Particle Physics

Elementary Particle

A particle with no internal structure.

Three types of elementary particles

Quarks

Leptons

Exchange Particles (Gauge Bosons)

elementary particles that feel strong force

elementary particles that do not feel strong force

Gauge Bosons

FERMIONS – follow Pauli exclusion principle

DO NOT follow Pauli exclusion principle

FERMIONS

Two types of fundamental particles are classified as FERMIONS (they follow Pauli’s exclusion principle and have ½ spin numbers)

Present theory states that these particles cannot be broken down into even “smaller” particles.

These two classes of fundamental particles are.

Leptons – do not feel the strong force

Quarks – feel the strong force

Leptons

There are six types of lepton and each has an antiparticle (opposite charge).

Family -1 charge zero charge

1 electron (e) electron-neutrino (ue)

2 muon (m) muon-neutrino (um)

3 tau (t) tau-neutrino (ut)

Each lepton has a designated lepton number of +1. The antiparticles of each lepton are -1. For any interaction, the sum of all the lepton numbers must remain constant. This is the lepton number conservation law.

Quarks (isolated quarks have never been detected)

There are six types of quarks and consequently six types of anti-quarks (with opposite charge).

Family +2/3 charge -1/3 charge

1 up (u) down (d)

2 charm (c) strange (s)

3 top (t) bottom (b)

Quarks and anti-quarks combine to form composite particles called HADRONS: two families of hadrons

3 quarks = baryon (ex. protons and neutrons)

2 quarks = meson (ex. pions)

elementary particles

gauge bosons

composite particlesmesons(one quark + one anti quark)

Fermions

elementary particles

composite particlesbaryons(made of 3 quarks)

Bosons

HADRONS

Elementary Particles

Exchange Particles – Mediate Fundamental Forces

gauge bosons

gluon(strong)

graviton(gravity)

w+, w -, z0

(weak) photon

(electromagnetic)

Range: gravity, electromagnetic >> strong > weak

Strength: strong > electromagnetic >> weak >> gravity

Mass: weak >>>> strong, gravity, electromagnetic

electroweak

The Higgs Boson

Not discovered yet, only theorized

An exchange particle that gains mass when it interacts with other particles.

The existence of Higgs is important because it is fundamental to theories about how particles have mass. If it doesn’t exist, much of the current theory will need to be revised.

Classifying Particles

There are many different properties used to classify a particle. These intrinsic properties are expressed as quantum numbers.

Quantum numbers tell us about- electric charge- spin- strangeness- .charm- color (not actual color)- lepton number - baryon number

Pauli’s Exclusion Principle

No two particles in a closed system (such as an atom) can have the same set of quantum numbers.

All fermions follow the PEP

Bosons do not follow the PEP

Quantum Number – electrical charge

Fundamental particles can have positive, negative or no charge.

An ANTIPARTICLE has the identical mass to a particle but opposite charge (if charged) and opposite spin (if there is spin).

Classifying Particles

There are many different properties used to classify a particle. These intrinsic properties are expressed as quantum numbers.

Quantum numbers tell us about- electric charge- spin- strangeness- .charm- color (not actual color)- lepton number - baryon number

Quantum Number - SPIN

All fermions have non-integer spin

example electrons +½ (or – ½ )

All bosons have integer (or zero) spin

Classifying Particles

There are many different properties used to classify a particle. These intrinsic properties are expressed as quantum numbers.

Quantum numbers tell us about- electric charge- spin- strangeness- .charm- color (not actual color)- lepton number - baryon number

Particles - Summary

All observed particles

fermions

leptons

bosons

quarks

baryons(3 quarks)

mesons(2 quarks)

gauge bosons

½ integral spinobey Pauli exclusion

zero or integral spindo not obey Pauli exclusion

Hadrons

Fundamental Interactions

The four fundamental interactions of nature are:

electromagnetic, strong, weak, and gravity

The electromagnetic and the weak interactions are two aspects of the same interaction, the electroweak interaction

Mediation of Fundamental Forces

The fundamental forces are mediated by the exchange of particles. These particles are called exchange bosons.

A Feynman diagram can be used to show how interactions between particles are mediated by bosons.

The electromagnetic force is mediated by photons. These photons are unobservable and are termed virtual photons to distinguish them from real ones.

Exchange Particles : the nature of force

All four of the fundamental forces involve the continuous exchange of “virtual” particles

The creation of “virtual” particles is a breach of conservation laws (as they are created from nothing) so they can only exist for a short period of time.

The maximum range of an exchange force is dictated by the Heisenberg uncertainty principle.

.

The Heisenberg Uncertainty Principle (HUP)

It is impossible to make precise measurements of both the position and momentum (velocity) of electrons or any other particles.

The very act of measuring changes these quantities. The more precise one measurement is, the less precise the other one becomes.

.

Implications of the Uncertainty Principle

The more massive the exchange particle, the shorter its life. Why is the range of the strong and weak nuclear force very small compared to the infinite range of the electromagnetic and gravitational force?

.

4

hE t

HUP can be applied to the

relationship between energy and time.

Here, the uncertainty principle implies that the life time of a virtual particle is inversely proportional to its mass (energy)

The uncertainty in the energy of a virtual photon is 7.1 × 10-19 J. Determine the uncertainty in the time for the electromagnetic interaction between two electrons exchanging the virtual photon.

.

3417

19

6.6 107.4 10

4 4 (7.1 10 )

ht s

E

Range of Interactions of Exchange Particles. The range of a virtual particle (and hence the force it

mediates) is governed by the equation below (from HUP)

4

hR

mc

h is Planck’s constantc is the speed of lightm is the REST MASS of the virtual particle

We see here again that

range is inversely proportional to the rest mass

The strong force has a range of about 10-15 m. Calculate the rest mass of the related exchange particle. What type of particle is this?

3428

15 8

6.6 102 10

4 4 (10 )(3.0 10 )

hR kg

mc

this is a gluon

FEYNMAN DIAGRAMS

Exchange forces are often pictured with Feynman diagrams.

At each vertex in a Feynman diagram, conservation laws such as charge, lepton number and baryon number must be obeyed

Different lines are drawn for different particles. There are some variations in the conventions that are applied.

or W and Z bosonssometimes gluons

Interactions

Interactions are illustrated using Feynman diagrams. Here are two examples:

Gluon exchange holds quarks together.

A meson interaction (which at the quark level involves gluons) holds nucleus together

Practice : Draw Feynman diagrams to illustrate the followinga) an electron absorbing a photon of energyb) a positron (anti-electron) emitting a photon of energyc) an electron-positron pair annihilation to form a photond) Formation of an electron and positron from a photon

Review Problem

Review Problem

Review Problem

Review Problem

Review Problem

Review Problem

Quarks (isolated quarks have never been detected)

There are six types of quarks and consequently six types of anti-quarks (with opposite charge).

Generation +2/3 charge -1/3 charge

1 up (u) down (d)

2 charm (c) strange (s)

3 top (t) bottom (b)

Quarks and anti-quarks combine to form hadrons. There are two classes of hadrons

3 quarks = baryon (ex. protons and neutrons)

2 quarks = meson (ex. pions)

Here are some examples of baryons and mesons.

Baryons (three quarks)

Baryon numbers are examples of quantum numbers.

Baryon numbers are +1 and -1 (anti-particles) respectively. The baryon number is conserved in any interaction.

All other particles have a baryon number of zero.

(only a Baryon can be +1 or -1)

Individual quarks have baryon numbers of 1/3 (or -1/3)

Protons consist of two up quarks and one down. This is written as uud and referred to as up, up, down.

Note that the overall baryon number is

1/3 + 1/3 + 1/3 = 1

And the overall electrical charge would be equal to

+ 2/3 + 2/3 + (-1/3) = +1

Charges in quarks

EZ to remember

Proton UUD

Neutron UDD

make sense?

Quarks and Spin

Recall

All fermions have non-integer spin

ex. electrons have spin number ½

ex. protons have spin number ½

ex. quarks have spin number ½

All bosons have integer (or zero) spin

There are two spin states referred to as UP and DOWN

So

spin number +½ UP

spin number - ½ DOWN

In a proton, the two up quarks cannot have the same spin number.

Quarks and QCD

Quarks also have different “colors”.

The color force between quarks is mediated by gluons.

quarks come in three colors: red, blue, green

anti-quarks are : anti-red (cyan), anti-blue (yellow) and anti-green (magenta)

The “colorless” property of bound quarks is called confinement.

Only combinations of color-neutral (add to white) quarks have been found.

Baryons R + G + B = white

Mesons color + anti-color = white

The combination though must always be color neutral (white or colorless). This is why particles consisting of 4 quarks have never been found.

.

Depends on number of strange (-1) and anti-strange (+1) quarks in a composite particle.

Only conserved in interactions involving gluons and photons.

(not the WEAK force)

Strangeness – yet another quantum number

Interactions

You do not need to worry about the composition of baryons (other than protons and neutrons) or mesons. You should however be able to apply conservation laws to interactions. They are:

Conservation of mass-energy.

Conservation of baryon and lepton numbers.

Conservation of electrical charge

Conservation of angular momentum. Each particle has a spin number. The total spin before and after the interaction remains the same.

Practice Problem

A common process examined is beta decay. neutron proton + electron + anti-neutrino

The anti-neutrino is required to conserve the lepton number : zero = zero + 1 – 1

udd

uud

?To convert a neutron to a proton a down quark must change its flavor.

Beta decay continued:

For udd uud conversion

All quarks have baryon number of 1/3 so baryon number is conserved. Charge however is not conserved. A negative charge must be removed.

udd

uud

w -

Beta decay is mediated by the weak force. The weak force boson w – changes the flavor of the up quark in the neutron.

Interactions and Other Processes

udd

uud

w - Arrows pointing down in a Feynman diagram indicate anti-particles, NOT direction.

e -

The electron and anti-neutrino lepton numbers are + 1 and -1 so lepton number is conserved, as is electrical charge.

Elementary Particles Composite Particles

Ob

ey P

EP

Do

No

t O

bey

PE

P

Hadrons

Baryons

MesonsGauge Bosons

EM Strong

Weak

graviton&

Higgs(undetected)

Do not feel strong force

Lepton # = 1(anti leptons = -1)

Feel strong force

Baryon # = 1/3 (anti quarks = -1/3)

Baryon # = 1

Color combinations = white