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!

)1( units atomicor 1 No

,41 :HL No

1 :SI No

1371, :Gaussian Yes

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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 !

The Standard Model

Composite particles: it’s like Greek to me

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!

The Universe today: little do we know!

Particle PhysicsAtomic Physics

Cosmology

Nuclear Physics

CM Physics

Particle colliders: the tools of discovery

CERN LHC videoPDG collider table

Particle detectors: the tools of discovery

Atlas detector: assemblyFirst Ze+e- event at Atlas

Feynman diagrams

Professor Oleg Sushkov’s notes, pp. 36-42:http://www.phys.unsw.edu.au/PHYS3050/pdf/Particles_classification.pdf

Feynman diagrams

Oleg Sushkov

Feynman diagrams

Oleg Sushkov

Feynman diagrams

Oleg Sushkov

Feynman diagrams

Oleg Sushkov

Running coupling constants

Renormalization……unification?

* No hope of colliders at 1014 GeV ! need to learn to be smart!

The atmospheric muon “paradox”

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

Lorentz transformations: adding velocities

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”

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)

Lorentz transformations: seen as hyperbolic rotations

Rapidities:

αstationary

moving

Symmetries, groups, conservation laws

• 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

Angular Momentum

First, a reminder from Atomic Physics

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

(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

(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

1 2( 1) 1(2 1)2

nl n n

(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

(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

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)

Wavefunctions of the H atom (cont’d)

Legendre Polynomials

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

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)

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

“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

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

In analogy, there is also spin magnetic moment :

Bohr magneton

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

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

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

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

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

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

Boring

Non-illuminating

Or stick with the cones ? Complicated Still wrong…

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

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!

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

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

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:

Not in real space! No Never mind terminology: isotopic, isobaric Strong interactions are invariant w.r.t. isospin

“projection”

Flavor Symmetry

Nucleons are isodoublet Pions are isotriplet:

Q: Does the whole thing seem a bit crazy? It works, somehow…

110111 0

Oleg Sushkov: Redundant slide

Oleg Sushkov:

110111 0

Redundant slide

Proton and neutron properties

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