# The Basic Laws of Nature: from quarks to cosmos by K2Tytb9

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```									The Higgs Boson

Jim Branson
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.
 x,t e  x,t 
i

   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.
 x,t e      i (x,t)
 x,t 
   Extra terms in Schrödinger Equation with derivatives of .
   We must make a related change in the EM potential at every point.
hc
A A       
e
   One requires the other for terms to cancel in Schrödinger equation.
   Electron’s phase symmetry requires existence of photon.
2
QuantumElectroDynamics
                                                   An A
Fn  j                                   Fn     
xn                                                  x xn
                
      ieA    m   0
 x
                   


• QED is quantum field theory (QFT) of electrons and
photons.
•   Written in terms of electron field  and photon field A.
•   Fields  and A are quantized.
   Able to create or annihilate photons with E=hn.
   Able to create or annihilate electron positron pairs.
• Gauge (phase) symmetry transformation
3
Phase (Gauge) Symmetry in QED
 x,t ei(x,t) x,t 
• 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.

4
Relativistic Quantum Field Theory
• Dirac Equation: Relativistic QM for electrons
   Matrix () eq. Includes Spin
   Negative E solutions understood as antiparticles
• Quantum Electrodynamics                                       
      ieA    m   0
   Field theory for electrons and photons    x
                   

   Rules of QFT developed and tested
   Lamb Shift
   Vacuum Polarization
   Renormalization (fixing infinities)
   Example of a “Gauge Theory”
   Very well tested to high accuracy

5
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

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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

7
2 Particles With the Same Mass...
1                      2

• 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

8
Angular Momentum and SU(2)
0 1
• Angular Momentum in QM also follows                x     
the algebra of SU(2).                                  1 0
   Spin ½ follows the simplest representation.
 0 i 
   Spin 1… also follow SU(2) algebra.            y       
• Pauli matrices are the simplest operators               i 0
that follow the algebra.                               1 0 
z       
 0 1
 x , y   2i z
         

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SU(2) Gauge Theory
n   i    n 
x,t
e
 e                  e
                    
• 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.

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1 2 3 the Standard Model
Massless vector

U(1)
(e)
(q)
 ei(x,t)                   Local gauge
transformation
boson

Bº
n                                                      SU(2) triplet of
       n     i    n 
x,t                 Local gauge     Massless vector
 e L
 e  e
bosons
SU(2)                           e
 
transformation
W  
u                                   (SU(2) rotation)       0
                                                          W 
 d L                                                      W  
      
SU(3) Octet of
u        u                   u 
i  x,t    
                  Local gauge     massless vector
          
SU(3)  u        u e          
u 
transformation       bosons
u        u                   u    (SU(3) rotation)         gº
                              
3 simplest gauge (Yang-Mills) theories                                      11
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.

 
2
V( )   2†   †        negative

QuickTime™ and a
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1  0 
 (x)=
2  v+H(x)
       
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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.

13
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.
14
40 Years of Electroweak
Broken Symmetry
• Many accurate predictions
 Gauge boson masses
 Mixing angle measured many ways

• Scalar doublet(s) break symmetry
• 40 years later we have still never seen
a “fundamental” scalar particle
 Certainly actual measurement of spin 1
and spin 1/2 led to new physics
15
SM Higgs Mass Constraints
Experiment                                      SM theory
Indirect constraints from precision EW data :   The triviality (upper) bound and
MH < 260 GeV at 95 %CL (2004)                 vacuum stability (lower) bound as
MH < 186 GeV with Run-I/II prelim. (2005)     function of the cut-off scale L
MH < 166 GeV (2006)                           (bounds beyond perturbation theory
are similar)
Direct limit from LEP: MH > 114.4 GeV

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SM Higgs production

pb   NLO Cross sections                M. Spira et al.

gg fusion

IVB fusion

17
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)
18
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.
Luminosity needed for 5  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…
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HZZ (*)4               ℓ (golden mode)

Background: ZZ, tt, llbb (“Zbb”)

Selections :
- lepton isolation in tracker and calo     HZZee 
- lepton impact parameter, , ee vertex
- mass windows MZ(*), MH                                21
HZZ4ℓ
• 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
ee                  ee

CMS
at 5 sign.                         CMS
at 5 sign.
22
HZZ4e        (pre-selection)

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HZZ4e              (selection)

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HZZ4e                 at 30          fb-1

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25
HZZ4

QuickTime™ and a                             QuickTime™ and a
TIFF (LZW) decompressor                      TIFF (LZW) decompressor
are neede d to see this picture.             are neede d to see this picture.

26
HZZ4

QuickTime™ and a
TIFF (LZW) decompressor
are neede d to see this picture.

27
HZZee

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HZZ4ℓ

29
HWW2ℓ2n In PTDR
• Dominates in narrow mass range
around 165 GeV
   Poor mass measurement
   Leptons tend to be collinear
• New elements of analysis
   PT Higgs and WW bkg. as at NLO
(re-weighted in PYTHIA)
   include box gg->WW bkg.
   NLO Wt cross section after jet veto
• Backgrounds from the data (and
theory)
   tt from the data; uncertainty 16% at 5
fb-1                                     after cuts:
   WW from the data; uncertainty 17%           - ETmiss > 50 GeV
at 5 fb-1                                   - jet veto in h < 2.4
   Wt and gg->WW bkg from theor.               - 30 <pT l max<55 GeV
uncertainty 22% and 30%                     - pT l min > 25 GeV
- 12 < mll < 40 GeV     30
Discovery reach with HWW2ℓ

31
Improvement in PTDR 4ℓ and
WW analyses (compared to
earlier analyses):

VERY SMALL

32
SM Higgs decays

WWllnn

ZZ4l

The real branching ratios!

33
HWW2ℓ2n
• 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

34
Higgs Mass Dependence

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

 WW                   fW  WW
BWW                         
 WW     ZZ   bb   fW  WW  fZ  ZZ   bb
35
Likelihood Ratio for M=160

e
Like sign
Help measure background

QuickTime™ and a
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WW background is the
most important

Has higher mass and less
lepton correlation

36
Likelihood Ratio for M=180

QuickTime™ and a
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Likelihood Ratio for M=140

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At LHC, the WW cross section increases by a factor of
10. The signal increases by a factor of 100.
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Could see Higgs over wider mass
range.

QuickTime™ and a                   QuickTime™ and a                   QuickTime™ and a
TIFF (LZW) decomp resso r          TIFF (LZW) decomp resso r          TIFF (LZW) decomp resso r
are neede d to see this picture.   are neede d to see this picture.   are neede d to see this picture.

At LHC, the WW cross section increases by a factor of
10. The signal increases by a factor of 100.
39
H
H → γγ
MH = 115 GeV
Very important
for low Higgs
masses.
80-140 GeV

Rather large
background.

Very good mass
resolution.
40
SM Higgs decays

WWllnn

ZZ4l

The real branching ratios!

41
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

42
Tracker Material Comparison

ATLAS                         CMS
CMS divides data into unconverted and converted
categories to mitigate the effect of conversions
43
r9 and Categories
signal
categories
unconverted

background

• (Sum of 9)/ESC (uncorrected)
• Selects unconverted or late converting
photons.
   Better mass resolution
   Also discriminates against jets.

44
45
Backgrounds for 1   fb -1

46
H0→ has large background
Higgs Mass Hypothesis   • To cope with the large background,
CMS measures the two isolated
signal        photons well yielding a narrow
peak in mass.
• We will therefore have a large
sample of di-photon background to
train on.
background               • Good candidate for aggressive,
discovery oriented analysis.

Di-photon Mass

47
New Isolation Variables

Not just
X
isolation
X
X
X                 Eff Sig./Eff. Bkgd

Powerful rejection of jet
background with ECAL
supercluster having ET>40.
48
ETi/Mass (Barrel)

Gluon fusion signal
VBoson fusion signal
Gamma + jet bkgd
g+j (2 real photon) bkgd
Born 2 photon bkgd
Box 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.
49
Separate Signal from Background
Use Photon Isolation and Kinematics

Background measured from sidebands            50
Understanding s/b Variation from NN
Strong peak < 1% supressed
Optimal cut at 1%

Category 0

Signal is rigorously flat;                   A factor of
b/s in 16 GeV Mass Window                       2 in s/b is
 additional factor of 10 from Mass                  like the
difference
between
Shashlik
and
crystals

1/10 of signal with
10 times better s/b
halves lumi needed
51
S/b in Categories
5
4

3

2

1

0

52
Discovery potential of H
SM

light h in MSSM
inclusive search

Significance for SM Higgs MH=130 GeV for 30 fb-1

•NN with kinematics and  isolation as input, s/b per event
•CMS result optimized at 120 GeV
53
Luminosity needed for 5  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…
54
MSSM Higgs
• Two Higgs doublets model
   5 Higgs bosons:                                 In the MSSM:
   2 Neutral scalars h,H                           Mh ≲ 135 GeV
   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
   Mhmax, gluophopic, no-mixing, small eff.

55
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
   ggbbH or bbA proportional to
tan2
   Decays to  (10%) or  (0.03%)
• Direct searches for charged
Higgs
   Decays to n or tb
• Search for Susyh (not here)
• Search for HSusy (not here)
56

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