Download Introduction to particle physics

Physics 129, Fall 2010; Prof. D. Budker
Some introductory thoughts
Reductionists’ science
 Identical particles are truly so (bosons, fermions)
 We will be using (relativistic) QM where initial
conditions do not uniquely define outcome:

     

99.988%
        
  e 


e
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Units

We use Gaussian units, thank you, Prof. Griffiths!
2
q1q2
e
1
Yes Gaussian : F  2 ,  

r
c 137
1 q1q2
No SI :
F
,
2
40 r
No HL :
No
1 q1q2
F
,
2
4 r
  c  1 or atomic units (  e  1)
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Useful resource:

Particle Data Group: http://pdg.lbl.gov/

The Particle Data Group is an international
collaboration charged with summarizing Particle
Physics, as well as related areas of Cosmology and
Astrophysics. In 2008, the PDG consisted of 170
authors from 108 institutions in 20 countries.

Order your free Particle Data Booklet !
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The Standard Model
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The Standard Model
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The Standard Model
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The Standard Model
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The Standard Model
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Composite particles: it’s like Greek to me
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
In the beginning…
First 4 chapters in Griffiths --- self review
 We will cover highlights in class
 Homework is essential!
 Physics Department colloquia and webcasts


Watch Frank Wilczek’s Oppenheimer lecture

Take advantage of being at Berkeley!
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The Universe today: little do we know!
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Nuclear Physics
Atomic Physics
Particle Physics
CM Physics
Cosmology
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Particle colliders: the tools of discovery
PDG collider table
CERN LHC video
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Particle detectors: the tools of discovery
Atlas detector: assembly
First Z e+e- event at Atlas
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Feynman diagrams
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Feynman diagrams
Professor Oleg Sushkov’s notes, pp. 36-42:
http://www.phys.unsw.edu.au/PHYS3050/pdf/Particles_classification.pdf
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Feynman diagrams
Oleg Sushkov
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Feynman diagrams
Oleg Sushkov
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Feynman diagrams
Oleg Sushkov
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Feynman diagrams
Oleg Sushkov
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Running coupling constants
Renormalization……unification?
* No hope of colliders at 1014 GeV !
need to learn to be smart!
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
The atmospheric muon “paradox”
Mean lifetime:
c
= 2.19703(4)×10−6 s
6×104 cm = 600 m
How do muons reach sea level?
Relativistic time dilation
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Lorentz transformations
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Lorentz transformations: adding velocities
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
By the way…

If we fire photons heads on, what is their
relative speed?

Moving shadows, scissors,…

Garbage (IMHO): superluminal tunneling

Confusing terminology (IMHO): “fast light”
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Lorentz transformations: Griffiths’ 3 things to remember
• Moving clocks are slower (by a factor of
> 1)
• Moving sticks are shorter (by a factor of
> 1)
•
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Lorentz transformations: seen as hyperbolic rotations
Rapidities:
x
moving
α
t
stationary
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Symmetries, groups, conservation laws
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Symmetries, groups, conservation laws
• Symmetry: operation that leaves system “unchanged”
• Full set of symmetries for a given system
• Elements commute
GROUP
Abelian group
• Translations – abelian; rotations – nonabelian
• Physical groups – can be represented by groups of matrices
• U(n) – n
n unitary matrices:
~*
U U
1
• SU(n) – determinant equal 1
• Real unitary matrices: O(n)
~
O O
1
• SO(n) – all rotations in space of n dimensions
• SO(3) – the usual rotations (angular-momentum conservation)
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Angular Momentum

First, a reminder from Atomic Physics
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Angular momentum of the electron
in the hydrogen atom

Orbital-angular-momentum quantum number l = 0,1,2,…

This can be obtained, e.g., from the Schrödinger Eqn., or
straight from QM commutation relations
The Bohr model: classical orbits quantized by requiring
angular momentum to be integer multiple of 
There is kinetic energy associated with orbital motion 
an upper bound on l for a given value of En
Turns out: l = 0,1,2, …, n-1



35
Angular momentum of the electron
in the hydrogen atom (cont’d)




In classical physics, to fully specify orbital angular
momentum, one needs two more parameters (e.g., two
angles) in addition to the magnitude
In QM, if we know projection on one axis (quantization
axis), projections on other two axes are uncertain
Choosing z as quantization axis:
Note: this is reasonable as we expect projection
magnitude not to exceed
36
Angular momentum of the electron
in the hydrogen atom (cont’d)



m – magnetic quantum number because B-field can be
used to define quantization axis
Can also define the axis with E (static or oscillating),
other fields (e.g., gravitational), or nothing
Let’s count states:


m = -l,…,l i. e. 2l+1 states
l = 0,…,n-1  n 1
1  2( n  1)  1
2
(2
l

1)


n

n

2
l 0
37
Angular momentum of the electron
in the hydrogen atom (cont’d)


Degeneracy w.r.t. m expected from isotropy of
space
Degeneracy w.r.t. l, in contrast, is a special feature
of 1/r (Coulomb) potential
38
Angular momentum of the electron in
the hydrogen atom (cont’d)


How can one understand restrictions that QM puts on
measurements of angular-momentum components ?
The basic QM uncertainty relation
leads to
(and permutations)

We can also write a generalized uncertainty relation

between lz and φ (azimuthal angle of the e):
This is a bit more complex than (*) because φ is cyclic
With definite lz , cos  0

(*)
39
Wavefunctions of the H atom



A specific wavefunction is labeled with n l m :
In polar coordinates :
i.e. separation of radial and angular parts
Spherical
functions
(Harmonics)
Further separation:
40
Wavefunctions of the H atom (cont’d)
Legendre Polynomials
41
Electron spin and fine structure


Experiment: electron has intrinsic angular momentum -spin (quantum number s)
It is tempting to think of the spin classically as a spinning
object. This might be useful, but to a point
L  I ~ mr 2
(1)
Presumably , we want  finite
The surface of the object has linear vel ocity ~ ωr  c (2)

If we have L ~ , Eqs. (1,2)  r 
  c  3.9 10 11 cm
mc
Experiment: electron is pointlike down to ~ 10-18 cm
42
Electron spin and fine structure (cont’d)

Another issue for classical picture: it takes a 4π rotation
to bring a half-integer spin to its original state.
Amazingly, this does happen in classical world:
from Feynman's 1986 Dirac Memorial Lecture
(Elementary Particles and the Laws of Physics, CUP 1987)
43
Electron spin and fine structure (cont’d)

Another amusing classical picture: spin angular
momentum comes from the electromagnetic field of the
electron:

This leads to electron size
Experiment: electron is pointlike down to ~ 10-18 cm
44
Electron spin and fine structure (cont’d)

s=1/2 

“Spin up” and “down” should be used with understanding
that the length (modulus) of the spin vector is >/2 !

The square of the projection is always 1/4
45
Electron spin and fine structure (cont’d)

Both orbital angular momentum and spin have
associated magnetic moments μl and μs
Classical estimate of μl : current loop

For orbit of radius r, speed p/m, revolution rate is

Gyromagnetic ratio
46
Electron spin and fine structure (cont’d)
Bohr magneton

In analogy, there is also spin magnetic moment :
47
Electron spin and fine structure (cont’d)




The factor 2 is important !
Dirac equation for spin-1/2 predicts exactly 2
QED predicts deviations from 2 due to vacuum
fluctuations of the E/M field
One of the most precisely measured physical
constants: 2=2 1:001 159 652 180 73 28 [0.28 ppt]
Prof. G. Gabrielse,
Harvard
48
Electron spin and fine structure (cont’d)
49
Electron spin and fine structure (cont’d)





When both l and s are present, these are not conserved
separately
This is like planetary spin and orbital motion
On a short time scale, conservation of individual angular
momenta can be a good approximation
l and s are coupled via spin-orbit interaction: interaction of
the motional magnetic field in the electron’s frame with μs
Energy shift depends on relative orientation of l and s, i.e., on
50
Electron spin and fine structure (cont’d)






QM parlance: states with fixed ml and ms are no
longer eigenstates
States with fixed j, mj are eigenstates
Total angular momentum is a constant of motion of
an isolated system
|mj|  j
If we add l and s, j ≥ |l-s| ; j  l+s
s=1/2  j = l  ½ for l > 0 or j = ½ for l = 0
51
Vector model of the atom
Some people really need pictures…
 Recall: for a state with given j, jz

jx  j y  0;

j2 = j ( j  1)
We can draw all of this as (j=3/2)
mj = 3/2
mj = 1/2
52
Vector model of the atom (cont’d)


These pictures are nice, but NOT problem-free
Consider maximum-projection state mj = j
mj = 3/2


Q: What is the maximal value of jx or jy that can be
measured ?
A:
that might be inferred from the picture is wrong…
53
Vector model of the atom (cont’d)


So how do we draw angular momenta and coupling ?
Maybe as a vector of expectation values, e.g.,

Simple

Has well defined QM meaning
?
BUT


Boring

Non-illuminating
Or stick with the cones ?
Complicated
 Still wrong…

54
Vector model of the atom (cont’d)

A compromise :


j is stationary
l , s precess around j
What is the precession frequency?
 Stationary state –
quantum numbers do not change
 Say we prepare a state with
fixed quantum numbers |l,ml,s,ms
 This is NOT an eigenstate
but a coherent superposition of eigenstates, each evolving as
 Precession  Quantum Beats
  l , s precess around j with freq. = fine-structure splitting
55

Angular Momentum addition
Q: q + anti-q = meson; What is the meson’s spin?
 A:

 0 = ½ - ½ pseudoscalar mesons (π, K,
 1 = ½ + ½ vector mesons (ρ,

,
,
…)
Can add 3 and more!
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
’, …)
Vector Model


Example: a two-electron atom (He)
Quantum numbers:




“good” no restrictions
for isolated atoms
l1, l2 , L, S
“good” in LS coupling
ml , ms , mL , mS “not good”=superpositions
J, mJ
“Precession” rate hierarchy:


l1, l2 around L and s1, s2 around S:
residual Coulomb interaction
(term splitting -- fast)
L and S around J
(fine-structure splitting -- slow)
57
jj and intermediate coupling schemes




Sometimes (for example, in heavy atoms),
spin-orbit interaction > residual Coulomb  LS coupling
To find alternative, step back to central-field approximation
Once again, we have energies that only depend on electronic
configuration; lift approximations one at a time
Since spin-orbit is larger, include it first 
58
Angular Momentum addition
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Flavor Symmetry
Protons and neutrons are close in mass
 n is 1.3 MeV (out of 940 MeV) heavier than p
 Coulomb repulsion should make p heavier
 Isospin:
1
 0
p   
n   
 0
1

Not in real space!
 No
 Never mind terminology: isotopic, isobaric
 Strong interactions are invariant w.r.t. isospin
“projection”

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Flavor Symmetry
Nucleons are isodoublet
 Pions are isotriplet:

   11
 0  10
   1 1
Q: Does the whole thing seem a bit crazy?
 It works, somehow…

Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Oleg Sushkov:
Redundant slide
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Oleg Sushkov:
Redundant slide
   11
 0  10
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
   1 1
Proton and neutron properties
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Proton and neutron properties
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html