Quanta to Quarks

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• Quantum, atomic, and sub-atomic physics; three parallel, yet strongly interacting topics

• We will concentrate on the “standard model”

• Highlight features and look at milestones and some of the background.

Quanta to Quarks – Nuclear path 1

• Becquerel 1896 radiation• Rutherford 1911 atom• Pauli 1930 neutrino• Chadwick 1932 neutron• Heisenberg 1932 Nucleus = n and p

• Hahn and Strassman 1938 fission

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Nuclei and nucleons probe nucleus

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6 MeV alpha

Closest distance for head–on approach

Rutherford scattering

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Detectors for scattering of electrons by protons and neutrons.Results consistent with nucleons having a substructure = quarks

Chadwick detection of the neutron

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Note:- charged particles not detected between beryllium and paraffin so photon or something else

Chadwick detection of the neutron

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Note:- charged particles not detected between beryllium and paraffin so photon or something else…Radiation not stopped by inserted lead plate, so must be another neutral particle

Lead plate

Heisenberg model of nucleus:-made up of protons and neutrons

Num

ber

of p

roto

ns Z

Number of neutrons N

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Nucleus:-

Z protons(atomic number)

N neutrons

TotalA = Z + N(mass number) nucleons

Various decay modes of nucleus

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Alpha decayX(A,Z) => Y(A-4,Z-2) +

Beta plus decayX(A,Z) => Y(A,Z-1) + e+ +

Beta minus decayX(A,Z) => Y(A,Z+1) + e- +

neutrons

prot

ons

Alpha decay-1Alpha decay is a two body decay

Both the alpha and the recoil nucleus have the same momentum in opposite directions.

The alphas always get the same proportion of the available energy, Q

And hence have the same range in matter

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mm

QmE

d

d

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In beta decay the electrons have a range of energies even though the total energy available is the same.

Pauli proposed that there is a third, undetected (hence neutral), particle which shares the energy and balances the momentum.

The maximum electron energy is nearly the total available and so the third particle must have a very low mass.

Beta decay

Energy spectrum of electron

Beta decay

Quanta to Quarks – Nuclear path 2

• Powell 1947 pion– pi => mu => electron decay observed

• Strange particles 1947-1950• Anti-particle – baryons 1955• Reines - neutrino detected 1956

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Too many particles for all to be fundamental

Quanta to Quarks – Nuclear path 3

• Gell-Mann/Zweig 1964 Quark model• Weinberg/Salam 1967electroweak• Glashow 1970 charm in theory• Richter/Ting J/ 1974charm observed• Perl 1975 tau observed

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Standard Model emerges

Quanta to Quarks – Nuclear path 4

• Lederman 1977 bottom observed

• Rubbia 1983 W’s and Z0

• CDF 1995 top observed

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1991-1992 Evidence indicates that there are only three generations of

leptons from study of Z0.

Inward bound

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object and size• grain, 1 mm• virus, 100 nm• atom, 100 pm• nucleus, 10 fm• nucleon, 1 fm• quark, <1 am

1 am = 10-18 m

Inward Bound

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object and size• grain, 1 mm• virus, 100 nm• atom, 100 pm• nucleus, 10 fm• nucleon, 1 fm• quark, <1 am

Inward bound

From DESY site

How can we examine small objects ?

By the light or particles they emit or reflect

For very small objects the wavelength of the light or particle plays an important role

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Scattering – wavelength dependence

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Diffraction of waves

Note that spread of patterndepends on /a :

For < a pattern depends on structure of object.

For > a pattern independentof structure of object

Particle diffraction

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Similar diffraction behaviour is observed for scattering of electrons, neutrons by nuclei and crystals etc.

Wavelength of particle given by the de Broglie relationship:-

422 cmE

hcph

T

Eg. A 1GeV electron has a wavelength (1.23 fm) about the same as the diameter of a nucleon. ( note:- for ET >> mc2 , = photon with same ET )

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CERN

LEPe+e-

Up to~200GeV+200GeV

LHCPp

8Tev+8Tev

Accelerator -1

8.6 kmdiameter

CERN photo

Accelerator -2

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CERN

LEPLHC

Tunnel

Beam pipes etc under constructionCERN photo

Detectors - ATLAS at CERNQtoQ06-ju

physicist

CERN photo

Visualization of particles tracks - 1

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The standard model

• The standard model describes the universe in terms of a set of different kinds of particles and the interactions between them.

• 12 particles (and their 12 antiparticles)– 6 leptons and their 6 antileptons– 6 quarks and their 6 antiquarks

• 4 interaction forces:- – gravity, electromagnetic, – weak, fundamental strong

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the leptons – charge and mass

name symbol charge MeV/c2 m/mproton

electron e- -e 0.511 0.0055

electron neutrino e 0 ~ 0

mu-minus -e 105.66 0.1126

mu-neutrino 0 0

tau-minus -e 1777 1.894

tau-neutrino 0 ~ 0

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anti-leptons- charge and mass

name symbol charge massMeV/c2 m/mproton

e-plus or positron e+ +e 0.511 0.0055

electron antineutrino e 0 ~ 0

mu-plus + +e 105.66 0.1126

mu antineutrino 0 ~ 0

tau-plus 

+ +e 1777 1.894

tau antineutrino 

0 ~ 0

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Origin:- particles of exactly the same mass but opposite chargeLater found to have other quantum numbers with opposite values

Symbol:- eitherthe electric charge as a superscript eg: - and +, e- and e+

or

particle P anti-particle (often said as P-bar)

Neutral particles/anti-particles:- some are the same (Majorana) eg 0 and some are different (Dirac) eg neutron, neutrino

P

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Classification of particles – particles/anti particles

63 MeV positron upwards emerges with 23 MeV)

3 electrons (bend to left) and 3 positrons ( bend to right)

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The first anti-particles:- positrons, 1932 - Anderson

lepton numbers

 lepton

  lepton number 

le l l 

anti-lepton numberle l l

electron e- 1 0 0 -1 0 0

electron neutrino e1 0 0 -1 0 0

mu 0 1 0 0 -1 0

mu-neutrino 0 1 0 0 -1 0

tau 0 0 1 0 0 -1

tau-neutrino 0 0 1 0 0 -1

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Decay + => + => e+

+ => + +

+ => +e+ + e

Note lepton numbers are conserved

quarks – charge and mass

name symbol chargee

mass MeV/c2 m/mproton

down d -1/3 ~ 3

up u +2/3 ~ 6

strange s -1/3 100 0.1

charm c +2/3 1250 1.3

bottom b -1/3 4500 4.8

top t +2/3 175000 187

 

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Quark picture 1983

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according to

Frank Close“Cosmic Onion”Heinemann Educational Books1983

Top-quark found 1995

q = +2e/3 q = -e/3

Anti-quark - charge and mass

 

name symbol chargee

massMeV/c2 m/mproton

anti- down d -1/3 ~ 3

anti-up u +2/3 ~ 6

anti-strange s -1/3 100 0.1

anti-charm c +2/3 1250 1.3

anti-bottom b -1/3 4500 4.8

anti-top t +2/3 175000 187

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quarks – flavour numbers

 quark

  quark flavour numbers

qd qu qs qc qb qt

anti-quark flavour numbers

qd qu qs qc qb qt

down d 1 0 0 0 0 0 -1 0 0 0 0 0

up u 0 1 0 0 0 0 0 -1 0 0 0 0

strange s 0 0 -1 0 0 0 0 0 1 0 0 0

charm c 0 0 0 1 0 0 0 0 0 -1 0 0

bottom b 0 0 0 0 -1 0 0 0 0 0 1 0

top t 0 0 0 0 0 1 0 0 0 0 0 -1

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leptons and quarks - masses

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p

Generations 1 2 3

Fundamental forces

force exchange boson

"charge" range massm/mp

how many different kinds?

gravity graviton mass infinite zero one

electro-magnetic

photon electric infinite zero one

weakW+

W-

Z0

 weak

 1 am

85.785.797.2

 three

Fundamental strong

gluon colour infinite zero eight

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forces acting between particles

  gravity weak electro-magnetic

 

strong

charged leptons y y y n

neutral leptons y y n n

quarks y y y y         

photons y n y n

Z0 y y n n

W+, W- y y y n

gluons y n n y

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Conservation laws - 1

• Charge

• Energy

• Linear momentum

• Angular momentum

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The following quantities are conserved in all interactionsIe:- the total before must be the same as the total afterwards

Conservation laws - 2

• Baryon number y y y

• Lepton flavour numbers y y y

• Quark flavour numbers y y n

• Colour y n/a n/a

The following quantities are conserved in interactions as indicated:- S strong; E electromagnetic; W weak

S E W

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Classification of particles:photons, leptons, mesons and baryons

• Originally described mass.– Photons no mass– Leptons light 0.5 MeV/c2

– Mesons medium 100-500 MeV/c2

– Baryons heavy > 900 MeV/c2

Still useful:-turns out that this also describes structure and quark content.

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Baryons Mesons

a quark andan anti-quark

hadrons

three quarks or

three anti-quarks(anti baryons)

Classification of particles – baryons and mesons and hadrons

Contain quarks

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Baryons Mesons

three quarks or

three anti-quarks(anti baryons)

a quark andan anti-quark

hadrons

valence quarks

gluons and sea quarks

Classification of particles – baryons and mesons and hadrons

Baryons:- proton and the neutron

du u

dd u

the proton uud + sea quarks and gluons

the neutron udd + sea quarks and gluons

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mesons:- the pion family

+ 0 -

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u:d-bar u:u-bar u-bar:dd:d-bar

“colour - 1”

Chromodynamics :- theory of the strong interaction,colour plays the same role as charge in electrodynamics.

Need three colours, but hadrons have to be colourlessUse red, green and blue (parallel to TV and photo and print)Anti-colours = white – colour ; cyan, magenta and yellow

Gluons have a colour and an anti colour

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Quarks have colour, anti-quarks have anti-colour

Baryons:- one (valence) quark of each colour (anti-baryons have three anti-colours)

Mesons:- quark(colour)+anti-quark(anti-colour)

Leptons, photons, W’s, Z0 do not have a colour

“colour - 2”

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Classification of particles - generations

s

c

b

t

d

u

e

e

First generation:

Second generation:

Third generation:

leptons quarks

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The upper member of each doublet is more positive

Classification of particles – fermions and bosons

Fermions obey the Pauli exclusion principle:-“two particles with the same quantum numbers can not

occupy the same quantum state”

Bosons don’t:-“any number of identical bosons can occupy the same

quantum state”

Another way of saying this is:-“Fermions follow Fermi/dirac statistics, bosons follow

Bose/Einstein statistics”

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Fermions:- leptons, quarks, neutron, proton and other baryons

Bosons:- photons, gluons, W’s and Z0

mesons

A nucleus can be either depending on its spin.

Classification of particles – fermions and bosons

Classification of particles – fermions and bosons

Fermions have half integral spin:- 1/2, 3/2, 5/2, 7/2 …..

Bosons have integral spin:- 0, 1, 2, 3 ….

Spin magnitude and its orientation are quantum numbers,as are the allowed projections onto a preferred direction.

Eg spin 3/2 : -3/2, -1/2, +1/2, +3/2spin 2: -2, -1, 0, +1, +2

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Are two different quantum states

+1/2 -1/2

Standard model and Nuclear Physics

The nucleons remain as individual particles in the quantum well formed by the other nucleons in the nucleus

Alpha, gamma decays, fission and fusion are reactions at the nuclear level. They are the result of nucleon to nucleon interactions via the “strong nuclear force”

Beta decay is an interaction at the quark level

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The "strong nuclear force" is an exchange force mediated by (mostly) pi-mesons:- + (u ), - ( d),0 ( mix of u and d )

The "strong nuclear force" is like the inter-molecular Van derWaals force, which is the result of the adding the electromagnetic forces, from the component electrons and nuclei, outside the neutral molecule.

Standard model and Nuclear Physics

d uu d

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alpha decay – quantum tunneling

-log(t1/2)

Gamow-Condon and Gurney prediction basedon alpha tunneling .

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EZ

Geiger–Nuttal rule:-large Z, low E = long half-life

Nparent (Z,A) => Ndaughter(Z-2, A-4) + + Q

mm

QmE

d

d

alpha decay – barrier penetrationQtoQ06-ju

energy

Energy ofemitted alpha

radial distance

free

bound

electrical potential of alpha infield of daughter nucleus

Alpha pre-formed in the nucleus

alpha tunnels through potential barrier –a quantum effect

beta decay – nuclear and nucleon level

Beta plus decay

N*(A, Z) => N(A, Z-1) + e+ + e

Beta minus decayN*(A, Z) => N(A, Z+1) + e- +

Nuclear level

Nucleon level –within a nucleus

n => p + e- +

p => n + e+ + e

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e

e also for free neutron

beta decay – quark level

duu

dud

+

e

u => d + W+

+ + e

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W+

beta decay – quark level

duu

dud

+

e

u => d + W+

+ + e

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W+

Quark flavour changed lepton/antilepton pair

created

The ENDnot really, but I’ll stop here anyway

Exchange potential – Yukawa model

infinite range

rg

rpm :0

r

gerpm

Rr :0

short range

pote

ntia

l p(r

)

radial distance r

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mcR

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10 sided “dice” – “decay” on 1 and 2Start with 100 “nuclei”

Dice thrown for each nucleus until get 1 or 2 then go to next nucleus

0

20

40

60

80

100

120

0 10 20 30 40

number of throws, N

nu

mb

er

su

rviv

ing

aft

er

N

thro

ws

Series1

Series2

Monte-Carlo simulation of nuclear decay