Download - Introduction to particle physics
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:
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
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Units We use Gaussian units, thank you, Prof. Griffiths!
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
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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
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
Particle PhysicsAtomic Physics
Cosmology
Nuclear Physics
CM Physics
Particle colliders: the tools of discovery
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
CERN LHC videoPDG collider table
Particle detectors: the tools of discovery
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Atlas detector: assemblyFirst Ze+e- event at Atlas
Feynman diagrams
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
Professor Oleg Sushkov’s notes, pp. 36-42:http://www.phys.unsw.edu.au/PHYS3050/pdf/Particles_classification.pdf
Feynman diagrams
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Oleg Sushkov
Feynman diagrams
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Oleg Sushkov
Feynman diagrams
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Oleg Sushkov
Feynman diagrams
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Oleg Sushkov
Running coupling constants
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Renormalization……unification?
* No hope of colliders at 1014 GeV ! need to learn to be smart!
The atmospheric muon “paradox”
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Mean lifetime: = 2.19703(4)×10−6 s
c 6×104 cm = 600 m
How do muons reach sea level?
Relativistic time dilation
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…
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
If we fire photons heads on, what is their relative speed?
Moving shadows, scissors,…
Garbage (IMHO): superluminal tunneling
Confusing terminology (IMHO): “fast light”
Lorentz transformations: Griffiths’ 3 things to remember
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
• Moving clocks are slower (by a factor of > 1)
• Moving sticks are shorter (by a factor of > 1)
•
Lorentz transformations: seen as hyperbolic rotations
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Rapidities:
t
x
αstationary
moving
Symmetries, groups, conservation laws
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
• Symmetry: operation that leaves system “unchanged”
• Full set of symmetries for a given system GROUP
• Elements commute Abelian group
• Translations – abelian; rotations – nonabelian
• Physical groups – can be represented by groups of matrices
• U(n) – n n unitary matrices:
• SU(n) – determinant equal 1
• Real unitary matrices: O(n)
• SO(n) – all rotations in space of n dimensions
• SO(3) – the usual rotations (angular-momentum conservation)
*1 ~UU
OO ~1
Angular Momentum
First, a reminder from Atomic Physics
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
35
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
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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
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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 1
2
0
1 2( 1) 1(2 1)2
n
l
nl n n
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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
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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
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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
Further separation:
Spherical functions
(Harmonics)
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Wavefunctions of the H atom (cont’d)
Legendre Polynomials
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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
Experiment: electron is pointlike down to ~ 10-18 cm
cm 109.3 (1,2) Eqs. ,~ have weIf
(2) ~ocity linear vel hasobject theof surface Thefinite want we,Presumably
(1) ~
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cωr
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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)
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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
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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
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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
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Electron spin and fine structure (cont’d)
In analogy, there is also spin magnetic moment :
Bohr magneton
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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
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Electron spin and fine structure (cont’d)
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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
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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
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Vector model of the atom Some people really need pictures… Recall: for a state with given j, jz
We can draw all of this as (j=3/2) 0; = ( 1)x yj j j j 2j
mj = 3/2 mj = 1/2
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Vector model of the atom (cont’d)
These pictures are nice, but NOT problem-free Consider maximum-projection state mj = j
Q: What is the maximal value of jx or jy that can be measured ?
A: that might be inferred from the picture is wrong…
mj = 3/2
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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…
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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 withfixed quantum numbers |l,ml,s,ms This is NOT an eigenstatebut a coherent superposition of eigenstates, each evolving as Precession Quantum Beats l , s precess around j with freq. = fine-structure splitting
Angular Momentum addition
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
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!
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Example: a two-electron atom (He) Quantum numbers:
J, mJ “good” no restrictions for isolated atoms
l1, l2 , L, S “good” in LS coupling ml , ms , mL , mS “not good”=superpositions
“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)
Vector Model
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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
Angular Momentum addition
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Flavor Symmetry
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
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:
Not in real space! No Never mind terminology: isotopic, isobaric Strong interactions are invariant w.r.t. isospin
“projection”
10
01
np
Flavor Symmetry
Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html
Nucleons are isodoublet Pions are isotriplet:
Q: Does the whole thing seem a bit crazy? It works, somehow…
110111 0
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:
110111 0
Redundant slide
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
Proton and neutron properties