The Higgs Boson

1
The Higgs Boson

• What it is and how to find it
• Roger Barlow
• Manchester University

2
Particle Physics the Goal

• To deduce the laws of physics using the minimum
  number of arbitrary assumptions
• "What really interests me is whether God had any
  choice in the creation of the world." --Albert
  Einstein

3
Elementary Particles (1) The electron
e-

• Known for 100 years
• Very common
• Very light mass of 9.109 10-31 kg
• Very small (pointlike?)
• Described by Quantum Mechanics. Wave function
  ?(r,t), a solution of the Schrödinger Equation
  (h2/2m)??2 ? E ?

4
(2) The photon

• ArgumentWave function ? has an arbitrary phase
• Constant change of phase ? ?ei?? does not change
  physics
• It would be nice if variable change of phase ?
  ?ei?(r) ? did not change physicsbut ?? terms
  mess up Schrödinger Equation
• Modify S.E. new term (h2/2m)?(?-ieA)2 ? E ?
• And if ? ? ei?? then A ?A(1/e) ?? (Gauge
  Transformation)
• A(r) describes another particle Gauge Boson.
  Spin 1, interacts with electron, has zero mass
  (no A2 term) the photon
• Hence electromagnetism,Maxwells Equations,Etc
  Everything predicted except the actual value of e

5
(3) The positron

• Relativity Schrödinger Equation replaced by
  Dirac Equation
• -iha.(?-ieA)???m?E ?
• is not just one complex function but 4.
• Extra components describe spin (up/down) and
  particle/antiparticle
• Antiparticle has opposite charge
• Many more processes possible
• QuantumElectroDynamics
• QED

e-
e
6
(4) The quark

• quark - like an electron (has charge, spin ½, has
  antiparticle)
• But also has an extra (triple) quantum number.
  Called colour red (1,0,0), green (0,1,0),
  blue (0,0,1)
• Needed because of the Pauli Exclusion Principle
  in particles such as the D ,
• made of 3 otherwise identical quarks.

7
(5) The gluon

• Argue the choice of red-green-blue axes
  arbitrary. Physics should not change if we switch
  around
• Or even if we rotate the axes in r-g-b space.
  Rotation matrix R
• Even if R varies with positiontime extra ? R
  terms in equations.
• Need extra function in equation with appropriate
  gauge transformation
• New massless particle
• Another Gauge Boson
• the gluon
• Similar to QED but more complicated due to matrix
  structureQuantumChromoDynamics - QCD.
• Arbitrary constant is much larger than e. Strong
  force.

8
Pause for breath

• Understand Electromagnetism and the Strong
  (nuclear) force, apart from a few arbitrary(?)
  constants. And technical details of calculations
• Thats everything except gravity and beta decay.
  Not a Theory of Everything but a Theory of
  quite a lot
• Cant do gravity. But should manage beta decay

9
Beta decay as it ought to be

• n?p e- ? d?u e- ?
• Quarks in protons/neutrons/nuclei are in two
  flavours u and d. (Different charges and
  masses)
• u and d are two states of the same fundamental
  entity - the quark
• e and ? are two states of the same fundamental
  entity the lepton
• (Weak) isospin up or down.
• Run gauge theory argument again for up-down
  predicts Gauge Bosons W, W0, W-

e
W-
n
d
u
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Slight(?) problem

• Gauge Bosons have got to be massless. Or the
  Gauge Invariance of the equations breaks down.
• Photons?
• Gluons ?
• The W bosons ?
• They exist alright but have masses 80 GeV.
• Theory stuck here for some time
• Mass The minimum energy needed to create a
  particle

11
The Higgs Field

• Suppose there is a field called H(r,t) that
  interacts with the electron, quark, W etc
• OK, why not
• Suppose that the lowest-energy stats is not
  H(r,t)0 but H(r,t)V
• Seriously weird

12
Masses that are not masses

• As a W propagates through space and time, it
  interacts with this nonzero Higgs field
• Which gives it an energy.
• Even if it has no kinetic or potential energy
• Which means it has, to all intents and purposes,
  a mass. Without breaking gauge invariance
• Happens to quarks and leptons too

13
The Standard Model

• Quarks and Leptons (x3 generations)
• Gauge Symmetries for the Weak, Strong and EM
  force
• Higgs mechanism giving masses to the W bosons
• Also mixing/unifying Weak and EM forces
• Also explains weak decays between generations
  (with a few more parameters)

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Is the Standard Model true?

• No!
• Does not predict quark and lepton masses
• Or coupling constants
• 28 free parameters altogether
• Or why there are 3 generations
• Or why there is parity violation
• Higgs is an ad-hoc addition

• Yes!
• Predicts W/Z mass ratio
• Predicts cross sections and branching ratios in
  many many particle decays
• Accounts for parity violation
• Accounts for CP violation in K and B sectors
• No experimental results in disagreement

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Testing Higgs from field to particle
Higgsness
H?

• Quantum excitations of the H field are H
  particles
• (Same as any particle, though usually about 0)
• The Higgs coupling of any particle is
  proportional to its mass.
• (actually the other way round)
• H is best made by massive particles
• H will decay to the heaviest allowed particles

16
Is the Higgs true?
?

• Probably not its a very arbitrary kludge
• Many alternative theories have been proposed that
  are more elegant/beautiful/natural
• All have very similar effects until you get to
  high (TeV) energies

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First Attempt LEP
q

Collide electrons and positrons at energies of
200 GeV
e
Z
?q
Z
b
H
e-
?b
18
Saw some events, but..
Consistent with background MHgt114 GeV
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Second Attempt the LHC

• Proton proton collisions at 14 TeV
• Start operation next year

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Experiments ATLAS and CMS

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Common features

• Tracking
• Magnetic Field
• Measure charged particle tracks with drift
  chambers or Silicon
• Curvature gives momentum
• Calorimetry
• Material so Neutral particles interact
• Measure total energy by scintillator etc
• Muon detection
• Muons get through the calorimeter

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Looking for signals

Decay depends on MH Plots shows signal if MH
fairly large Smaller values more difficult
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Handling the data

• Collision rate 40 MHz
• Several events/collision
• Each event gives massive amount of data
• Massive data stream. gt10 TB/y
• Tiny number of interesting events

Handled by Grid of computers all over Europe -
and the world 10,000 CPUs
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Third Attempt the ILC

• Electron positron collisions at 1 TeV
• Still at the design stage

Straight (not circular) Chicago? Japan?? 38 km?
6Bn? Start 2015?
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Why?
LHC

• LHC is a proton-proton collider
• Protons are made of quarks
• LHC is actually a quark-quark collider
• Quarks share proton energy in a random way

7 TeV
7 TeV

• A 14 TeV proton-proton collision gives a whole
  spectrum of energies for quark-quark collisions
• And the unused energy appears as background
  particles

Exploration
ILC
500 GeV
500 GeV
1 TeV
Precision measurements
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The Future

• LHC will start next year
• First serious data 2008
• Interesting results 2-3 years? after that
• Should find Higgs - probably not quite as
  expected
• Other new particles/new effects predicted by
  speculative models (SUSY? GUTs?)
• Exploration will be followed by precision
  measurements at the ILC
• Build Beyond the Standard Model theory with fewer
  arbitrary parameters
• Understand the universe we live in a little bit
  better