Elementary Particles

Fundamental forces in Nature

Ch 43

Finer Structure observed

As the momentum of a particle increases, its wavelength

decreases, providing details of smaller and smaller structures:Cf: the Heisenberg microscope

1) Deep Inelastic Scattering (similar to Rutherford scattering); seeing smaller details

"for his pioneering studies of

electron scattering in atomic nuclei

and for his thereby achieved discoveries

concerning the structure of the nucleons"

The Nobel Prize in Physics 1961

Robert Hofstadter

l (20 GeV) ~ 10-16 m

2) With additional kinetic energy more massive particles can be produced: particle physics =

high energy physics

Cyclotron/Synchrotron

Charged particles are maintained in

near-circular paths by magnets, while

an electric field accelerates them

repeatedly. The voltage is alternated

so that the particles are accelerated

each time they traverse the gap.

High-Energy Particles and Accelerators

The Nobel Prize in Physics 1939

"for the invention and development

of the cyclotron and for results

obtained with it"

Ernest Lawrence

The Nobel Prize in Chemistry 1951

"for the chemistry of

transuranium elements"

Inventor of the synchrotron

Edwin McMillan

Cyclotron Frequency

Lorentz force keep the particles in orbit

(via magnetic Field)

Alternating electric field accelerates the particles

qvBr

mvFc

2

m

qBrv

Period of revolution:qB

m

mqBr

r

v

rT

2

/

22

Required field acceleration frequency

m

qB

Tf

2

1

Kinetic energy

m

RBqmvK

22

1 2222

Small cyclotron: R=25 cm, B=1.7 T

f=26 MHz (RF)

K=8.7 MeV (non-relativistic)

(Note: Voltage does not appear)

Synchrotron: relativistic speeds

(Note: Radiation problem/ energy loss

The principle of particle “creation”

Based on:2mcE

LHC CERN

Mproton ~ 1 GeV

Collision energy =

2 x 7 TeV

Sufficient for

15000 protons

The electromagnetic force acts over a distance – direct contact

is not necessary. How does that work?

Because of the wave–particle duality, we can regard the

electromagnetic force between charged particles as due to:

1. an electromagnetic field, or

2. an exchange of photons.

Particle Exchange

Visualization of interactions using Feynman diagrams

The photon is emitted by one electron and absorbed by the other; it is

never visible and is called a virtual photon. The photon carries the

electromagnetic force.

Originally, the strong force was thought to be carried by mesons. The

mesons have nonzero mass, which is what limits the range of the force, as

conservation of energy can only be violated for a short time.

Virtual particle limited energy

Limited lifetime

Maximum distance travelled (Range)

Particle Exchange

2~

mct

Et

mctcx

~

Electromagnetism

Gravitation

Infinite range

m = 0 Strong force

Weak force

Finite range

m ≠ 0

The mass of the meson can be calculated,

assuming the range, d, is limited by the

uncertainty principle:

For d = 1.5 x 10-15 m, this gives 130

MeV.

Particle Exchange

Yukawa predicted a particle that

would mediate the strong forces

in the bonding of a nucleus: M ~ 100 MeV

(Yukawa assumed: d = 2 fm)

Later is was found: m(+)=m(-)=140 MeV/c2

m(0)=135 MeV/c2 Hideki Yukawa

The Nobel Prize in Physics 1949

"for his prediction of the existence

of mesons on the basis of

theoretical work on nuclear forces"

(NOT the muon with 106 MeV/c2)

IntermezzoWave equations, quantum fields

Schrödinger equation

free particle

non-relativistic

time-dependent

txt

itxxm

,,2 2

22

xip

ˆ

tiE

ˆ

txEtxm

p,,

2

ˆ 2

Operators

Relativistic analog for the energy txEtxcmtxpc ,ˆ,,ˆ 24222

txt

txcmtxx

c ,,,2

2242

2

222

Or (use operators):

Klein-Gordon equation: valid for spinless massive particles

“Similar”

relativistic wave equation

for particles with spin tx

titxmctx

xci

ii ,,, 2

for “spinor”

wave functions

Dirac equation: valid for massive particles with spin

IntermezzoInteractions via virtual particles

2

22

2

2

2

2 1

cm

tc

Klein-Gordon equation

(rewrite and 3-dimensional)

0mMassless 01

2

2

2

2

tc

This is the classical wave equation

for electromagnetism:

Photons are the (virtual) partciles

mediating the force

Static problem: 01 2

2

2

dr

dr

dr

d

r

Solution:

r

e

0

2

4

mm Mass Solution:

r

eg

rr '/2

with:cm

r

'

Concept of the Yukawa potential-mesons mediate the nuclear force

(“residual strong force”)

Strong force: The meson was soon discovered, and is called the pi

meson, or pion, with the symbol π.

Pions are created in interactions in particle accelerators. Here are

two examples:

Particle Exchange

The weak nuclear force is also carried by particles; they are called

the W+, W-, and Z0. They have been directly observed in

interactions.

A carrier for the gravitational force, called the graviton, has been

proposed, but there is as yet no theory that will accommodate it.

(Note, mesons not the true carriers gluons)

four known forcesrelative strengths for two protons in a nucleus, and their field particles

Particle Exchange

Intermezzo

Relativistic quantum fields and antiparticles

txt

txcmtxx

c ,,,2

2242

2

222

Klein-Gordon equation:

For every solution (E, p)

tiExp

iNtx p

exp,

There is also a solution:

tiExp

iNtxtx p

exp,,

~ **

Corresponding to negative energy and momentum -p 24222 mccmcpEE p

Note: Dirac equation more elegant: four solutions found :

two with positive energy, two with negative energy

For each spin= ½ and spin = -½ The Nobel Prize in Physics 1933

"for the discovery of new

productive forms of atomic theory"

Interpretation by Dirac Anti-particle

Intermezzo

The Dirac SeaQuestion; What are those negative energy states ?

Vacuum:All the negative energy states are normally filled

The vacuum is a “sea of electrons”

Pair creation

Pauli principle

Fermi-energy level

Choice of zero-level for energy

A photon excites an electrom from the vacuum

A positron is a hole in the electron sea

cf: semi-conductors

The positron is the same as the

electron, except for having the

opposite charge (and lepton

number).

Every type of particle has its own

antiparticle, with the same mass

and most with the opposite

quantum number.

A few particles, such as the photon

and the π0, are their own

antiparticles, as all the relevant

quantum numbers are zero for

them.

Particles and Antiparticles

bubble chamber photograph

incoming antiproton and a proton

(not seen) that results in the creation

of several different particles and

antiparticles.

In the study of particle interactions, it was found

that certain interactions did not occur, even

though they conserve energy and charge, such as:

A new conservation law was proposed: the

conservation of baryon number. Baryon number is a

generalization of nucleon number to include more

exotic particles.

+ Conservation of

Energy, Momentum, Angular momentum, Charge

Particle Interactions

and Conservation Laws

Concept of Particle Physics: Isospin

- Protons and neutrons undergo the same nuclear force

- No need to make a distinction between the two

- There is just a two-valuedness of the same particle

Define protons and neutrons as identical particles

But with different quantum numbers

Isospin I = ½ , MI = + ½ for proton

MI = - ½ for neutron

Importance of symmetry in particle physics

Intermezzo

Baryon Number:

B = +1; protons, neutrons,

B = -1; anti-protons, anti-neutrons

B = 0 : electrons, photons, neutrino’s (all leptons and mesons)

Conservation of Baryon number: principle of physics

Leptons :

- Electron

- Muon (about 200 times more massive)

- Tau (about 3000 electron masses)

Conservation of Lepton numbers; Le, Lm, Lt

Particle Interactions and Conservation Laws

Conservation of energy, momentum, and angular momentum

Noether theorems:

Conservation laws Fundamental symmetries in nature

Emmy Noether

This accounts for the following decays (weak interaction):

Decays that have an unequal mix of e-type and μ-type leptons are

not allowed.

(Neutrino-oscillations seem to suggest that this is not always

true; That is an unsolved question of contemporary physics)

Particle Interactions

and Conservation Laws

B=1, Le=0

B=0, Lm=0

Which of the following decay schemes

is possible for muon decay?

(a)

(b)

(c)

Left: Lm=1; Le=0

All of these particles have Lτ = 0.

Particle Interactions and Conservation Laws

Particle Classification

Bosons

Bosons

Fermions

Fermions

BE-FD

statistics

Note:

Fermions

obey

Pauli

principle !

Gauge bosons are the particles that

mediate the forces.

• Leptons interact weakly and (if

charged) electromagnetically, but not

strongly.

• Hadrons interact strongly; there are

two types of hadrons, baryons (B = 1)

and mesons (B = 0).

Particle Classification

Weak force

Strong force

Hadron decay Weak force

A Peculiarity of the weak force:

Parity nonconservation

Discuss : Real vectors vs. Axial vectors

Almost all of the particles that have been discovered are unstable.

Weak decay: lifetimes ~ 10-13 s

Electromagnetic: ~ 10-16 s

Strong decay: ~ 10-23 s.

Particle Stability and Resonances

The lifetime of strongly decaying particles is calculated from the variation

in their effective mass using the uncertainty principle.

These resonances are often called particles.

When the K, Λ, and Σ particles were first discovered in

the early 1950s, there were mysteries associated with

them:

• They are always produced in pairs.

• Never alone:

•They are created in a strong interaction, decay to

strongly interacting particles, but have lifetimes

characteristic of the weak interaction.

To explain this, a new quantum number, called

strangeness, S, was introduced.

Strangeness is not conserved in weak interactions

Partially conserved quantity

Strange Particles? Charm?

Toward a New Model

00 Kp

nKp 0

Particles such as the K, Λ, and Σ have S = 1 (and

their antiparticles have S = -1); other particles have

S = 0.

The strangeness number is conserved in strong

interactions but not in weak ones; therefore, these

particles are produced in particle–antiparticle

pairs, and decay weakly.

More recently, another new quantum number

called charm was discovered to behave in the

same way.

(Later: Bottomness, Topness)

Strange Particles? Charm?

Toward a New Model

Particle classifications; symmetry schemes

Quantum numbers, symmetries, and methods of “Group theory”: SU(3), SU(2), etc.

Meson octet Baryon decuplet

Murray Gell-Mann

The Nobel Prize in Physics 1969

"for his contributions and discoveries

concerning the classification of

elementary particles and their interactions"

Prediction of the W- particle;

observation after two years

So these symmetry models work !

quark compositions for some

baryons and mesons:

Quarks

Due to the regularities seen in the

particle tables, as well as electron

scattering results that showed

internal structure in the proton

and neutron, a theory of quarks

was developed.

There are six different “flavors”

of quarks; each has baryon

number B = ⅓.

Hadrons are made of three

quarks; mesons are a quark–

antiquark pair.

Table : properties of the six known quarks.

Quarks

Flavor Mass of the proton ?

hadrons that have been discovered

containing c, t, or b quarks.

Quarks

Truly elementary particles (having no internal structure):

quarks, the gauge bosons, and the leptons.

Three “generations” ; each has the same pattern of electric charge,

but the masses increase from generation to generation.

Quarks

Only three ?

Have we missed

the fourth because

of high mass ?

Three generations – Three families

Note: weak decay between families

Heavier families

are unstable

Cro

ss s

ect

ion

energy (GeV)

Z0 decays in

quark pairs

(no top quarks!)

lepton pairs

ee, mm, tt

neutrino pairs

Lifetime

1/t G with

G S GiSum over all decay channels

4th family entirely forbidden ?

Only three families, it seems

Soon after the quark theory was proposed, it was suggested that quarks have

another property, called color, or color charge.

Unlike other quantum numbers, color takes on three values. Real particles

must be colorless; this explains why only 3-quark and quark–antiquark

configurations are seen. Color also ensures that the exclusion principle is still

valid.

Color

The need for an additional quantum number (satisfy Pauli principle)

Otherwise uuu or ddd cannot exist ...

Baryons and mesons do not have color (white)

The color force becomes much larger as quarks separate; quarks are

therefore never seen as individual particles, as the energy needed to

separate them is less than the energy needed to create a new quark–

antiquark pair.

Conversely, when the quarks are very close together, the force is very

small.

Quantum Chromodynamics (QCD)

Quark Confinement

short

distance

large

distance

rTr

cU s

0color3

4

T0 0.9 GeV/fm

confinement

These Feynman diagrams show a quark–quark interaction mediated by

a gluon; a baryon–baryon interaction mediated by a meson; and the

baryon–baryon interaction as mediated on a quark level by gluons.

The “Standard Model”:

Quantum Chromodynamics (QCD) and gluons

time

The Electroweak Theory

Range of weak force.

The weak nuclear force is of very short range, meaning it acts

over only a very short distance. Estimate its range using the

masses of the W± and Z: m ≈ 80 or 90 GeV/c2 ≈ 102 GeV/c2.

Compare to Yukawa’s theory and analysis

n0

Kp0

0

eep n

mnm e

S 0

n SW 0

S 00

Consider the following decay reactions

Argue whether they are allowed or not

Based on the conservation laws

Not allowed; Energy conservation is violated;

E()=1115 MeV; E(p)=938 MeV; E(K)=493 MeV

Baryon number is not conserved

Not allowed; Charge conservation is violated; also strangeness.

Not allowed: Baryon number is violated

Spin is violated

Strangeness is violated

Electron leption number Le is not conserved

Strangeness is not conserved (still a possibility under weak decay)

Energy is not conserved; E()=1315 MeV; E(S)=1189 MeV; E()=140 MeV

Lepton number is not conserved

Decay is possible; Charge, Baryon number, Lepton number, Strangeness

are all conserved. Energy conservation

The DS+ meson

What is the quark structure of such a particle.

Look up in Table and find:

Charge Q=+1; Baryon number B=0; Charm C=1;

Mass M= 1968 MeV/c2.

In view of mass No bottomness, no topness.

For the charm there must be a c-quark, with charge +2/3e

To get a charge of +1 there must be another quark with +1/3 e

To have B=0 the second quark must be an anti-quark.

To have strangeness s=+1, the second quark must be an anti-strange.

scDs