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

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 . 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.

ψ rx,t( )→ ei( rx,t)ψ rx,t( )

ψ rx,t( )→ eiψ rx,t( )

Aur→ A

ur−

hce

∇ur

3

QuantumElectroDynamics

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

• Written in terms of electron field ψ and photon field A.

• Fields ψ and A are quantized. Able to create or annihilate photons with E=h. Able to create or annihilate electron positron pairs.

• Gauge (phase) symmetry transformation

xjF

∂=

∂AA

Fx x

∂∂= −∂ ∂

∂∂x

+ ieA

⎛

⎝⎜

⎞

⎠⎟γ +m

⎡

⎣⎢⎢

⎤

⎦⎥⎥Ψ=0

4

Phase (Gauge) Symmetry in QED

• Phase symmetry in electron wavefunction corresponds to gauge 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.

ψ rx,t( )→ ei( rx,t)ψ rx,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

∂∂x

+ ieA

⎛

⎝⎜

⎞

⎠⎟γ +m

⎡

⎣⎢⎢

⎤

⎦⎥⎥Ψ=0

6

Strong and Weak Interactions were thought not to be QFT

• No sensible QFT found for Strong Interaction; particles were not points… Solved around 1970 with quarks and Negative 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 the problem

• Around 1970, WS used the mechanism of Higgs (and Kibble) to have spontaneous symmetry breaking which gives massive bosons in a renormalizable theory.

• QFT was reborn

8

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 replaced electrons of type 1 with electrons of type 2.

• We can choose any linear combination of electrons 1 and 2. This is called a global SU(2) symmetry. (spin also has an 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 follows the algebra of SU(2). Spin ½ follows the simplest representation. Spin 1… also follow SU(2) algebra.

• Pauli matrices are the simplest operators that follow the algebra.

0 1

1 0

0

0

1 0

0 1

, 2

x

y

z

x y z

i

i

i

σ

σ

σ

σ σ σ

⎛ ⎞=⎜ ⎟

⎝ ⎠−⎛ ⎞

=⎜ ⎟⎝ ⎠

⎛ ⎞=⎜ ⎟−⎝ ⎠

⎡ ⎤=⎣ ⎦

10

SU(2) Gauge Theory

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

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

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

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

e

⎛

⎝⎜⎞

⎠⎟→ ei

rε x,t( )grσ

e

⎛

⎝⎜⎞

⎠⎟

11

1 2 3 the Standard Model

U(1)(e)

(q)Local gauge

transformation

Massless vector boson

Bº

SU(2)Local gauge

transformation

(SU(2) rotation)

SU(2) triplet of Massless vector

bosons

SU(3)Local gauge

transformation

(SU(3) rotation)

SU(3) Octet of massless vector

bosons

gº

Le

⎛ ⎞⎜ ⎟⎝ ⎠

L

u

d

⎛ ⎞⎜ ⎟⎝ ⎠

0

W

W

W

+

−

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

u

u

u

⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠

,u u

u

u u

u

i x te

α ⎛ ⎞⎜ ⎟⎝ ⎠

⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠

−→

rr g

e

⎛

⎝⎜⎞

⎠⎟→ ei

rε x,t( )grσ

e

⎛

⎝⎜⎞

⎠⎟

ψ → ei( rx,t)ψ

3 simplest gauge (Yang-Mills) theories

12

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

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

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

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

V (φ) =2φφ† + φφ†( )

2 negative

ϕ (x)= 1

2

0

v+H(x)

⎛⎝⎜

⎞⎠⎟

13

The Higgs

• Makes our QFT of the weak interactions renormalizable.

• 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.

14

Higgs Mrchanism Predictions

• W boson has known gauge couplings to Higgs so masses 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.

15

40 Years of Electroweak Broken 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

16

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 (bounds beyond perturbation theory are similar) Direct limit from LEP: MH > 114.4 GeV

17

SM Higgs production

NLO Cross sections M. Spira et al.

gg fusion

IVB fusion

pb

18

SM Higgs decays

When WW channel opens up pronounced dip 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 at L=2x1033cm-2s-1

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

Many full simulation studies with systematic error analysis.

20

Luminosity needed for 5 σ discovery

Discover SM Higgs with 10 fb-1

Higgs Evidence or exclusion as early as 1 fb-1

(yikes)

2008-2009 if accelerator and detectors work…

21

HHZZZZ(*)(*)44ℓ (golden mode) (golden mode)

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

Selections :Selections :- lepton isolation in tracker and calolepton isolation in tracker and calolepton impact parameter, lepton impact parameter, , ee vertex , ee vertex - mass windows Mmass windows MZ(*)Z(*), M, MHH

HZZee

22

HHZZZZ44ℓ

ee

CMSCMSat 5at 5σσ sign. sign.

ee

CMSCMSat 5at 5σσ sign. sign.

• Irreducible background: ZZ production

• Reducible backgrounds: tt and Zbb small after selection

• ZZ background: NLO k factor depends on m4l

• Very good mass resolution ~1%• Background can be measured from sidebands

23

HHZZZZ44e (pre-selection)

QuickTime™ and aTIFF (LZW) decompressor


24

HHZZZZ44e (selection)



25

HHZZZZ44e at 30 fb-1



26

HHZZZZ44





27

HHZZZZ44



28

HHZZZZeeee



29

HHZZZZ44ℓ

30

HHWWWW22ℓ22 In PTDR In PTDR • Dominates in narrow mass range Dominates 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 bkg. as at NLO Higgs and WW bkg. as at NLO

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

• Backgrounds from the data (and Backgrounds from the data (and theory)theory) tt from the data; uncertainty 16% at 5 tt 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 bkg from theor. Wt and gg->WW bkg from theor. uncertainty 22% and 30%uncertainty 22% and 30%

after cuts: - ET

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

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

31

Discovery reach with HDiscovery reach with HWWWW22ℓ

32

Improvement in PTDR 4ℓ and WW analyses (compared to

earlier analyses):

VERY SMALL

33

SM Higgs decays

The real branching ratios!

ZZ4l

WWll

34

HHWWWW22ℓ22

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

• Eliot thinks that it will be powerful below 160 GeV because the background from WW drops more rapidly (in mWW) than the signal does! But you need to estimate mWW

35

Higgs Mass Dependence

BWW =ΓWW

ΓWW + ΓZZ + Γbb

→fWΓWW

fWΓWW + fZΓZZ + Γbb

If ΓWW is large compared to the other modes, the branching ratio doesn’t fall as fast as the continuum production of WW.

36

Likelihood Ratio for M=160



eLike signHelp measure background

WW background is the most important

Has higher mass and less lepton correlation

37




38




At LHC, the WW cross section increases by a factor of 10. The signal increases by a factor of 100.

39

Could see Higgs over wider mass range.







At LHC, the WW cross section increases by a factor of 10. The signal increases by a factor of 100.

40

Hγγ

H → γγ MH = 115 GeVVery important

for low Higgs masses.80-140 GeV

Rather large background.

Very good mass resolution.

41

SM Higgs decays

The real branching ratios!

ZZ4l

WWll

42

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

• Large irreducible backgrounds from gg→ γγ, qq → γγ, gq

→ γ jet → 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

43

Tracker Material Comparison

ATLAS CMS

CMS divides data into unconverted and converted categories to mitigate the effect of conversions

44

r9 and Categories

• (Sum of 9)/ESC (uncorrected)• Selects unconverted or late converting

photons. Better mass resolution Also discriminates against jets.

signal

unconverted

background

categories

45

46

Backgrounds for 1 fb-1

47

H0→γγ has large background• To cope with the large background,

CMS measures the two isolated photons well yielding a narrow peak in mass.

• We will therefore have a large sample of di-photon background to train on.

• Good candidate for aggressive, discovery oriented analysis.

Di-photon Mass

background

signal

Higgs Mass Hypothesis

48

New Isolation Variables

XX

XX

Not just isolation

Eff Sig./Eff. Bkgd

Powerful rejection of jet background with ECAL

supercluster having ET>40.

49

ETi/Mass (Barrel)

Gluon fusion signalVBoson fusion signalGamma + jet bkgdg+j (2 real photon) bkgdBorn 2 photon bkgdBox 2 photon bkgd

Signal photons are at higher ET.• since signal has higher di-photon ET• and background favors longitudinal momentum

Some are in a low background region.

50

Separate Signal from Background

Background measured from sidebands

Use Photon Isolation and Kinematics

51

Understanding s/b Variation from NN

Category 0

Signal is rigorously flat;b/s in 16 GeV Mass Window

additional factor of 10 from Mass

Strong peak < 1% supressedOptimal cut at 1%

A factor of 2 in s/b is like the difference between Shashlik

and crystals

1/10 of signal with 10 times better s/b halves lumi needed

52

0

1

2

3

45

S/b in Categories

53

Discovery potential of Hγγ

SMSM

light hlight hγγγγ in MSSM in MSSMinclusive searchinclusive search

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, s/b per event isolation as input, s/b per event•CMS result optimized at 120 GeVCMS result optimized at 120 GeV

54

Luminosity needed for 5 σ discovery

Discover SM Higgs with 10 fb-1

Higgs Evidence or exclusion as early as 1 fb-1

(yikes)

2008-2009 if accelerator and detectors work…

55

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 determined by 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

56

MSSM Search Strategies• Apply SM searches with

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

like.

• Direct searches for H or A ggbbH or bbA proportional to

tan2 Decays to (10%) or (0.03%)

• Direct searches for charged Higgs Decays to or tb

• Search for Susyh (not here)• Search for HSusy (not here)

Documents

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