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Particle Physics 2. Prof. Glenn Patrick . Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013. Last Week - Recap. Particle Physics & Cosmology Matter Particles, Generations Spin – Fermions & Bosons Charged Leptons Antimatter Neutral Leptons - Neutrinos

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Particle physics 2

Particle Physics 2

Prof. Glenn Patrick

Quantum, Atomic and Nuclear Physics, Year 2

University of Portsmouth, 2012 - 2013


Last week recap

Last Week - Recap

Particle Physics & Cosmology

Matter Particles, Generations

Spin – Fermions & Bosons

Charged Leptons

Antimatter

Neutral Leptons - Neutrinos

Hadrons

Strange Particles and Strangeness

Symmetries, Conservation Laws

Quantum Numbers, Isospin

Eightfold Way and Quark Model

Charm, Bottom, Top, Quark Counting


Today s plan

Today’s Plan

20 November Particle Physics 2

Force Carriers

Four Fundamental Interactions

Quantum Field Theory

Feynman Diagrams

Higher Orders/Radiative Corrections

Anomalous magnetic moment of muon

Charged and Neutral Currents

Z and W Vector Bosons

Gluons

Colour Charge and Quantum Chromodynamics (QCD)

Unification of Fundamental Forces,

Running Coupling Constants

Higgs Boson and Field

Copies of Lectures:http://hepwww.rl.ac.uk/gpatrick/portsmouth/courses.htm

BOOKS

B.R. Martin & G. Shaw, Particle Physics, 3rd Edition, Wiley

Donald H. Perkins, Introduction to High Energy Physics, 4th edition, CUP

Coughlan et al, The Ideas of Particle Physics, Cambridge


Particle physics 2

I

II

III

Observed in

2000


Force carriers

Force Carriers

Last week we looked at the Matter Particles (quarks and leptons).

This week we look at the four gauge bosons that make up the Force Particles.

Now the smallest Particles of Matter may cohere by strongest Attractions, and compose bigger Particles of weaker Virtue.

There are therefore Agents in Nature able to make Particles of Bodies stick together by very strong Attractions. And it is the business of experimental Philosophy to find them out.

ISAAC NEWTON (1680)


The four forces of nature

The Four Forces of Nature

STRONG

ELECTRO -

MAGNETIC

WEAK

GRAVITY


Forces in classical physics

Forces in Classical Physics

Classically, forces are described by charges and fields

Field is a physical quantity which has a value for each point in space-time.

Can be a scalar or vector field.


Quantum field theory

Quantum Field Theory

Forces are transmitted by exchange of force particles between matter particles.

4 forces with different force particles.

Quantum Mechanics + Relativity

Heisenberg

Uncertainty Principle

Energy ΔE is “borrowed for a time Δt

Maximum distance of exchange particle

Photon has zero mass,

so infinite range

If we associate M with the pion mass, we get the Yukawa potential that we saw when we talked about the “nuclear force” in Nuclear Physics 1.


Four forces of nature

Four Forces of Nature

STRONG FORCE

Strength: 1, Range: 10-15 m

Exchange: Gluon

ELECTROMAGNETIC FORCE

Strength: 1/137, Range: Infinite

Exchange: Photon

A FIFTH FORCE?

GRAVITY

Strength: 6x10-39 m,

Range: Infinite, Exchange: ?

WEAK FORCE

Strength: 10-6 m, Range: 10-18 m

Exchange: W±, Z0

Modified gravity?

Dark matter,

Dark energy, etc.


Fundamental interactions

Fundamental Interactions

u

u

e-

e-

gluon

Z0

d

d

e-

e-

Strong

Weak

EM

e

e

e-

e-

e-

W-

d

n

Weak

d

e

u

u

p

d

u


Feynman diagrams

Feynman Diagrams

electron

At each ‘vertex’ charge is conserved. Heisenberg Uncertainty Principle allows energy borrowing.

Virtual Particle

Does not have mass of a physical particle.

Known as “off –mass shell”

(e.g. not zero for photon)

Richard Feynman

Quantum Electrodynamics (QED)

positron

(anti-electron)


Feynman diagrams1

Feynman Diagrams

Exchange

Annihilation

  • External legs represent amplitudesof initial and final state particles.

  • Positron is drawn as electron travelling backwards in time.

  • Internal lines (propagators) represent amplitude of exchanged particle.

  • Charge, baryon number and lepton number conserved at each vertex. Quark flavour conserved for strong and EM interactions.

  • Vertices represent coupling strength of interacting particles.

  • Perturbation theory. Expand and keep the most important terms for calculations.


Feynman diagrams2

Feynman Diagrams

Associate each vertex with the square root of the appropriate

coupling constant, i.e. .

When the amplitude is squared to yield a cross-section

there will be a factor ,

where n is the number of vertices (known as the “order” of the diagram).

For QED:

Lowest order

Second order

Add the amplitudes from all possible diagrams to get the total amplitude, M, for a process  transition probability.

Fermi’s Golden Rule


Bhabha scattering

Bhabha Scattering

e-

e-

e-

e-

Z0

e+

e+

e+

e+

e-

e-

e-

e-

Z0

e+

e+

e+

e+

4 Born Diagrams (Electroweak)

+

Amplitude =

+

+


Radiative corrections

Radiative Corrections

Vacuum polarisation

Higher Order Quantum Loop Diagrams (QED only)


Anomalous magnetic moment of the muon

Anomalous Magnetic Moment of the Muon

+

e

QED

-

e

B

µ

µ

0

Z

µ

µ

WEAK

W

W

µ

+

e

+

e

+

e

-

e

-

-

e

e

3rd order corrections

Dirac theory predicts g=2, but this is modified

by quantum fluctuations.

+ STRONG

Radiation and re-absorption of virtual photons contributes an anomalous magnetic moment.

Lowest order correction

~3.6σ effect

New Physics?

Hundreds of diagrams!


Muon g 2 testing the standard model

Muon g-2: Testing the Standard Model

Experimental

measurements of aμ

Beyond the

Standard Model (BSM) Physics?

Uncertainty on aμ and physics reach as the uncertainty has decreased.

J.P. Miller et al,

Ann. Rev. Nucl. Part. Sci., 62 (Nov. 2012), 237


Photon em boson

Photon – EM Boson

Quantum energy of photon

h = Planck’s constant

 = frequency

1900Planck Black Body Radiation explained in terms of light quanta

 Nobel Prize.

1905Einstein explained the

Photoelectric Effectin terms of quanta of energy

 Nobel Prize.

1925G.N. Lewisproposed the name Photon for quanta of light.

1925Compton showed quantum (particle) nature of X-rays

 Nobel Prize.


Charged and neutral currents

Charged and Neutral Currents







-

W+

Z0

X

X

N

N

Neutral Current

Charged Current


Discovery of weak neutral currents 1973

Discovery of Weak Neutral Currents (1973)

Bremsstrahlung effects

electron



Gargamelle Bubble Chamber


Z and w story

Z and W Story

Carlo Rubbia (UA1)

Simon van der Meer

Two Experiments:

UA1 and UA2.

Rubbia came up with idea and led UA1.

Super Proton Synchrotron turned into proton-antiproton collider. Stochastic cooling technique.

1984

UA1

UA2


W boson discovery ua1 1982

W Boson Discovery – UA1 (1982)

“Missing Energy” = neutrino

electron


Z boson discovery ua1 1983

Z Boson Discovery – UA1 (1983)

electron

positron


Weak charged current and quarks

Weak Charged Current and Quarks

t

b

u

d

c

s

W

W

W

W-

d

n

d

e

u

u

d

p

u

Flavour Changing Charged Currents.

Quark flavour never changes except by weak interactions that involve W± bosons.

In decay processes,

quark always decays to

lighter quark to conserve energy.

t  b  c  s  u  d

+ ..

 decay finally understood!

Weak charged current changes lepton and quark flavours.

Possible that flavour changing neutral currents exist beyond (tree level) Standard Model.


Gluon discovery 1979

Gluon Discovery (1979)

PETRA e+e- Collider, DESY, Hamburg

JADE, TASSO, MARK-J, PLUTO

Third jet produced by

gluon bremsstrahlung

3-Jet Event

quark

anti-quark

gluon


Inside the proton

Inside the Proton

There are 3 “valence”quarks

inside the proton bound together

by gluons.

Quantum theory allows quarks to

change into quark-antiquark pairs

for a short time.

There is a bubbling “sea” of gluons,

quarks and antiquarks.

There is however a problem with the basic quark model…..


C o l our charge

Colour Charge

Some particles apparently contain quarks in the same state

violates Pauli Exclusion Principle(e.g. ++ = uuu).

Proposed that quarks carry an extra quantum number

called “colour”.

Green

Blue

Red

Quarks

Cyan

Magenta

Yellow

Anti-quarks

All physical particles are colour neutral or “white”.

baryon

meson


Quark species

Quark Species

u

u

u

d

d

d

c

c

c

charm

top

t

t

t

b

b

b

bottom

quarks

antiquarks

up

down

strange

s

s

s


8 interacting gluons

8 Interacting Gluons

Expect 9 gluons from all combinations (3 colours x 3 anti-colours):

rb,rg, gr,gb,bg,br,rr,gg,bb

However, real gluons are a linear combinations of states.

This combination is colourless and symmetric.

Does not take part in the strong interaction.

Hence, we have 8 gluons. These two plus those from , , , , ,


Counting colours

Counting Colours

In Particle Physics 1, we counted quarks. Can also count colours using R.

below top energy threshold


Quantum c h r omodynamics qcd

Quantum Chromodynamics (QCD)

Gluons carry colour+anti-colour

charge, e.g. red-anti blue.

Colour charge always conserved

so quarks can change colour when

emitting a gluon.

Quantum Chromodynamics (QCD)is the theory of the

Strong Interaction in the Standard Model.

Since gluons (8) carry colour charge,

they can interact with one another!

Fragmentation

If a quark is pulled from a neighbour,

the colour field “stretches”.

At some point, it is easier for the field to snap into two new quarks.


Confinement

Confinement

Confinement

Confinement is a property of the strong force.

The strong force works by gluon exchange,

but at “large” distance the self-interaction of the gluons

breaks the inverse square-law forming “flux tubes”:

Quarks and gluons carry “colour “ quantum numbers

analogous to electric charge –

but only “colourless” objects like baryons (3-quark states)

and mesons (quark-antiquark states) escape confinement.


Quark interactions

Quark Interactions

Only one pair of quarks interact, the rest are spectators.


Residual forces

Residual Forces

How do molecules form if

atoms are electrically neutral?

How do protons bind to form

the nucleus? Protons & neutrons

are colour neutral.

Residual EM Force

Electrons in one atom are attracted to protons in another atom.

Residual Strong Interaction

between quarks in different protons overcomes EM

repulsion.


Force particles

Force Particles

Bosons = Spin 1

ForceParticle Charge Mass Relative Range

(GeV) Strength (m)

Stronggluon (g)00110-15

EMphoton ()001/137infinite

WeakZ0 boson091.210-510-18

W boson180.4

Bosons = Spin 2

Gravitygraviton0010-39infinite

(not observed yet!)


Particles and forces

Particles and Forces

Summary of how different particles feel the different forces:

ChargeStrongEMWeak

u quark+2/3YesYesYes

d quark-1/3YesYesYes

electron-1NoYesYes

e0NoNoYes

c quark+2/3YesYesYes

s quark-1/3YesYesYes

muon-1NoYesYes

 0NoNoYes

t quark+2/3YesYesYes

b quark-1/3YesYesYes

tau-1NoYesYes

 0NoNoYes


Unification of the forces

Unification of the Forces

Grand Unification – Unite strong interaction with electroweak interaction.

Grand Unified Theories (GUTs) predict that protons are unstable.

Final step would then be to add quantum gravity to form a Theory of Everything (TOE).

Because gravitons interact with one another field theory is non-re-normalisable. Graviton has not been discovered!

~Planck scale

Planck Units

Length1.62 x 10-35 m

Time5.39 x 10-44 s

Energy1.22 x 1019 GeV/c2

Temp1.42 x 1032 K


Electroweak force

Electroweak Force

or EW symmetry breaking


Running coupling constants

Running Coupling Constants

at low

energy

EM coupling constant

= fine structure constant

Weak

Strong

Gravity

Coupling constants have an energy dependence due to (higher order) virtual interactions.

These change the measured value of the coupling constant and make it depend on the energy scale at which it is measured (logarithmic dependence).

The strong and weak couplings decrease with energy whilst the EM coupling increases.

It is therefore possible that at some energy scale, all 3 forces become equal.


Grand unification

Grand Unification

  • Grand-Unified Theories (GUT), favoured, (e.g. by non-zero masses) predict the 3 coupling constants (QED, Weak, QCD) to unify at GUT scale of 3x1016GeV.

  • This unification does not happen in the Standard Model (+GUT), but does in Supersymmetry with a 1 TeV scale.

  • Starting from the measured values of

  • αQED(mZ) and sin2W as input, one can predict:

  • To be compared to the experimental

  • value (mostly constrained by LEP):

  • Baryon Number violated in GUTs. Conflict with measurements?

Standard Model + GUT

LEP, Amaldi et al, 1991

SUSY at 1 TeV + GUT


Missing ingredient higgs sector

Missing Ingredient: Higgs Sector

Generates mass?

Graviton

not yet found


The mystery of mass

The Mystery of Mass

The masses of composite

particles like protons and neutrons are mainly given by the motion of the constituents.

u

However, for fundamental particles, like electrons and quarks it has long been a mystery how they acquire their masses and why they are so different.

d

u

Proton

Why do some particles

have large masses

whilst others have little

or no mass?

W

Electron

Mass = 511 eV

Photon

Mass < 10-18 eV

e

W boson

Mass = 80 x 109 eV

Neutrino

Mass < 2eV


Top quark heavier than silver atom

Top Quark Heavier than Silver Atom!

Silver

(A=108)

M(top) = 172 GeV ± 0.9 ± 1.3 GeV


Higgs mechanism

Higgs Mechanism

Standard Model in basic form leads to massless particles.

1961- 1968: Glashow, Weinberg & Salam developed theory that unifies EM and weak forces into one electroweak force. Predicted weak neutral current.

Nobel Prize: 1979

1964: Higgs, Kibble, Brout, Englert et al introduced the Higg’s field. Gives mass to Z and W bosons.

Nobel Prize: ??

1971: Veltman, t Hooft - Solved the problems of infinities through renormalisation.

Nobel Prize: 1999

Peter Higgs

  • Higgs boson is a neutral, scalar (spin=0) particle.

  • Coupling to particles is proportional to their mass.

  • No prediction for Higgs mass.

  • Vacuum should be filled with Higgs field – boson is the quantum of this field in the same way that the photon is the quantum of the EM field.


Space is not empty

Space is not Empty

The classical vacuum just consists of empty space-time and is featureless.

In reality, it’s sea of virtual particle-antiparticle pairs from quantum fluctuations.

Vacuum is the state of minimum energy for the Universe.

WARNING: Quantum field theory gives cosmological constant (or zero point energy) 120 orders of magnitude too high!


Higgs field and higgs boson

Higgs Field and Higgs Boson

H

Higg’s Boson

H

H

H

H

H

H

H

H

H

H

H

H

Higg’s Field


Mexican hat potential

Mexican Hat Potential

State in which the Higgs field is zero is not the lowest energy state.

EW - Higgs Field

(Scalar)

EM - Electric & Magnetic Fields

(Vector)

Energy lowest when

field is zero.

Energy lowest when

field is not zero.

Law is basically symmetric, but equilibrium state is not.

Symmetry is said to be spontaneously broken.


Electroweak symmetry breaking

Electroweak Symmetry Breaking

At high enough temperatures, particles were (symmetrically) massless.

As the Universe cooled, ring of stable points appeared.

W and Z got mass from the field, but the  stayed massless.


Higgs hunting

Higgs Hunting

f

f

e-

Z*

Z0

H

e+

f

f

Indirect

Fit to LEP EW Measurements

Direct Searches

at LEP Collider

Also, limits from Tevatron


Higgs particle discovery

Higgs Particle Discovery?

4 Jul 2012, CERN

Francois Englert & Peter Higgs


Particle physics 2

Higgs does not couple to zero mass photon.

Possible via a top quark loop.

CMS

ATLAS

Phys. Lett. B 716 (17 Sept 2012), Issue 1


Particle physics 2

CMS

ATLAS

Phys. Lett. B 716 (17 Sept 2012), Issue 1


Higgs particle properties

Higgs Particle – Properties?

MASS

Phys. Lett. B 716 (17 Sept 2012), Issue 1

Spin/Parity of Standard Model Higgs is expected to be J 0+

Spin 0 consistent with decay channels seen so far.

Spin 1 already ruled out.

The first scalar elementary particle.


Higgs spin

Higgs Spin

Spin is quantised and measured wrt an axis. Sz = -S, -S+1, -S+2, … +S-1, +S

  • However, photon is massless, so in this case Sz can only be +1 or -1

c/o Aidan Randle, ATLAS

ATLAS and CMS will need to do a proper spin analysis by analysing angular distributions of decay products to get the definitive answer.


Beyond the standard model

Beyond the Standard Model?

  • 18 input parameters from experiment (e.g. particle masses, coupling constants).

  • Gravity not included. Hierarchy problem.

  • Why 3 generations of particles?

  • Are these particles fundamental?

  • What is mass? (Higg’s particle) 

  • Missing antimatter?

  • Missing matter (dark matter & dark energy)?

  • Neutrino masses.

  • Cosmological constant predicted to be 10120 too large for vacuum.


Particle physics 2

End

CONTACT

Professor Glenn Patrick

email: [email protected]


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