for for the Higgs Boson CCP-2013, Moscow, 21-24 August 2013 – p. 33

The (Compact Muon) Solenoid itself


The CMS Collaboration (2012)

179 institutions of 41 countries

3275 physicists (incl. 1535 students)

790 engineers and technicians

Participants by countries of institutes:USA: 1149, Italy: 439, Germany: 298, Russia: 234

Huge joint effort:3000 people worked on it for 20 years!


Formation of the SM Higgs bosonin p-p collisions at LHC

q H

g

g

gluon fusion

q_

q_

HW,Z

q q

vector bosonfusion


Decay of the SM Higgs boson

March 2012Not excluded by 2011

CMS data:

114 < MH < 127 GeV

(at 95% CL)

(where many decay

processes contest)

Best identified:

H → γγ

Excess observed

2 − 3σ at ∼125 GeV!

⇑Dezso Horváth: Search for for the Higgs Boson CCP-2013, Moscow, 21-24 August 2013 – p. 37

CMS: elektromagnetic calorimeteroptimized for studying H →γγ

75,848 PbWO4 single crystal scintillators


A CMS event: H → γγ candidate


4 July 2012: we have something!ATLAS and CMS, at LHC collision energies 7 and 8 TeV, intwo decay channels H → γγ and H → ZZ → ℓ+ℓ−ℓ+ℓ−,at invariant mass of m ≈ 126 GeV see a new boson at aconvincing statistical significance of 5σ conf. level each withproperties corresponding to those of the SM Higgs boson.

H → γγ ⇒ JH = 0 or 2

Data analysis was optimized for SM Higgs search...

Nevertheless, it has to be shown to be the SM Higgs, e.g.

JH = 0: H → ZZ and H →WW angular distribution ofdecay products

H → XY... cross sections follow the SM predictions

There is one Higgs boson only(no charged or more neutral ones)


CMS: H → γγ (VBF)

Vertex for measuring the γγ invariant mass:two hadron jets from vector boson fusion.


CMS: 78 identified vertices!

Many p-p collisions can be in the same event (same bunchcollision). Record: 78 identified vertices. This increases

data taking speed and makes life hard.


CMS and ATLAS: A new boson

ATLAS: 2931 authors

CMS: 2899 authors


CMS: H → γγ mass distribution

CMS Collaboration:Observation of a newboson at a mass of125 GeV with the

CMS experiment atthe LHC

Phys. Lett. B 716(2012) 30-61

text: 50%,2899 authors

in 16 pp.


ATLAS: H → γγ mass distribution

ATLAS Collaboration(2931 authors):

Observation of a new particle inthe search for the StandardModel Higgs boson with theATLAS detector at the LHC

Phys. Lett. B 716 (2012) 1–29


CMS: H → ZZ∗ → ℓ+ℓ−ℓ+ℓ−


p-valueThe probability of obtaining a test statistic at least as

extreme as the one that was actually observed, assumingthat the null hypothesis is true.

Higgs search: The probability that random fluctuation of themeasured background could give the observed excess.

Discovery:excess above 5σ

p-value:how much above


The Look Elsewhere effect

Looking for something with threshold p value p < α?If you did not find it you will look elsewhere(e.g. at different simulated Higgs-masses).

ndf (degrees of freedom) independent tests should givep = 1/n possibly leading to false discovery.

Threshold α should be increased to ndf × α

(Bonferroni correction)


CMS: p−distributions (4 July 2012)

The probability that random fluctuation of the measured background couldgive the observed excess.

γγ and ZZ: 5.0σ γγ, ZZ and WW: 5.1σ All together: 4.9σ

ATLAS got the same: γγ and ZZ: 5.0σAdding WW increased the ATLAS excess to 6.0σ


CMS, Dec. 2012: significance

Doubling 8 TeV statistics increased CMS excess to 6.9 σSharp peak, close to SM exp. at 126 GeV, far less elsewhere


CMS, March 2013: mass vs. x-sec

< MX >= 125.7 ± 0.3(stat) ± 0.3(syst)


CMS, March 2013: spin, parity

CMS data favor + parity for SX = 0CMS Physics Analysis Summary HIG-13-005


CMS: is it the SM Higgs boson?

Branching ratios of different decay channelsas compared to SM predictions for a 126 GeV Higgs boson

< σ/σSM >= 0.80 ± 0.14CMS Physics Analysis Summary HIG-13-005

ATLAS result is similar (ATLAS-CONF-2013-034):< σ/σSM >= 1.3 ± 0.13 (stat) ±0.14 (syst)


Signal strengths vs. SM expectationsCMS preliminary

results

Relative signalstrengths for variousproduction and decay

channels

68% confidence levelcontours

All agree with the SM

CMS Physics AnalysisSummary HIG-13-005,

14 March 2013


Conclusion

We very probably observed the Standard Model Higgsboson or (unfortunately, less probably) a Higgs bosonof a more general model.

The LHC will restart in 2015 with much higher energyand luminosity.

Let us hope for some deviation from the StandardModel (although none seen yet).

Thanks for your attention!


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