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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
Wigner Research Centre for Physics,
Institute for Particle and Nuclear Physics, Budapest, Hungary
& ATOMKI, Debrecen, Hungary
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – 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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 2
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 3
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)
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 4
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.Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – 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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 6
The Higgs boson of the Standard Model
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?”
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 7
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.
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 8
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...
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 9
Last 2 PHYSTAT-LHC Workshops
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 10
Statistics Committees
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 11
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.
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 12
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]
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 13
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 14
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 15
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 channelsHorváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 16
The Large Electron Positron collider
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 17
Accelerators at CERN, LEP era
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 18
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 19
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 20
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 21
Hunting the Higgs boson
Compose a complete SM background using Monte Carlo simulationtaking all types of possible events normalized to their cross-sections.
Higgs signal: simulation of all possible production and decayprocesses with all possible Higgs-boson masses
Put all these through the detector simulation to get eventsanalogous to the measured ones.
Optimize the event selection: reduce B background, enhance S
signal via maximizing e.g.NS/
√NB or NS/
√NS + NB or 2 · (
√NS + NB −
√NB)†
Calculate at experimental luminosity expected nr. of events forsignal and background at various conditions.
SM background ∼ experiment? (YES ⇓ / NO ⇑).
†Bityukov and Krasnikov, 1999
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 22
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.
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 23
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 !!
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 24
LEP: exclusion by experiment
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 25
LEP: exclusion by channel
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 26
ALEPH event (e+e−→bbqq)
b quark: long lifetime ⇒ secondary vertexHorváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – 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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 28
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 29
LHC and its main experiments
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 30
Steering magnets of LHC
1232 superconducting magnets (before installation)(L = 15 m, M = 35 t, T = 1.9 K, B = 8.3 T)
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 31
Dipole magnets of LHC in the tunnel
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 32
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!!Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 33
The (Compact Muon) Solenoid itself
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 34
The CMS Collaboration (2013)
181 institutions of 42 countries
3275 physicists (incl. 1535 students)
790 engineers and technicians
Participants by countries of institutes:USA: 1426, Italy: 545, Germany: 349, Russia: 270
Participants by nationality:USA: 861, Italy: 697, Germany: 375, Russia: 353
390 publications since 2010, the start of LHC data taking
Huge joint effort:3000 people worked on it for 20 years!
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 35
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 36
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!
⇑Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 37
CMS: elektromagnetic calorimeteroptimized for studying H →γγ
75,848 PbWO4 single crystal scintillators
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 38
A CMS event: H → γγ candidate
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 39
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)
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 40
CMS: H → γγ (VBF)
Vertex for measuring the γγ invariant mass:two hadron jets from vector boson fusion.
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 41
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.
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 42
CMS and ATLAS: A new boson
ATLAS: 2931 authors
CMS: 2899 authors
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 43
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.
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 44
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 45
CMS: H → ZZ∗ → ℓ+ℓ−ℓ+ℓ−
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 46
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 47
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 giveprobability p = 1/ndf possibly leading to false discovery.
CMS recommendation: quote 2 p-values
local (discovery place) and
global (whole region)
No such effect in exclusion
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 48
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 49
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 50
CMS, March 2013: mass vs. x-sec
< MX >= 125.7 ± 0.3(stat) ± 0.3(syst)
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 51
CMS, March 2013: spin, parity
CMS data favor + parity for SX = 0CMS Physics Analysis Summary HIG-13-005
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 52
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)
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 53
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
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 54
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!
Horváth Dezso: Higgs Boson CMS-HU, Budapest, 2013.10.14 – p. 55