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Quarks, Leptons and the Big Bang
2006. 12.12
particle physics
Study of fundamental interactions
of fundamental particles in
Nature
 Fundamental interactions

1. strong interactions
2. weak interactions
3. electromagnetic interactions
4. gravitational interactions
Gravitational force: very weak at atomic
scale
 Electromagnetic force: acts on all
electrically charge particles
 Strong force: the force binding nucleons
together
 Weak force: involved in beta decay
acts on all particles

Basic tools
Special relativity and Quantum
mechanics -> Relativistic Quantum
Field Theory
Schrodinger equation is valid only for
nonrelativistic particle.

What is a particle?
Pointlike object with no internal
structures. It is characterized by
mass and spin.
(cf. Baseball )
spin: intrinsic angular momentum
spin without spin
can be nonzero without rotation in space

Spin statistics theorem
Particle can have either half-integer
spin or integer spin in units of h
 Particles with integer spin: Bosons
Particles with half-integer spin: Fermions
 Fermions should obey Pauli’s exclusion
principle. No two identical particles can
be at the same quantum state, while
bosons need not.

Fundamental Particles

Fermions : building blocks of matter
Paulis’s exclusion principle
leptons: electron(e), muon(  ), tau( )

 )
neutrinos( e
quarks: u
s
t
d
b
c
Strong force acts on quarks and not on
leptons(only weak force and possibly
electromagnetic force)
Bosons : mediating the forces between
fermions
photons (light) no self interactions
electromagnetic interactions
gluons : quarks, nuclear force

W, Z : weak interactions,  decay
gravitons : gravitational interactions
The emergence of the force
Qq
r2
Coulomb force
 When electrons emit and absorb
(virtual) photons, momentum transfer
occurs. Coulomb force is generated by
this process. Virtual photons are
those not satisfying energy-time
uncertainty relation Et  h
 All other forces arise in the same way

Relativistic Quantum Field Theory
Basic tools in theoretical particle physics
 Combination of special relativity and
the quantum
mechanics
2
p
-> E 2  p 2c 2  m2c 4
E 
2m
 particle and antiparticle (same mass, opposite
charge, opposite quantum numbers)
> 2mc 2 pair creation and annihilation occur
E
 infinite degrees of freedom
 strong, weak, electromagnetic interactions
well described-> standard model

Why are there more particles than
antiparticles?

Some processes and the
conservation laws of various kinds

Pair annihilation/pair creation
e e  



Charge conservation
p  p  4  4


Angular momentum and lepton number
conservation



  

decay process is a weak interaction
 Muon decay (separate lepton number
conservation is needed)
   e   e  
Baryon conservation law

Forbidden process
p  e

 e
Assign baryon number B=+1 to every baryon,
B=-1 for antibaryon
Hadrons
Bound states of quarks
loosely called particles
 Baryons (qqq): Fermions
ex) proton, neutron
Mesons ( qq ): Bosons
ex) pions, Kaons

Another conservation law
Strangeness (strange quark)
kaon and sigma always produced in pairs

  p  K 




process which does not occur
  p  



The above Kaon has S=+1 and sigma particle
has S=-1

Strangeness is preserved in strong interactions

Eightfold way ( hadrons with
u,d,s quarks)
Classification of 8 spin ½ baryons
and nine spin zero mesons
via charge and strangeness

u,d,s … quark flavors
 Why are quarks always bound?
quark confinement
 fractional charges for quarks
proton (uud), neutron (udd)

  (ud )
Using the eightfoldway, Gellman predicted
the existence of a new particle in a decuplet

Similar classification scheme can be
applied for hadrons involving c,b,t
quarks

Beta decay
d  u  e   e
n  p  e  e
Weak force mediated by massive
boson, short range force

h
h
t 

E m
W 80.6 GeV
Z 91 GeV
Strong force (color force)
Messenger particles are gluons
massless, quarks can have various
color charges (red, yellow, blue)
so can gluons in contrast with the
photons
 All hadron states are color neutral
(quark confinement)
Quantum chronodynamics (QCD)
 Linear potential V~kr (color tubes)

Strong forces are responsible for
quarks binding into baryons and
mesons. They make the nuclear binding
possible.
 Quantum Gravity
so far not by the relativistic quantum
field theory based on the point particle
but by the string theory

General Gravity

Special relativity+gravitation
matter and energy make spacetime
curved
Universe is expanding
Einstein’s greatest blunder(?)
:introducing the cosmological constant
for the Einstein’s field equation
(No static universe solution for Einstein’s
field equation)
 Hubble’s observation (1929)
All stars are moving away from us
Universe is expanding (everywhere)

v=Hr
H Hubble’s constant=71.0 km/s Mpc
1 Mpc=3 X 1019 km
 If H is constant, then the estimated
age of the universe is 1/H
( 13.7 X 10 9 year)
Based on the Big Bang scenario

Cosmic Background Radiation
The universe is filled with the 2.7 K
radiation (microwave region)
In the early universe, the temperature
is very hot and the atoms cannot be
formed. (kT=2m c 2 )
 After the atoms can be formed, lights can
be travelled without scattering much
about 379000 year old of the universe.)

If the cosmic background is too uniform
this will be problematic for structure
formation such as stars and galaxies.
 Such slight deviation from uniformity
has been observed indeed.
1992 Cosmic Backgrouns Explorer(COBE)
2003 Wilikinson Microwave Anisotropy
Probe (WMAP)

Brief history of the Universe
43
10
sec

concepts of the space and time
can have meaning
30
 10 34 sec inflation (factor of 10
)
4
10
sec Quarks can combine to form protons

and neutrons. Slight excess of matter

1min Low mass nuclei form
Universe is opaque
 379000 year Atoms form, light can travel farther
Black Holes
Gravitational field is so strong, once
the light is trapped it cannot escape.
Heuristically

GMm

 mc 2  0
r
GM
r  R
c2
R; black hole radius
For the mass of sun, R few km
(extremely dense object)
Black hole theormodynamics
Black hole has temperature and entropy
1
1. Black hole temperature
M
Black hole is not black
(Hawking radiation; black body
radiation with T  1
)

M
2. Black hole entropy is proportional
to the surface area S /(10 33 cm) 2
76
very large number 10
for a black
hole of solar mass
 Entropy ~ number of states (?)
 Classically black hole has few
parameters
(mass, charge and angular momentum)