9 february 2011modern physics iii lecture 51 modern physics for frommies iii a universe of leptons,...

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9 February 2011 Modern Physics III Lecture 5 1 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary Particles Lecture 5 Fromm Institute for Lifelong Learning, University of San Francisco

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Page 1: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 1

Modern Physics for Frommies IIIA Universe of Leptons, Quarks and

Bosons; the Standard Model of Elementary Particles

Lecture 5

Fromm Institute for Lifelong Learning, University of San Francisco

Page 2: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 2

Agenda• Administrative Matters• Quantum Field Theories

• Second or Field Quantization• Electromagnetic InteractionElectromagnetic Interaction• Weak Interaction• Strong Interaction

• Patterns and Symmetries in Nature

Page 3: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 3

Administrative Matters

•Full schedule of colloquia is posted on the Wiki and should be posted in Fromm Hall•A list of popular books pertaining to Elementary Particle Physics is posted on the Wiki. It will be updated when appropriate.

Page 4: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 4

Exchange vector bosons form a T =1 triplet

W+ (T3 = +1) is emitted in transitions {(T3 = +1⁄2) → (T3 = −1⁄2)} W− boson (T3 = −1) is emitted in transitions {(T3 = −1⁄2) → (T3 =+ 1⁄2)}.

0

3

03

3

1

or 0

1

W

W

W

TW

W T

W T

W0 rather than Z0 for technical reasons involving electro-weak unification

d uW

W e

e.g. decay

Page 5: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 5

It took a great deal of effort to get a renormalizable electro-weak QFT

Sheldon Glashow Abdus Salam Steven Weinberg1926 - 1996

1979 Nobel Prize

Page 6: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 6

Strong Interaction:

1911 Rutherford discovers the nucleus

1932 Chadwick discovers the neutron→ Nucleus is protons + neutrons

A little history:

What holds the nucleus together?

Need a strong but short range force.

2 2

SI SI 2( ) or ar arg g a

V r e F er r

1935 Yukawa potential

P+

P+

Could be mediated by a scalar boson of mass 200 me

Muon, not it.

1947 Powell et al. discover pion, in cosmic rays

Page 7: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 7

Hideki Yukawa1907 -1981

1949 Nobel Prize

In the 1960s both theory and experiment began to substructure to “elementary” particles

Partons: quarks, antiquarks and gluons

Update Yukawa’s picture

Page 8: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 8

Simple Quark Model (no color):

u

u

d

Arrows are quark spins

Sq = 1/2u

d

d

Baryons:

Proton Neutron

Mesons:

u d d uu u

or dd

Page 9: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 9

Color and Color Charge: Color was originally introduced to beat the Pauli principle.

u

u

u

3 2s

Arrows are quark spins

Sq = 1/2 Clearly Pauli blocked

u

u

uAdd a new number, color

Mrs. Pauli’s favorite son is now happy!

There are also anticolors for the antiquarks

Page 10: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 10

Theory of strong interactions between quarks is called quantum chromodynamics (QCD)

Mediated by force carriers called gluons

Bound states: color - color meson

3 3 different colors baryon

3 3 different colors antibaryon

qq

q

q

Note that in all of the above the colors add up to “white”. Color is not observed in our “usual” particles (p, n, , K etc.).

Gluons: 8 of them carrying both color and anticolor

rb

BLUE ANTIRED GLUON

Page 11: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 11

From the 3 color states, one can form 9 bicolor color - anticolor states

,

,

,

,

,

,

B

B BB

G

G

G G

RR R R

B

B

R

R GG

Removing the colorless state of the trace reduces us to 8 combinations which exchange color between quarks

Confinement: Why don’t we see free quarks?

Gluons themselves carry color charge (unlike the photon which is electrically neutral). They participate in strong interactions.

These g – g interactions constrain color fields to string like objects, flux tubes.

Page 12: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 12

Stretching the tube requires more and more energy

At some distance it is energetically more favorable to pull a pair out of the vacuum than to increase the tubelength.

qq

0e p K

0

(4) An pair is

(5)

(1-3) strikes e

quarks rearrange

xciting

into co

cre

the

qua

lor

r

singlets, an

a

d

k

ted

e p

d

s

K

s

Page 13: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 13

Color Screening and Running Coupling Constants:

In QED we had some trouble with loop diagrams.

We fixed this up by invoking the dressing or screening of the bare electron

Vacuum polarization or charge screening reduces the observed charge.

As we increase probe energy (probe shorter distances) the observed charge grows

The EM, EM, coupling constant increases with energy

What happens in QCD?

Page 14: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 14

In QCD the virtual gluons emitted by quarks not only create pairs but also more gluons with all the allowed bicolor signatures

qq

In QCD the virtual quark-antiquark pairstend to screen the color charge. However, QCD has an additional wrinkle: its force-carrying particles, the gluons, themselves carry color charge, and in a different manner. Each gluon carries both a color charge and an anti-color magnetic moment. The net effect of polarization of virtual gluons in the vacuum is not to screen the field, but to augment it and affect its color. This is sometimes called antiscreening. Getting closer to a quark diminishes the antiscreening effect of the surrounding virtual gluons, so the contribution of this effect would be to weaken the effective charge with decreasing distance.

1 Fermi = 1 fm = 1x10-15 m

Page 15: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 15

Page 16: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 16

H. David Politzer Frank Wilczek David Gross

Nobel Prize 2004

Asymptotic freedom

Page 17: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 17

Patterns and Symmetries in Nature

Our normal space E3, Physics doesn’t change when moved. It is invariant under translation and rotation.

Symmetry groupsGroup: A set of elements closed under a prescription relating the elements. e.g. and in the group in the group a b a b

is associative but not necessarily commutative A unit element 1 a a a 1 1

Each element has an inverse a-1 aa-1 = 1

Examples: The integers form a group under addition, 1 + 3 =4.

Hours on a clock. A finite number of elements (12).1 = 12 because h +12 = h

If h = 1, h-1 = 11 because 1 + 11 =12 = 1

Page 18: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 18

In Physics, groups are associated with manipulations, e.g translation and rotation

Translation group: Carry from here to there Rotation group: Rotate so much about a specified axis.

Things that remain the same when manipulated by an element are said to be symmetrical.

Examples: A sphere under all rotations. A cube under 90° rotations about 3 specific axes. A shoe is not symmetric but a pair is.

Approximate symmetries: Still useful. The Earth is not a perfect sphere but can often be treated as one.

Some groups can be shown to be equivalent, e.g. group of rotations of 30° is equivalent to the clock number group above.

Representation specific instance of a group, e.g. the clock numbers are a representation of the 2-D 30°rotation group

Page 19: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 19

Rotations in a plane commute or are Abelian.

NOW RESTRICT OURSELVES TO FINITE GROUPS

The elements of a represntation are classified into multipletse.g. A sphere is a singlet under rotation

A square in a plane is a quartetAn equilateral triangle in a plane is a tripletA cube about 3 orthogonal axes is an octet

All 1-D groups are Abelian

Finite 3-D rotations are non-Abelian, see Rubik’s Cube

Invariants: Symmetries leave something unchanged. e.g. translation maintains the distance between points, r2 = x2 + y2.

a conserved quantity, . Rotations preserve distances and anglesp

conserved quantity, L

Page 20: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 20

Symmetries in Relativity:

The frame independence of c a “super distance” in 4-D spacetime which is invariant under a corresponding “super rotation”. This is the 4-length or interval 2 2 2 2s x y z

The super rotations are of course the Lorentz trnsforms a.k.a. the Lorentz group.

Quantizing Spin: Magnetic fields with their “vector product behavior” arise from the spin of the exchanged The occurrence of both repulsive and attractive forces also requires consideration of the exchanged spin (the ball throwing analogy breaks doen here).

Recall the wave justification of Bohr’s quantization rule: must be a standing wave around the equator.

Page 21: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 21

22 1,2,3, and =r n n

mv

mvr n

Angular momentum

S n

We are dealing here with the rotation of the particle itself so we have the spin angular momentum

It doesn’t matter that we have used a finite radius for the path of this phase measurement; This is merely an accounting device for the phase, a pure number independent of physical size.

Now suppose we measure the phase for multiple loops around the equator

rotation 1 revolution = 2radians = 360°Corresponds to 1 complete wavelength n = 1

Phase Wheel

marker

Page 22: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 22

Our requirement is just that the path closes after an integral number n of revolutions of the wheel.

This could easily well happen going around the equator twice

Suppose n is even, say n = 4

13

24

n = 4 Clearly mark 3 coincides with 1 and 2 with 4

Superposition of two indistinguishable paths each with n/2 wavelengths

n even n/2 = m is also an integer

We end up with a class of particles with spin quantized according to

S m just as before

Page 23: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 23

1 2

3n = 3

Now let n be an odd integer, say 3

The pair wise coincidence is replaced by an anticoincidence

Each mark on the 2nd loop is midway between 2marks on the 1st.

The 2 loops are not the same. We obtain a class of particles with an equatorial circumference of n2 with quantized spin

odd2

nS n

This process can be generalized to more looping of the phase wheel.The above 2 classes of particles are the only 2 that appear and are the bosons and fermions respectively.

Page 24: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 24

Boson: Phase wrapping is a simple circle. A boson turned 360° is indistinguishable from its original

Space is rotationally symmetric so no surprise that 360° turns a particle into itself

Fermion: Phase wrapping consists of 2 different loops. A fermion turned 360° does not turn into itself. Instead it requires a turn of 720°. So, what state do we obtain with a 360° rotation?

360°does not return the same amplitude but we really believe space to be rotationally symmetric.

Only way out appears to be → - for a fermion turned through 360°

Remember, we don’t observe amplitudes only probabilities (P). 2 2

P

Page 25: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 25

What happens if we superpose 2 indistinguishable particles. Distinguishable different quantum numbers, momenta or positions

2 particles in a 1-D box. In analogy to going to a higher D box

1 2 1 21 2 1 2( , )n n n nx x x x

Particles are identical so we actually have to write

1 2 1 2 2 11 2 1 2 1 2

1( , )

2n n n n n nx x x x x x

bosons

fermions

For fermions: ( , ) 0nn x x

Page 26: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 26

Truly identical fermions cannot exist.

Forces fermions to aggregate in finite sized lumps when piled together

Prevents fermions from building up large scale coherent fields when exchanged as virtual particles

Identify fermions with matter

Bosons have no objection to being identical

Bosons aggregate together in the lowest allowed energy state without building up finite sized lumps.

Responsible for phenomena such as superconductivity and superfluidty.

Identify bosons with forces

Page 27: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 27

Fermion Boson? Demo with string

Have to change the topology of the phase path.

Unless you are allowed to go outside the plane you cannot make these transformations

Unless you can step out of space into another dimension, you can never change fermion to boson or vice–versa.

It can be shown formally that, unless the universe has extra freedom beyond space-time, spin can only change in whole units of ħ.

Page 28: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 28

Polarization and Gauge Invariance:A particle with non-zero-spin can have a certain orientation in space called the polarization.

Pick a fixed, but otherwise arbitrary, direction (call it the z-axis)

s = 1/2 ms = +1/2

ms = -1/2 s = 1

ms = +1

ms = 0

ms = -1For a given value of s, there are 2s + 1 values for ms ranging from s to –s in steps of 1.

Page 29: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 29

Examples of picking a z-axis:Apply a magnetic or electric fieldDirection of motionThe line drawn in the sand by Col. Travisetc.The choice of a direction is called fixing a gauge and the fact that the Physics is independent of this choice is called gauge invariance

Zero mass particles: e,g, 2 2 2 2Lorentz symmetry is invariants x c t

2 4 2 2 2so is m c p c E Let m → 0, so we get E = pc, and apply E = hf and p = h/

pc = hf = (h/c or c =f a wave propagating with velocity c

Page 30: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 30

Now, let’s fix the gauge so that the z-axis is in the direction of motion. This is called the radiation gauge or helicity frame.

c

ms = -1 ms = 0 ms = +1

A particle with zero rest mass can only have 2 degrees of spin freedom. Similarly the handedness of a massless particle cannot be reversed.

ms = -1/2 ms = +1/2

c

Page 31: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 31

We have seen that the laws of relativity and the law of spin and statistics are consequences of the Lorentz invariance of space time.

Can we extend the use of symmetries to Multiplets forces, i.e. the way in which fermions and bosons couple at a vertex

Multiplets: Sets of things that have something in common.

Singlet an object that is not changed under a symmetry operation e.g. a circle is a singlet under rotation, a square is a singlet under rotations of 90°

Doublet a pair of objects that transform into each other. e.g. p,n are a doublet under 180° rotations in strong isospin space.

etc..

Page 32: 9 February 2011Modern Physics III Lecture 51 Modern Physics for Frommies III A Universe of Leptons, Quarks and Bosons; the Standard Model of Elementary

9 February 2011 Modern Physics III Lecture 5 32

Rx for invoking a symmetry group at a vertex:

1) Identify or postulate a set of N fermions that are observed, or expected, to act as a ‘fundamental’ multiplet. N is the dimension of a symmetry group G, and the set of fermions is an N-plet under G.

2) An operation from G when applied to a member of the N-plet transmutes it into another member.

3) Every transmutation is interpreted as being due to the emission or absorption of a field boson (aka a gauge boson).

e.g. e is a fermion that cannot be changed into something else electromagnetically it is a singlet under some 1-D group, call it U(1)

There is only one boson associated with the group, .