As 11b Quarks&Leptons

8/12/2019 As 11b Quarks&Leptons

1/51

1.1b Particles & Radiation

Quarks & LeptonsBreithaupt pages 18 to 27

April 8th, 2010


2/51

AQA AS SpecificationLessons Topics

1 & 2 Classification of particles

Hadrons: baryons (proton, neutron) and antibaryons (antiproton and antineutron) and

mesons (pion, kaon).

Hadrons are subject to the strong nuclear force.

Candidates should know that the proton is the only stable baryon into which other baryons

eventually decay; in particular, the decay of the neutron should be known.

Leptons: electron, muon, neutrino (electron and muon types).

Leptons are subject to the weak interaction.Candidates will be expected to know baryon numbers for the hadrons. Lepton numbers for

the leptons will be given in the data booklet.

3 to 5 Quarks and antiquarks

Up (u), down (d) and strange (s) quarks only.

Properties of quarks: charge, baryon number and strangeness.

Combinations of quarks and antiquarks required for baryons (proton and neutron only),

antibaryons (antiproton and antineutron only) and mesons (pion and kaon) only.Change of quark character in - and + decay.

Application of the conservation laws for charge, baryon number, lepton number and

strangeness to particle interactions. The necessary data will be provided in questions for

particles outside those specified.


3/51

Cosmic rays and particle generation

Cosmic rays consist of high energy protons and

nuclei emitted from stars including the Sun.

The protons strike gas atoms in the upper

atmosphere and produce new short livedparticles and antiparticles.

These new particles can be detected at ground

level by cloud chambers and other detectors.

The first new particles to be detected were

muons (1937), pions (1947) and kaons (1947).
http://en.wikipedia.org/wiki/Cosmic_radiationhttp://en.wikipedia.org/wiki/Cloud_chamberhttp://en.wikipedia.org/wiki/Cloud_chamberhttp://en.wikipedia.org/wiki/Cosmic_radiation


4/51

AcceleratorsThese enable more controlledconditions than occur withcosmic radiation interactions.

High voltages are used toaccelerate charged particles

(electrons, positrons, protonsand antiprotons) to near lightvelocities.

The particles are made tocollide into a stationary targetor head-on with each other.

The energy produced in thesecollisions can be used tocreate other particles.

The largest linear accelerator is atStanford in California which uses a50 000 million volts (50 GV) toaccelerate electrons over adistance of 3km to an energy of 50GeV.

Linear particle accelerator game

The largest circular accelerator isthe Large Hadron Collider (LHC)at CERNnear Geneva. This usesa circular tube of circumference27km within which protons and

antiprotons are made to makehead-on collisions at energies ofup to 7000 GeV

LHC Simulator

LHC Rap
http://en.wikipedia.org/wiki/Particle_acceleratorhttp://en.wikipedia.org/wiki/Stanford_Linear_Accelerator_Centerhttp://en.wikipedia.org/wiki/Stanford_Linear_Accelerator_Centerhttp://microcosm.web.cern.ch/Microcosm/RF_cavity/ex.htmlhttp://en.wikipedia.org/wiki/Large_Hadron_Colliderhttp://public.web.cern.ch/Public/Welcome.htmlhttp://www.particledetectives.net/html/main.htmlhttp://www.youtube.com/watch?v=j50ZssEojtMhttp://www.youtube.com/watch?v=j50ZssEojtMhttp://www.particledetectives.net/html/main.htmlhttp://public.web.cern.ch/Public/Welcome.htmlhttp://en.wikipedia.org/wiki/Large_Hadron_Colliderhttp://microcosm.web.cern.ch/Microcosm/RF_cavity/ex.htmlhttp://en.wikipedia.org/wiki/Stanford_Linear_Accelerator_Centerhttp://en.wikipedia.org/wiki/Stanford_Linear_Accelerator_Centerhttp://en.wikipedia.org/wiki/Particle_accelerator


5/51

Hadrons and leptons

HADRONSare particles that interact through the stronginteraction

examples: protons, neutrons, pions and kaons

LEPTONSare particles that do not interact through thestrong interaction

examples: electrons, positrons, muons and neutrinos

Leptons interact through the weak interaction.

All charged particles interact through the electromagnetic interaction


6/51

Baryons and mesons

Baryonsare hadronsthat are protons orparticles that eventuallydecay into protons.

The proton is the onlystable baryon.

Neutrons are baryonsbecause they decay intoprotons with a half-life of12 minutes. Other

baryons have muchshorter half-lives.

Baryons are also calledfermions

Mesonsare hadronsthat do not includeprotons in their decayproducts.

All mesons are unstable Examples of mesons

include pions (mesons)and kaons (K mesons)


7/51

Pions or mesons

Pionsor mesonscan be positivelycharged (+), negatively charged (- ) oruncharged (0).

They have rest masses between themuon and proton (about 300 x theelectron).

They are all very unstable and decay bythe weak interaction.

+decays into an antimuon and a neutrino

- decays into an muon and an antineutrino0decays into two high energy photons


8/51

Kaons or K mesons

Kaonsor K mesonscan be positively charged (K+),negatively charged (K- ) or uncharged (K0).

They have rest masses greater than pions but less than aproton (about 1000 x the electron).

They are all unstable and decay by the weak interactionfar more slowly than pions.

This relatively slow rate of decay (about 10 - 10 s) wasunexpected and led to these particles being called strangeparticles.

Kaons decay into pions, muons and neutrinos.


9/51

Strangeness

This is a property possessed by some hadronsthat has been assigned in order to explain why

some particle interactions take place more

slowly than others or do not occur at all.

The K +mesonwas the first particle with

strangeness to be discovered and has been

assigned a strangeness number (S) of +1

Strangeness is a property, like charge, that isreversed in an antiparticle. Therefore the

K -meson has strangeness of1.


10/51

Baryon number (B)

Conservation of baryon number

In all interactions the total baryon number is conserved.

You are expected to recal l baryon numbers in

the AS exam inat ion !

antibaryons:(e.g. antiproton)

non-baryons(e.g. mesons and leptons)

baryons:(e.g. protons and neutrons) + 1

- 1

0


11/51

Leptons

Leptons are believed to be fundamental

particles. This means that they do not decay

into any other particles except leptons.

There are three families of leptons andantileptons. In order of increasing rest mass:

1. electrons and their neutrinos

2. muons and their neutrinos

3. tauons and their neutrinos

Only electrons and their neutrinos are stable.


12/51

Muons (-)

These are negatively charged like electrons but

about 200 times more massive

There also exists the positively charged

antimuon (+) Muons are unstable and decay by the weak

interactioninto electrons and antineutrinos

Antimuons decay into positrons and neutrinos

Tauons are heavier versions of muons (about 20 x more massive).

You are not expected to know about these in AS physics


13/51

Lepton and antileptons

increasing mass

leptons

electron e - muon - tauon -

electron

neutrino e

muon

neutrino

tauon

neutrino

antileptons

positron e + antimuon + antitauon +

electron

antineutrino e

muon

antineutrino

tauon

antineutrino

leptons

electron, e-

electron

neutrino, ve

muon, -

muon

neutrino, v

tauon, -

tauon

neutrino, v

anti-leptons

positron, e+

electron

antineutrino, ve

antimuon,+

muon

antineutrino,vtauon

antineutrino,v

antitauon,+


14/51

Lepton number (L)

Conservation of lepton number

In all interactions the total lepton number isconserved.

Lepton numbers are given in the AS examination

leptons: (electrons, muons and theirneutrinos)

+ 1

antileptons: (positrons, antimuons

and their antineutrinos)

- 1

non-leptons (e.g. hadrons and photons) 0

leptons:(electrons, muons andtheir neutrinos)

antileptons:(positrons, antimuons

and their antineutrinos)

non-leptons(e.g. hadrons andphotons)

+ 1

- 1

0


15/51

Answers:

particle matter orantimatter hadron orlepton

electromagnetic

interaction ? baryon, mesonor neither

proton matter hadron yes baryon

positron antimatter lepton yes neither

K0 matter hadron no meson

antineutrino antimatter lepton no neither

muon matter lepton yes neither

neutron matter hadron no baryon

hadron yes baryon

antimatter lepton neither

matter no meson

antineutrino neither

matter yes neither

matter hadron no

Complete:


16/51

Particle overview

matter and antimatter

hadrons leptons

baryons mesons


17/51

Interaction conservation rules

All interactions must conserve:

ENERGY

CHARGE LEPTON NUMBER & TYPE

BARYON NUMBER

and with strong interactions only:STRANGENESS


18/51

Energy and matter

Accelerators such as the Large Hadron Collider increase the kineticenergy of particles involved in collisions.

The total energy of the particles before the collision is equal to the rest

plus kinetic energies of the particles.

Likewise the total energy of the particles present after the collision.

Using the conservation of energy:

rest energy = total energy + kinetic energy

of the products before of the products

The smaller the final kinetic energy the better. This allows more energy

to go into particle creation. Head-on collisions such as those with the

LHC given the minimum final kinetic energy.

LHC Simulator
http://en.wikipedia.org/wiki/Large_Hadron_Colliderhttp://www.particledetectives.net/html/main.htmlhttp://www.particledetectives.net/html/main.htmlhttp://en.wikipedia.org/wiki/Large_Hadron_Collider


19/51

Question

A proton and an antiproton, both with 1.5 GeV of kineticenergy, make a head-on collision.

If the collision only produces K mesons and photons what isthe maximum number of K mesons that could be produced?

[Take the rest energy of a proton = 938 MeV;

K meson = 490 MeV]


20/51

Total energy before collision:

= 2 x (rest energy + kinetic energy)

= 2 x (938 MeV + 1500 MeV)= 4876 MeV

therefore the number of possible K mesons

= 4876 / 490

= 9.95

but only a whole number of K mesons can be formed

therefore up to 9 K mesons could be formed

The remainder of the energy would emerge in theform of photon and particle kinetic energy.


21/51

Lepton type conservation

The total electron or muon lepton numbers must also

be conserved in any interaction.

Example:

The total lepton number on both sides is the same = +1

However, in terms of muons and muon antineutrinos the

number changes from +1 to1

In terms of electrons and electron neutrinos the numberchanges from 0 to +2

Therefore this interaction is not permitted


22/51

Allowed interactions

Beta-minus decayLepton number before

= 0

Lepton number after

= 0 + 11 = 0

Muon decay

Lepton number before

= + 1Lepton number after

= + 11 + 1 = + 1

n p + e-+ ve

- e- + ve

+ v


23/51

Questions

1. Write an equation for beta-plus decay:

2. Write an equation for +decay:

3. Can the interaction shown below occur?

Yes, lepton numbers: +1 +0 = 0 +1

and it also conserves electron lepton type number

p n + e++ ve

+ e++ ve+ v


24/51

Sigma particlesThese are all baryons (B= +1) with a strangeness, S of -1.

sigma-plus +

charge = + 1 (equals proton charge)

sigma-zero 0

charge = 0

sigma-minus

charge = - 1

(Note: This is NOTthe antiparticle of +

)

Like all baryons they eventually decay into protons for example: n + -, after which the neutron decays into a proton


25/51

Conservation of strangeness

Strangeness is always

conserved in all strong

interactions (no leptons

involved).

Strangeness is not

always conserved in

weak interactions.

Strangeness conserved:

S: 0 + 0 -1 + 1


26/51

Can the following interactions occur ?

-

+ n K

-

+ 0

1.

2.

3.

YES: baryon numbers are: 0 + 1 1 + 0

AND strangeness numbers are: 0 + 0 -1 + 1

NO: baryon numbers are: 0 + 1 0 + 0

strangeness numbers are: 0 + 0 -1 + 0

NO: baryon numbers are: 0 + 1 0 + 1

BUT strangeness numbers are: 0 + 0 -1 + (-1)


27/51

Further interactions to check

4.

YES

5.

NOCharge is not conserved (neither is strangeness)

6.YES

e- + e+ p + p + ve + ve


28/51

Quarks

Baryons and mesons are not fundamentalparticles of matter (unlike leptons) but are

composed of smaller particles called

quarks. Quarks feel the STRONG force (unlike

leptons).

Quarks are never found in isolation butalways in pairs or triplets.
http://en.wikipedia.org/wiki/Quarkshttp://en.wikipedia.org/wiki/Quarks


29/51

The quark model of hadrons

BARYONSConsist of three quarks:

ANTIBARYONS

Consist of three antiquarks:

MESONS

Consist of a quark-antiquark pair:

q q q

q q q

q q

This is called the Standard Model.
http://en.wikipedia.org/wiki/Standard_Modelhttp://en.wikipedia.org/wiki/Standard_Model


30/51

Types of quark

There are six types (flavours) of quarks: up (u);down (d);charm (c); strange (s);top (t) andbottom (b)

Charm and top quarks are increasingly moremassive versions of the up quark.

Strange and bottom quarks are increasinglymore massive versions of the down quark.

There are also six corresponding antiquarks(anti-up, anti-down etc..).

Only knowledge of the up, down and strangequarks is required for AS physics.


31/51

Properties of quarkssymbol relative

mass

charge

proton = 1

baryon

number

strangeness

up u 1 + + 0

down d 2 - + 0

strange s 40 - + -1

charm c 600 + + 0

top t 90 000 + + 0

bot tom b 2000 - + 0

1

2

40

+

- +

+

+

-

0

0

- 1

up u

down d

strange s

charm c 600 + + 0

bot tom b 2000 - + 0

top t 90 000 + + 0

Antiquarks have the same mass but opposite

charge, baryon number and strangeness.


32/51

Protons and neutrons

Protons consist of two up and

one down quark (uud)

Charge = + + - = +1

Baryon number = + + + = +1

Neutrons consist of one up and

two down quarks (udd)

Charge = + - - = 0

Baryon number = + + + = +1

u

d

u

u

d

d


33/51

Antiprotons and antineutrons

Antiprotons consist of two upantiquarks and one downantiquark (uud)

Charge = - - + = -1

Baryon number = - - - = -1

Antineutrons consist of one upantiquark and two downantiquarks (udd)

Charge = - + + = 0

Baryon number = - - - = -1

u u

d

u

d

d


34/51

Sigma particle questionInsert the missing information below:

sigma-plus +

Quarks: uus

Charge = + + - = + 1

B = + + + = + 1

S = 0 + 01 =1

sigma-zero 0

Quarks: uds

Charge = + - - = 0

B = + + + = + 1

S = 0 + 01 =1

sigma-minus

Quarks: ddsCharge = - - - = 1

B = + + + = + 1

S = 0 + 01 =1

anti-sigma-plus +

Quarks: u u s

Charge = - - + = 1

B = - - - = 1

S = 0 + 0 + 1 = + 1

anti-sigma-zero 0

Quarks: u d s

Charge = - + + = 0

B = - - - = 1

S = 0 + 0 + 1 = + 1

anti-sigma-minus

Quarks: d d sCharge = + + + = + 1

B = - - - = 1

S = 0 + 0 + 1 = + 1


35/51

Charged mesons

These are made up

of a quark and an

antiquark pair made

of up and downquarks and

antiquarks

+= ud

charge = + + = +1

B = + - = 0

-= ud

charge = - - = -1

B = - + = 0


36/51

Uncharged mesons

These are made upof a quark and anantiquark pair of up,down or strangequarks

0

= uucharge = + - = 0

B = + - = 0

S = 0 + 0 = 0

OR 0= dd

charge = - + = 0

B = + - = 0

S = 0 + 0 = 0

OR 0= ss

charge = - + = 0B = + - = 0

S = -1 + 1 = 0


37/51

K mesons

These combinations a strange quark along withan up or down quark

normal particles:

K+= us (S = 0 + 1 = +1)

K0= ds (S = 0 + 1 = +1)

antiparticles:

K-= su (S = - 1 + 0 = - 1)K0= sd (S = - 1 + 0 = - 1)


38/51

Meson summary diagram

(du)

+

(ud)

K +

(us)

K

(su)

K 0

(ds)

K 0

(sd)

0

(uu, dd or ss)


39/51

Answers

name symbol quarks charge B S

proton p u u d + 1 + 1 0

neutron n u d d 0 + 1 0

pion

plus

+ u d + 1 0 0

omegaminus

- s s s - 1 + 1 - 3

neutral

lambda

0 u d s 0 + 1 - 1

Complete:

proton

pion plus

neutron

p

n

ud

+ 1

0

0

- 1 + 1

+ 1

+ 1

0

0

- 3

- 1


40/51

Quark interactions

Quarks undergo both strongand weakinteractions.

In stronginteractions the numbers and types

of quark are conserved.In weakinteractions the overall number of

quarks can change and individual quarks

can change from one type to another.


41/51

Example of a STRONG quark interaction:

Quark annihilation

In quark terms the interaction is:

An up quark and an up antiquark annihilate each other in a strong forceinteraction producing two pions with the release of radiation.

ENERGY: mass-energy is converted into kinetic energy and photons

CHARGE: + 11 = + 11 conserved

LEPTON NUMBER: strong interactionno leptons involvedBARYON NUMBER: + 11 = 0 + 0 conserved

STRANGNESS NUMBER: 0 + 0 = 0 + 0 conserved

This reaction can occur.

u u d + u u d u d + u d


42/51

Examples of a WEAK quark interaction:1. Beta-minus decay

With beta-minus decay a

neutron (udd) changes into

a proton (uud).

This can be represented on

a Feynman diagram as a

down quark changing into

an up quark.

Note: An early version of the text

book shows, incorrectly, an electron-

neutrino.

d u + -+ e

d

u-

ve

time

W-


43/51

Examples of a WEAK quark interaction:2. Beta-plus decay

With beta-plus decay a

proton (uud) changes into a

neutron (udd).

u d +++ e

This can be represented on

a Feynman diagram as an

up quark changing into a

down quark.

Note: An early version of the text

book shows, incorrectly, an electron-

antineutrino.

u

d+

ve

time

W+


44/51

Strong or weak interaction ?

Do any of the following occur ?

1) leptons involved

2) total strangeness changes

3) quarks change type

4) W+or W-exchange particle

NO

YES

STRONGINTERACTION

e.g.: p + p ++ -

when a proton undergoes

annihilation with anantiproton to produce two

pions

WEAK INTERACTIONExample: Beta decay: n p + e -+ e


45/51

Internet Links

Fifty-Fifty Game on What particles are

positive- by KT - Microsoft WORD

Hidden Pairs Game on Quark-Lepton

Symmetry - by KT - Microsoft WORD

Sequential Puzzle onParticle Masses

order- by KT - Microsoft WORD .
http://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://www.ktaggart.com/physics/Games/SelectionPositive.dochttp://www.ktaggart.com/physics/Games/SelectionPositive.dochttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://www.ktaggart.com/physics/Games/SequenceParticleMasses.dochttp://www.ktaggart.com/physics/Games/SequenceEnergySize.dochttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://www.ktaggart.com/physics/Games/SequenceEnergySize.dochttp://www.ktaggart.com/physics/Games/SequenceParticleMasses.dochttp://www.ktaggart.com/physics/Games/SequenceParticleMasses.dochttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://www.ktaggart.com/physics/Games/PairsQuarkLepton.dochttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://www.ktaggart.com/physics/Games/SelectionPositive.dochttp://www.ktaggart.com/physics/Games/SelectionPositive.dochttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.htmlhttp://subscription.echalk.co.uk/Science/chemistry/atomicStructure/atomicStructure.html


46/51

Core Notes from Breithaupt pages 18 to 271. What are muons, pions and kaons?

Give their approximate masses andcharges.

2. Explain how muons, pions and kaonsdecay. State what interactions areinvolved and what is produced.

3. Define what is meant by (a) a hadron;(b) a lepton; (c) a baryon & (d) ameson. Give two examples of each

type of particle.4. How many baryons are stable? Namethem.

5. Why is a neutron a baryon?

6. What are the two types of neutrinos?

7. Explain the lepton rules in (a)interactions between leptons andhadrons and (b) muon decay

8. Give and explain an example of a non-allowed interaction where lepton numberis conserved. (see the weak puzzle)

9. Copy table 1 on page 25. Definebaryons, antibaryons and mesons interms of quark composition.

10. State the quark compositions of protons,neutrons, antiprotons and the threevarieties of pion.

11. Explain beta-minus and beta-plus decayin terms of quark change. Illustrate withFeynman diagrams.

12. Define what is meant by Baryon number.State the baryon numbers of quarks,antiquarks, protons, neutrons,antiprotons and mesons.

13. List the conservation rules that mustapply to all interactions. State howstrangeness is exceptional.

14. Give and explain an example of aninteraction where quarks are annihilated.


47/51

2.1 The Particle Zoo

Notes from Breithaupt pages 18 & 19

1. What are muons, pions and kaons? Give theirapproximate masses and charges.

2. Explain how muons, pions and kaons decay. Statewhat interactions are involved and what is produced.

3. Write a paragraph in each case about (a) the StanfordLinear Accelerator and (b) the LHC at CERN.

4. Try the summary questions on page 19


48/51

2.2 Particle Sorting


1. Define what is meant by (a) a hadron; (b) a lepton; (c) abaryon & (d) a meson. Give two examples of each typeof particle.

2. How many baryons are stable? Name them.

3. Why is a neutron a baryon?

4. Explain how conservation of energy controls whichparticles are produced in particle collisions.



49/51

2.3 Leptons at work


1. What are the two types of neutrinos?2. Explain the lepton rules in (a) interactions

between leptons and hadrons and (b) muondecay

3. Give and explain an example of a non-allowedinteraction where lepton number is conserved.(see the weak puzzle)



50/51

2.4 Quarks and antiquarks

Notes from Breithaupt pages 24 to 25

1. Copy table 1 on page 25. Define baryons, antibaryonsand mesons in terms of quark composition.

2. State the quark compositions of protons, neutrons,antiprotons and the three varieties of pion.

3. Explain beta-minus and beta-plus decay in terms of

quark change. Illustrate with Feynman diagrams.

4. Why is it necessary for some particles to be assigned astrangeness number. Show how the strangenessnumbers for K-mesons and sigma particles are

allocated.5. Try the summary questions on pages 25


51/51

2.5 Conservation rules

Notes from Breithaupt pages 26 to 27

1. Define what is meant by Baryon number. Statethe baryon numbers of quarks, antiquarks,protons, neutrons, antiprotons and mesons.

2. List the conservation rules that must apply to

all interactions. State how strangeness isexceptional.

3. Give and explain an example of an interactionwhere quarks are annihilated.

4. Try the summary questions on pages 27

Documents

As 11b Quarks&Leptons