The Higgs Boson

Jim Branson

2

Phase (gauge) Symmetry in QM• Even in NR Quantum Mechanics, phase symmetry requires

a vector potential with gauge transformation. Schrödinger Equation invariant under global change of the phase

of the wavefunction.

There is a bigger symmetry: local change of phase of wfn. We can change the phase of the wave function by a different

amount at every point in space-time.

Extra terms in Schrödinger Equation with derivatives of λ. We must make a related change in the EM potential at every point.

One requires the other for terms to cancel in Schrödinger equation. Electron’s phase symmetry requires existence of photon.

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3

QuantumElectroDynamics

• QED is quantum field theory (QFT) of electrons andphotons.

• Written in terms of electron field ψ and photon field Aµ.• Fields ψ and Aµ are quantized.

Able to create or annihilate photons with E=hν. Able to create or annihilate electron positron pairs.

• Gauge (phase) symmetry transformation

xjFµ!

!

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4

Phase (Gauge) Symmetry in QED

• Phase symmetry in electron wavefunction corresponds togauge symmetry in vector potential. One requires the other for terms to cancel in Schrödinger equation. Electron’s phase symmetry requires existence of photon.

• The theory can be defined from the gauge symmetry.• Gauge symmetry assures charge is conserved and that

photon remains massless.

! !

x,t( )"ei#(!x ,t)! !

x,t( )

5

Relativistic Quantum Field Theory• Dirac Equation: Relativistic QM for electrons

Matrix (γ) eq. Includes Spin Negative E solutions understood as antiparticles

• Quantum Electrodynamics Field theory for electrons and photons Rules of QFT developed and tested

Lamb Shift Vacuum Polarization

Renormalization (fixing infinities) Example of a “Gauge Theory” Very well tested to high accuracy

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6

Strong and Weak Interactionswere thought not to be QFT

• No sensible QFT found for Strong Interaction;particles were not points… Solved around 1970 with quarks and Negative β function which gave

Confinement Decreasing coupling constant with energy

• Weak Interaction was point interaction Massive vector boson theory NOT renormalizable Goldstone Theorem seemed to rule out broken

symmetry. Discovery of Neutral Currents helped

7

Higgs Mechanism Solves theproblem

• Around 1970, WS used the mechanism ofHiggs (and Kibble) to have spontaneoussymmetry breaking which gives massivebosons in a renormalizable theory.

• QFT was reborn

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2 Particles With the Same Mass...

• Imagine 2 types of electrons with the same mass, spin,charge…, everything the same.

• The laws of physics would not change if we replacedelectrons of type 1 with electrons of type 2.

• We can choose any linear combination of electrons 1 and2. This is called a global SU(2) symmetry. (spin also hasan SU(2) sym.)

• What is a local SU(2) symmetry? Different Lin. Comb. At each space-time point

11 22

9

Angular Momentum and SU(2)

• Angular Momentum in QM also followsthe algebra of SU(2). Spin ½ follows the simplest representation. Spin 1… also follow SU(2) algebra.

• Pauli matrices are the simplest operatorsthat follow the algebra.

0 1

1 0

0

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1 0

0 1

, 2

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z

x y z

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10

SU(2) Gauge Theory

• The electron and neutrino are massless and have the sameproperties (in the beginning).

• Exponential (2X2 matrix) operates on state giving a linearcombination which depends on x and t.

• To cancel the terms in the Schrödinger equation, we mustadd 3 massless vector bosons, W.

• The “charge” of this interaction is weak isospin which isconserved.

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11

1 2 3 the Standard Model

SU(3)

SU(2)

U(1)(e)(q)

SU(3) Octet ofmassless vector

bosons

gº

Local gaugetransformation

(SU(3) rotation)

SU(2) triplet ofMassless vector

bosonsLocal gauge

transformation(SU(2) rotation)

Massless vectorboson

BºLocal gauge

transformation

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3 simplest gauge (Yang-Mills) theories

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Higgs Potential• I symmetric in SU(2) but minimum energy

is for non-zero vev and some direction ispicked, breaking symmetry.

• Goldstone boson (massless rolling mode) iseaten by vector bosons.

V (!) = µ2!!† + " !!†( )

2

µ negative

!(x)= 1

2

0

v+H(x)

"#$

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13

The Higgs

• Makes our QFT of the weak interactionsrenormalizable.

• Takes on a VEV and causes the vacuum to enter a‘‘superconducting’’ phase.

• Generates the mass term for all particles.• Is the only missing particle and the only fundamental

scalar in the SM.• Should generate a cosmological constant large

enough to make the universe the size of a football.

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Higgs Mrchanism Predictions

• W boson has known gauge couplings to Higgs somasses are predicted.

• Fermions have unknown couplings to the Higgs.We determine the couplings from the fermion mass.

• B0 and W0 mix to give A0 and Z0.• Three Higgs fields are ‘‘eaten’’ by the vector

bosons to make longitudinal massive vector boson.• Mass of W, mass of Z, and vector couplings of all

fermions can be checked against predictions.

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40 Years of ElectroweakBroken Symmetry

• Many accurate predictionsGauge boson massesMixing angle measured many ways

• Scalar doublet(s) break symmetry• 40 years later we have still never seen

a “fundamental” scalar particleCertainly actual measurement of spin 1

and spin 1/2 led to new physics

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SM Higgs Mass ConstraintsSM Higgs Mass Constraints

Indirect constraints from precision EW data : MH < 260 GeV at 95 %CL (2004) MH < 186 GeV with Run-I/II prelim. (2005) MH < 166 GeV (2006)

ExperimentExperiment SM theorySM theory

The triviality (upper) bound andvacuum stability (lower) bound asfunction of the cut-off scale Λ(bounds beyond perturbation theoryare similar)Direct limit from LEP: MH > 114.4 GeV

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SM Higgs production

NLO Cross sections M. Spira et al.

gg fusion

IVB fusion

pb

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SM Higgs decays

When WW channelopens up pronounceddip in the ZZ BR

For very large mass the width of the Higgs boson becomes very large(ΓH >200 GeV for MH ≳ 700 GeV)

CMS PTDR contains studies of Higgs detection atL=2x1033cm-2s-1

CERN/LHCC 2006-001 CERN/LHCC 2006-021

Many full simulation studies with systematic error analysis.

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Luminosity needed for 5 σ discovery

Discover SMHiggs with 10 fb-1

Higgs Evidence orexclusion as earlyas 1 fb-1

(yikes)

2008-2009 ifaccelerator anddetectors work…

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HH→→ZZZZ(*)(*)→→44ℓ (golden mode) (golden mode)

Background: ZZ, tt, Background: ZZ, tt, llllbb bb ((““ZbbZbb””))

Selections :Selections :-- lepton isolation in tracker and lepton isolation in tracker and calocalo-- lepton impact parameter, lepton impact parameter, µµµµ, , ee ee vertexvertex-- mass windows M mass windows MZ(*)Z(*), M, MHH

H→ZZ→ee µµ

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HH→→ZZZZ→→44ℓ

eeµµ

CMSCMSat 5at 5σσ sign. sign.

eeµµ

CMSCMSat 5at 5σσ sign. sign.

• Irreducible background: ZZ production• Reducible backgrounds: tt and Zbb small afterselection

• ZZ background: NLO k factor depends on m4l• Very good mass resolution ~1%• Background can be measured from sidebands

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HH→→ZZZZ→→44e (pre-selection)

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HH→→ZZZZ→→44e (selection)

25

HH→→ZZZZ→→44e at 30 fb-1

26

HH→→ZZZZ→→44µµ

27

HH→→ZZZZ→→44µµ

28

HH→→ZZZZ→→eeeeµµµµ

29

HH→→ZZZZ→→44ℓ

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HH→→WWWW→→22ℓ22νν•• Dominates in narrow mass rangeDominates in narrow mass range

around 165 GeVaround 165 GeV Poor mass measurementPoor mass measurement Leptons tend to be collinearLeptons tend to be collinear

•• New elements of analysisNew elements of analysis PPTT Higgs and WW Higgs and WW bkgbkg. as at NLO. as at NLO

(re-weighted in PYTHIA)(re-weighted in PYTHIA) include box gg->WW include box gg->WW bkgbkg.. NLO Wt cross section after jet vetoNLO Wt cross section after jet veto

•• Backgrounds from the data (andBackgrounds from the data (andtheory)theory) tt from the data; uncertainty 16% at 5tt from the data; uncertainty 16% at 5

fbfb-1-1

WW from the data; uncertainty 17%WW from the data; uncertainty 17%at 5 fbat 5 fb-1-1

Wt and gg->WW Wt and gg->WW bkg bkg from from theortheor..uncertainty 22% and 30%uncertainty 22% and 30%

after cuts: - ET

miss > 50 GeV - jet veto in η < 2.4 - 30 <pT

l max<55 GeV - pT l min > 25 GeV - 12 < mll < 40 GeV

31

HH→→WWWW→→22ℓ22νν

• UCSD group at CDF has done a goodanalysis of this channel. Far more detailed than the CMS study

• Eliot thinks that it will be powerful below160 GeV because the background from WWdrops more than the signal does!

32

Discovery reach with HDiscovery reach with H→→WWWW→→22ℓ

33

Improvement in PTDR 4ℓ andWW analyses (compared to

earlier analyses):

VERY SMALL

34

Inclusive H→→γγ

H → γγMH = 115 GeVVery important

for low Higgsmasses.

Rather largebackground.

Very good massresolution.

35

H→ γγ• Sigma x BR ~90 fb for MH = 110-130 GeV

• Large irreducible backgrounds from gg→ γγ, qq → γγ, pp → γjet → γγ jet

• Reducible background from fake photons from jets and isolated π0

(isolation requirements)• Very good mass resolution ~1%• Background rate and characteristics well measured from sidebands• Vertex estimated from the underlying event and recoiling jet

36

Backgrounds for 1 fb-1

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Separate Signal from Background

Background measured from sidebands

Use Photon Isolation and Kinematics

38

Discovery potential of H→→γγ

SMSM

light hlight h→→γγγγ in MSSMin MSSMinclusive searchinclusive search

8.7 8.7

New, NLONew, NLOlikelihoodlikelihood

6.3 6.3

New, NLONew, NLOCut basedCut based

3.9 3.9

TDR (LO)TDR (LO)

ATLASATLAS NLO NLOoptimized*optimized*

NLO NLOcut basedcut based

NLO NLOcount. expcount. exp

8.2 8.2 6.0 6.0~ 7.5~ 7.5

CMS PTDR CMS PTDR CMS CMSECAL TDRECAL TDR

Significance for SM Higgs MSignificance for SM Higgs MHH=130 GeV for 30 fb=130 GeV for 30 fb-1-1

••NN with kinematics and NN with kinematics and γγ isolation as input, isolation as input, s/b s/b per eventper event••CMS resultCMS result optimized at 120 GeVoptimized at 120 GeV

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forwardjets

Higgsdecayproducts

VB Fusion qqH (low mass H)

Tagging jets from qqare at high rapidityand large Δη

• Background is highly reducedby tagging the two forward

jets requiring low activity in the

central detector• Signal to BG ratio is increased

reducing the effect of BGuncertainty

qqH → qqγγMH = 120GeV

ATLAS

40

Luminosity needed for 5 σ discovery

Discover SMHiggs with 10 fb-1

Higgs Evidence orexclusion as earlyas 1 fb-1

(yikes)

2008-2009 ifaccelerator anddetectors work…

41

Higgs Mass and Width

42

MSSM Higgs• Two Higgs doublets model

5 Higgs bosons: 2 Neutral scalars h,H 1 Neutral pseudo-scalar A 2 Charged scalars H±

• In the Higgs sector, all masses and couplings are determinedby two independent parameters (at tree level)

• Most common choice: tanβ – ratio of vacuum expectation values of the two doublets MA – mass of pseudo-scalar Higgs boson

• New SUSY scenarios Mh

max, gluophopic, no-mixing, small αeff.

In the MSSM:Mh ≲ 135 GeV

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MSSM Search Strategies• Apply SM searches with

rescaled cross sections andbranching ratios. Mainly h searches when it is SM-

like.• Direct searches for H or A

gg→bbH or bbA proportional totan2β

Decays to ττ (10%) or µµ (0.03%)• Direct searches for charged

Higgs Decays to τν or tb

• Search for Susy→h (not here)• Search for H→Susy (not here)