QtoQ06-ju
Quanta to Quarks
• 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.
QtoQ06-ju
Quanta to Quarks – Nuclear path 1
•
•
•
•
•
•
Becquerel 1896
Rutherford 1911
Pauli 1930
Chadwick 1932
Heisenberg 1932
Hahn and Strassman 1938
radiation
atom
neutrino
neutron
Nucleus = n and p
fission
Nuclei and nucleons probe nucleus
QtoQ06-ju
Rutherford scattering
6 MeV alpha
Closest distance for head–on approach
QtoQ06-ju
Detectors for scattering of electrons by protons and neutrons.
Results consistent with nucleons having a substructure = quarks
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Chadwick detection of the neutron
Note:- charged particles not detected between
beryllium and paraffin so photon or something else
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Chadwick detection of the neutron
Lead plate
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
QtoQ06-ju
Nucleus:-
Z protons
(atomic number)
N neutrons
Total
A=Z+N
(mass number)
nucleons
Number of protons Z
Heisenberg model of nucleus:made up of protons and neutrons
Number of neutrons N
QtoQ06-ju
protons
Various decay modes of nucleus
Beta minus decay
X(A,Z) => Y(A,Z+1) + e- + n
Beta plus decay
X(A,Z) => Y(A,Z-1) + e+ + n
Alpha decay
X(A,Z) => Y(A-4,Z-2) +a
neutrons
QtoQ06-ju
Alpha
decay
is
a
two
body
decay
Alpha decay-1
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
Qmd
Ea 
md  ma
And hence have the same range in matter
QtoQ06-ju
Beta decay
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.
Energy spectrum
of electron
The maximum electron energy is
nearly the total available and so the
third particle must have a very low
mass.
Beta decay
QtoQ06-ju
Quanta to Quarks – Nuclear path 2
• Powell 1947
– pi => mu => electron
pion
decay observed
• Strange particles
• Anti-particle – baryons
• Reines - neutrino detected
1947-1950
1955
1956
Too many particles for all to be fundamental
QtoQ06-ju
Quanta to Quarks – Nuclear path 3
•
•
•
•
•
Gell-Mann/Zweig 1964
Weinberg/Salam 1967
Glashow 1970
Richter/Ting J/y 1974
Perl 1975
Quark model
electroweak
charm in theory
charm observed
tau observed
Standard Model emerges
QtoQ06-ju
Quanta to Quarks – Nuclear path 4
• Lederman U 1977
• Rubbia 1983
• CDF 1995
bottom observed
W’s and Z0
top observed
1991-1992 Evidence indicates that
there are only three generations of
leptons from study of Z0.
QtoQ06-ju
Inward bound
•
•
•
•
•
•
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
QtoQ06-ju
Inward Bound
bound
Inward
•
•
•
•
•
•
object and size
grain, 1 mm
virus, 100 nm
atom, 100 pm
nucleus, 10 fm
nucleon, 1 fm
quark, <1 am
From DESY site
QtoQ06-ju
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
QtoQ06-ju
Scattering – wavelength dependence
Diffraction of waves
Note that spread of pattern
depends on l/a :
For l < a pattern depends on
structure of object.
For l > a pattern independent
of structure of object
QtoQ06-ju
Particle diffraction
Similar diffraction behaviour is observed for scattering of
electrons, neutrons by nuclei and crystals etc.
Wavelength of particle given by the de Broglie relationship:-
h
hc
l 
2
2 4
p
ET  m c
Eg. A 1GeV electron has a wavelength (1.23 fm) about the
same as the diameter of a nucleon.
( note:- for ET >> mc2 , l = l photon with same ET )
QtoQ06-ju
Accelerator -1
CERN
LEP
e+eUp to~
200GeV+200GeV
LHC
Pp
8Tev+8Tev
8.6 km
diameter
CERN photo
QtoQ06-ju
Accelerator -2
CERN
LEP
LHC
Tunnel
Beam pipes etc under construction
CERN photo
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Detectors - ATLAS at CERN
physicist
CERN photo
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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
QtoQ06-ju
the leptons – charge and mass
MeV/c2
m/mproton
-e
0.511
0.0055
ne
0
~0
mu-minus
m
-e
105.66
mu-neutrino
nm
0
0
tau-minus
t
-e
1777
tau-neutrino
nt
0
~0
symbol
charge
electron
e-
electron neutrino
name
0.1126
1.894
QtoQ06-ju
anti-leptons- charge and mass
name
symbol
charge
e-plus or positron
e+
+e
electron antineutrino
ne
0
mu-plus
m+
+e
mu antineutrino
nm
0
tau-plus
t+
+e
tau antineutrino
nt
0
mass
MeV/c2 m/mproton
0.511
0.0055
~0
105.66
0.1126
~0
1777
~0
1.894
QtoQ06-ju
Classification of particles – particles/anti particles
Origin:- particles of exactly the same mass but opposite charge
Later found to have other quantum numbers with opposite
values
Symbol:- either
the electric charge as a superscript eg: p- and p+, e- and e+
or
particle
P
anti-particle
P
(often said as P-bar)
Neutral particles/anti-particles:some are the same (Majorana) eg p0 and
some are different (Dirac) eg neutron, neutrino
QtoQ06-ju
The first anti-particles:- positrons, 1932 - Anderson
63 MeV positron
upwards emerges with
23 MeV)
3 electrons (bend to left) and
3 positrons ( bend to right)
QtoQ06-ju
lepton numbers
lepton number
lepton
le
lm
lt
anti-lepton
number
le lm lt
electron
e-
1
0
0
-1
0
0
electron neutrino
ne
1
0
0
-1
0
0
mu
m
0
1
0
0 -1
0
mu-neutrino
nm
0
1
0
0 -1
0
tau
t
0
0
1
0
0 -1
tau-neutrino
nt
0
0
1
0
0 -1
QtoQ06-ju
Decay p+ => m+ => e+
m+ => nm + e+ + n e
p+ => m+ + nm
Note lepton numbers are conserved
QtoQ06-ju
quarks – charge and mass
name
symbol
charge
e
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
QtoQ06-ju
q = +2e/3 q = -e/3
Quark picture 1983
according to
Frank Close
“Cosmic Onion”
Heinemann Educational
Books
1983
Top-quark found 1995
QtoQ06-ju
Anti-quark - charge and mass
name
symbol
charge
e
mass
MeV/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
QtoQ06-ju
quarks – flavour numbers
quark flavour
numbers
qd qu q s qc qb qt
quark
anti-quark flavour
numbers
q d 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
QtoQ06-ju
leptons and quarks - masses
p
Generations
1
2
3
QtoQ06-ju
Fundamental forces
force
exchange
boson
"charge"
range
mass
m/mp
how many
different
kinds?
gravity
graviton
mass
infinite
zero
one
electromagnetic
photon
electric
infinite
zero
one
three
eight
weak
Fundamental
strong
W+
WZ0
weak
1 am
85.7
85.7
97.2
gluon
colour
infinite
zero
QtoQ06-ju
forces acting between particles
gravity
weak
strong
y
electromagnetic
y
charged leptons
y
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
n
QtoQ06-ju
Conservation laws - 1
The following quantities are conserved in all interactions
Ie:- the total before must be the same as the total afterwards
•
•
•
•
Charge
Energy
Linear momentum
Angular momentum
QtoQ06-ju
Conservation laws - 2
The following quantities are conserved in interactions as
indicated:- S strong; E electromagnetic; W weak
•
•
•
•
S
Baryon number
y
Lepton flavour numbers y
Quark flavour numbers y
Colour
y
E
y
y
y
n/a
W
y
y
n
n/a
QtoQ06-ju
Classification of particles:
photons, leptons, mesons and baryons
• Originally described mass.
–
–
–
–
Photons
Leptons
Mesons
Baryons
no mass
light
medium
heavy
0.5 MeV/c2
100-500 MeV/c2
> 900 MeV/c2
Still useful:turns out that this also describes structure and quark content.
QtoQ06-ju
Classification of particles – baryons and mesons and hadrons
hadrons
Baryons
three quarks
or
three anti-quarks
(anti baryons)
Contain quarks
Mesons
a quark and
an anti-quark
QtoQ06-ju
Classification of particles – baryons and mesons and hadrons
hadrons
Baryons
Mesons
valence quarks
three quarks
or
three anti-quarks
(anti baryons)
gluons and
sea quarks
a quark and
an anti-quark
QtoQ06-ju
Baryons:- proton and the neutron
d
the proton uud
+ sea quarks and gluons
u u
the neutron udd
+ sea quarks and gluons
d
d u
QtoQ06-ju
mesons:- the pion family
p+
p0
p-
u:d-bar
u:u-bar
d:d-bar
u-bar:d
QtoQ06-ju
“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 colourless
Use 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
QtoQ06-ju
“colour - 2”
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
QtoQ06-ju
Classification of particles - generations
First generation:
Second generation:
Third generation:
leptons
quarks
 ne 
 
e 
 nm 
 
m 
u
 
d 
c
 
s 
 nt 
 
t 
t 
 
b
The upper member of each doublet is more positive
QtoQ06-ju
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”
QtoQ06-ju
Classification of particles – fermions and bosons
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.
QtoQ06-ju
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 :
spin 2:
-3/2, -1/2, +1/2, +3/2
-2, -1, 0, +1, +2
Are two different quantum states
+1/2
-1/2
QtoQ06-ju
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
QtoQ06-ju
Standard model and Nuclear Physics
The "strong nuclear force" is an exchange force
mediated by (mostly) pi-mesons:- p+ (u d ), p- (u d),
p0 ( mix of u u and d 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.
QtoQ06-ju
alpha decay – quantum tunneling
Nparent (Z,A) => Ndaughter(Z-2, A-4) + a + Q
Ea 
Qmd
md  ma
-log(t1/2)
Geiger–Nuttal rule:large Z, low Ea = long half-life
Gamow-Condon and
Gurney prediction based
on alpha tunneling .
Z
Ea
QtoQ06-ju
alpha decay – barrier penetration
Alpha pre-formed
in the nucleus
electrical potential of alpha in
field of daughter nucleus
energy
Energy of
emitted alpha
free
bound
alpha tunnels through
potential barrier –
a quantum effect
radial distance
QtoQ06-ju
beta decay – nuclear and nucleon level
Nuclear level
Beta minus decay
N*(A, Z) => N(A, Z+1) + e- + n e
Beta plus decay
N*(A, Z) => N(A, Z-1) + e+ + ne
Nucleon level –within a nucleus
n => p + e- + n e
p => n + e+ + ne
also for free neutron
QtoQ06-ju
beta decay – quark level
u => d + W+
b+ + ne
d
u
u
W+
d
u
d
b+
ne
QtoQ06-ju
beta decay – quark level
u => d + W+
b+ + ne
d
u
u
W+
Quark flavour
changed
d
u
d
b+
ne
lepton/antilepton pair
created
The END
not really, but I’ll stop here anyway
QtoQ06-ju
Exchange potential – Yukawa model
infinite range
potential p(r)
g
m  0 : p r  
r
short range
radial distance r
ger
m  0 : p r  
r

R
mc
R
QtoQ06-ju
Monte-Carlo simulation of nuclear decay
10 sided “dice” – “decay” on 1 and 2
Start with 100 “nuclei”
number surviving after N
throws
120
100
80
Series1
Series2
60
40
20
0
0
10
20
30
40
number of throws, N
Dice thrown for each nucleus until get 1 or 2 then go to next nucleus