1

Particle Physics 2

Quantum, Atomic and Nuclear Physics, Year 2 University of Portsmouth, 2012 - 2013

Prof. Glenn Patrick

2

Last Week - RecapParticle Physics & CosmologyMatter Particles, GenerationsSpin – Fermions & BosonsCharged LeptonsAntimatterNeutral Leptons - NeutrinosHadronsStrange Particles and StrangenessSymmetries, Conservation LawsQuantum Numbers, IsospinEightfold Way and Quark ModelCharm, Bottom, Top, Quark Counting

3

Today’s Plan 20 November Particle Physics 2

Force CarriersFour Fundamental InteractionsQuantum Field TheoryFeynman DiagramsHigher Orders/Radiative CorrectionsAnomalous magnetic moment of muonCharged and Neutral CurrentsZ and W Vector BosonsGluonsColour Charge and Quantum Chromodynamics (QCD)Unification of Fundamental Forces, Running Coupling ConstantsHiggs Boson and Field

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

BOOKSB.R. Martin & G. Shaw, Particle Physics, 3rd Edition, WileyDonald H. Perkins, Introduction to High Energy Physics, 4th edition, CUPCoughlan et al, The Ideas of Particle Physics, Cambridge

4

I

II

III Observed in 2000

5

Force Carriers

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)

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.

6

The Four Forces of NatureELECTRO -MAGNETIC

WEAK GRAVITY

STRONG

7

Forces in Classical PhysicsClassically, 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.

8

Quantum Field TheoryForces are transmitted by

exchange of force particles between matter particles.

4 forces with different force particles.

HeisenbergUncertainty Principle

tEEt

Mctcx 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.

particle exchange of mass1 Force of Range

Quantum Mechanics + Relativity

9

Four Forces of NatureSTRONG FORCE

Strength: 1, Range: 10-15 mExchange: Gluon

ELECTROMAGNETIC FORCEStrength: 1/137, Range: Infinite

Exchange: Photon

GRAVITYStrength: 6x10-39 m,

Range: Infinite, Exchange: ?

WEAK FORCEStrength: 10-6 m, Range: 10-18 m

Exchange: W±, Z0

A FIFTH FORCE?

Modified gravity?Dark matter,

Dark energy, etc.

10

1~4

2

cgS

S

1371~

4

2

ce

EM

52 10~ pFmG

362 10~ pNmG

11

Fundamental InteractionsEM

e- e-

e- e-

Strongu

gluon

u

d d

Weak

Z0

e-

Weak

e e

e- e-

ddu u

du

W-

en

p

12

Feynman Diagrams

positron (anti-electron)

electron

At each ‘vertex’ charge is conserved. Heisenberg

Uncertainty Principle allows energy borrowing.

Virtual ParticleDoes not have mass of a

physical particle.

Known as “off –mass shell”

(e.g. not zero for photon)

222XXX pEm

Richard Feynman Quantum Electrodynamics

(QED)

13

Feynman Diagrams

External legs represent amplitudes of 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.

AnnihilationExchange

14

Feynman DiagramsAssociate 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).

1371

4

2

c

e

Lowest order Second order

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

For QED:

)space phase(2Rate Transition 2 M

Fermi’s Golden Rule

15

Bhabha Scattering

e- e-

e+ e+

e-

e+

e-

e+

Z0

e-

e+

e-

e+

e- e-

e+ e+

Z0

Amplitude = +

++

4 Born Diagrams (Electroweak) eeee

16

Radiative Corrections

Vacuum polarisation

Higher Order Quantum Loop Diagrams (QED only)

17

3rd order corrections

Anomalous Magnetic Moment of the Muon

Dirac theory predicts g=2, but this is modifiedby quantum fluctuations.

00116.02

)2(21

ga

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

ee

+-

e-e+

e-e-

e+e+QED

µZ0

µ µ µW W

µ

WEAK

B

+ STRONG

Hundreds of diagrams!

ppm) (0.54 10116592089(exp) 11a

ppm) (0.42 10116591802)( 11thea

111080287 a ~3.6σ effectNew Physics?

Lowest order correction

18

Muon g-2: Testing the Standard Model

Experimentalmeasurements of aμ

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

Beyond the Standard Model (BSM) Physics?

newweakhadQEDthe aaaaa

19

Photon – EM Boson

1900 Planck Black Body Radiation explained in terms of light quanta Nobel Prize.

1905 Einstein explained thePhotoelectric Effect in terms of quanta of energy Nobel Prize.

1925 G.N. Lewis proposed the name Photon for quanta of light.

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

hE Quantum energy of photon

h = Planck’s constant = frequency

20

Charged and Neutral Currents

Z0

NX

W+

N X

-

XN XN

Neutral Current Charged Current

21

Discovery of Weak Neutral Currents (1973)

21Gargamelle Bubble Chamber

electron

ee

Bremsstrahlung effects

22

Z and W Story

UA1

UA2

Super Proton Synchrotron turned

into proton-antiproton collider. Stochastic cooling technique.

Carlo Rubbia (UA1) Simon van der MeerTwo Experiments:

UA1 and UA2.Rubbia came up with

idea and led UA1.

1984

23

W Boson Discovery – UA1 (1982)

electron

“Missing Energy” = neutrino

24

Z Boson Discovery – UA1 (1983)electron

positron

𝒁 𝟎→𝒆+¿+𝒆−¿

25

Weak Charged Current and QuarksFlavour Changing Charged Currents.Quark flavour never changes except by

weak interactions that involve W± bosons.

c s

W

t b

W

u d

W

ddu u

du

W-

en

p

+ ..

decay finally understood!

In decay processes,quark always decays tolighter quark to conserve

energy.

t b c s u d

Weak charged current changes lepton and quark

flavours.Possible that flavour

changing neutral currents exist beyond (tree level)

Standard Model.

26

quark

anti-quark

gluon

Gluon Discovery (1979)

JADE, TASSO, MARK-J, PLUTO

3-Jet Event

PETRA e+e- Collider, DESY, Hamburg

Third jet produced bygluon bremsstrahlung

gqqee

27

Inside the Proton

There are 3 “valence” quarksinside the proton bound together

by gluons.

Quantum theory allows quarks tochange 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…..

28

Colour Charge Some particles apparently contain quarks in the

same state violates Pauli Exclusion Principle (e.g. ++ = uuu).

Quarks

Anti-quarks

Proposed that quarks carry an extra quantum numbercalled “colour”.

All physical particles are colour neutral or “white”.

baryon meson

Red Green Blue

Cyan Magenta Yellow

29

Quark Speciesquarks

s

ud

u ud d

s s

antiquarks

c c c

u

d

s

u u

d d

s s

updown

c c c charmstrange

tb

t tb b

tb

ttb b

topbottom

30

8 Interacting GluonsExpect 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.

3ggbbrr

62 ggbbrr

2bbrr This combination is

colourless and symmetric.

Does not take part in the strong interaction.

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

31

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

below top energy

threshold

32

Quantum Chromodynamics (QCD)

Gluons carry colour+anti-colourcharge, e.g. red-anti blue.

Colour charge always conservedso quarks can change colour when

emitting a gluon.

Since gluons (8) carry colour charge,they can interact with one another!

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.

Quantum Chromodynamics (QCD) is the theory of the Strong Interaction in the Standard Model.

Fragmentation

33

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”:

Confinement

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.

Confinement

34

Quark Interactions

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

35

Residual Forces

How do protons bind to formthe nucleus? Protons & neutrons

are colour neutral.

Residual Strong Interactionbetween quarks in different

protons overcomes EMrepulsion.

How do molecules form ifatoms are electrically neutral?

Residual EM Force Electrons in one atom are

attracted to protons in another atom.

36

Force Particles

36

Bosons = Spin 1Force Particle Charge Mass Relative

Range (GeV) Strength

(m)Strong gluon (g) 0 0 1 10-15

EM photon () 0 0 1/137 infinite

Weak Z0 boson 0 91.2 10-5 10-18

W boson 1 80.4

Bosons = Spin 2Gravitygraviton 0 0 10-39 infinite

(not observed yet!)

37

Particles and Forces

Charge Strong EM Weaku quark +2/3 Yes Yes Yesd quark -1/3 Yes Yes Yeselectron -1 No Yes Yese 0 No No Yesc quark +2/3 Yes Yes Yess quark -1/3 Yes Yes Yesmuon -1 No Yes Yes 0 No No Yest quark +2/3 Yes Yes Yesb quark -1/3 Yes Yes Yestau -1 No Yes Yes 0 No No Yes

Summary of how different particles feel the different forces:

38

Unification of the Forces

38

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 UnitsLength 1.62 x 10-35 mTime 5.39 x 10-44 sEnergy 1.22 x 1019 GeV/c2

Temp 1.42 x 1032 K

~Planck scale

39

Electroweak Forceor EW symmetry breaking

40

035999074.1371

4 0

2

c

e

Running Coupling Constants

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.

EM coupling constant = fine structure constant

53

2

1003.1~

cMGFW

1~)()(2

cEgE S

S

at lowenergy

Weak

Strong40

2

105~4

c

MGNg

Gravity

41

Grand Unification

LEP, Amaldi et al, 1991

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 3x1016 GeV.

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 sin2W as input, one can

predict:

To be compared to the experimental value (mostly constrained by LEP):

Baryon Number violated in GUTs. Conflict with measurements? SUSY at 1 TeV + GUT

Standard Model + GUT

GUT) (Standard 002.0073.0)( ZS mGUT) (SUSY 010.0129.0)( ZS m

003.0118.0)( ZS m

(SuperK) 10)( 340 yrsep

42

Missing Ingredient: Higgs SectorGenerates mass?

Gravitonnot yet found

43

Why do some particles have large masses whilst others have little or no mass?

The Mystery of MassThe masses of compositeparticles like protons and

neutrons are mainly given by the motion of the constituents.

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.

We

PhotonMass < 10-18 eV

ElectronMass = 511 eV

W bosonMass = 80 x 109 eV

d

u

u

NeutrinoMass < 2 eV

Proton

44

Top Quark Heavier than Silver Atom!

Silver(A=108)

M(top) = 172 GeV ± 0.9 ± 1.3 GeV

45

Higgs MechanismStandard 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: 19791964: 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.

46

Space is not EmptyThe 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!

47

Higgs Field and Higgs BosonH

H

H

HH

H HH H

HH

H

H

Higg’s Boson

Higg’s Field

48

Mexican Hat Potential

Energy lowest whenfield is not zero.

EM - Electric & Magnetic Fields(Vector)

EW - Higgs Field(Scalar)

Energy lowest whenfield is zero.

Law is basically symmetric, but equilibrium state is not. Symmetry is said to be spontaneously broken.

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

49

Electroweak Symmetry BreakingAt 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.

50

Higgs Hunting

GeV94 29

24- Value Preferred

e+H

e-

Z0Z*f

ff

f

IndirectFit to LEP EW Measurements

Direct Searches at LEP Collider

CL) (95% GeV 114.4Hm

CL) (95% GeV 185HmAlso, limits from Tevatron

51

Higgs Particle Discovery?

4 Jul 2012, CERNFrancois Englert & Peter Higgs

52

𝑯→𝜸𝜸 𝑪𝒉𝒂𝒏𝒏𝒆𝒍

ATLASCMS

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

Higgs does not couple to zero mass photon.Possible via a top quark loop.

53

𝑯→𝒁 𝒁∗→𝟒ℓ𝑪𝒉𝒂𝒏𝒏𝒆𝒍

ATLAS CMS

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

ℓ𝒎𝒆𝒂𝒏𝒔𝒍𝒆𝒑𝒕𝒐𝒏

54

Higgs Particle – Properties?ATLASGeVsysstatM H )(4.0)(4.00.126

)(5.0)(4.03.125 CMSGeVsysstatM H

MASS

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

55

Higgs SpinSpin 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

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

c/o Aidan Randle, ATLAS

56

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.

57

CONTACTProfessor Glenn Patrickemail: glenn.patrick@stfc.ac.uk

End