option j: particle physics j1 particles and interactions

Option J: Particle physicsJ1 Particles and interactionsThis part of Option J has already been covered in

Option D4 Particles and interactions.

It is replicated here without any changes.

Description and classification of particles

J.1.1 State what is meant by an elementary particle.

J.1.2 Identify elementary particles.

J.1.3 Describe particles in terms of mass and various quantum numbers.

J.1.4 Classify particles according to spin.

J.1.5 State what is meant by an antiparticle.

J.1.6 State the Pauli exclusion principle.

Option J: Particle physicsJ1 Particles and interactions


State what is meant by an elementary particle.

An elementary particle is one which has no internal structure.


PRACTICE: At one time it was thought that atoms were elementary particles. Explain why they are not.SOLUTION: They have an internal structure: Namely protons, neutrons and electrons.EXAMPLE: At one time it was thought that protons and neutrons were elementary particles. Explain why they are not.

SOLUTION: Protons and neutrons are each built from three elementary particles called quarks.


Identify elementary particles.

There are three major divisions in the elementary particles that have been identified, to date.

The force carriers are the particles that allow compatible particles to sense and react to each other’s presence through exchange of these carriers.

The quarks are the heavier, tightly bound particles that make up particles like protons and neutrons.

The leptons are the lighter, more loosely bound particles like electrons.


FYIFor example, quarks interact via the strong force particles called gluons.



The force carriers:

There are four force carriers…

INTERACTION 1: STRONG: Strongest of all the interactions between particles. We can give it an arbitrary value of 1 for comparison.

INTERACTION 2: ELECTROMAGNETIC: This is the NEXT strongest. In comparison to the strong interac-tion, it has a relative strength of 10-2.

INTERACTION 3: WEAK: This interaction has a relative strength of 10-6.

INTERACTION 4: GRAVITATIONAL: This interaction has a relative strength of 10-39.


1.0

0.01

0.000001

0.000000000000000000000000000000000000001



The force carriers:

In 1933 Hideki Yukawa developed the theory of exchange forces.

The basic idea is that all forces are due to the exchange of particles between like elementary particles.

Consider two protons in space.Yukawa postulated that the protons exchange photons and repel each other because of this exchange.


FYIThis photon exchange is the electromagnetic force.



The force carriers:

Yukawa explained that the electromagnetic force was long range (in fact infinite in range) because photons "live forever" until they are absorbed.

Yukawa explained that the strong force was short range (in fact only in the nuclear range) because the strong force exchange particle (the gluon) has a very short life.


LONG RANGE EXCHANGE PARTICLE

SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE



The force carriers:

The following table compares the exchange particles (force carriers) by range and mass.


INTERACTION EXCHANGE PARTICLERANGE REST MASS

STRONG GLUON g10-15 m 120 MeV / c2

Electromagnetic PHOTON 0

WEAK W+, W- and Z10-18 m 80 GeV / c2

Gravitation GRAVITON 0



The quarks:Although you have heard of protons and neutrons, both of which react to the strong force exchange particle (the gluon), you have probably not heard of most of the following particles:


Particle Symbol

proton p

neutron n

delta ++

delta +

delta 0

delta -

lambda 0

sigma +

sigma 0

sigma -

xi 0omega -

Particle Symbol Particle Symbol

FYIWith the advent of particle research the list of new particles became endless!



The quarks: In 1964 the particle model was looking quite complex and unsatisfying. Murray Gell-Mann proposed a model where all the strong-force particles were made up of three fundamental particles called quarks.


FYIA proton is uud and a neutron is udd.

Quark

Flavor

UpDown

StrangeCharmBottomTop

Symbol

udscbt

Charge

+ 2/3- 1/3- 1/3+ 2/3- 1/3+ 2/3

uu

d

proton



The quarks: Each quark has an antiquark, which has the opposite charge as the corresponding quark.


FYIBaryons are particles made up of 3 quarks or 3 antiquarks.Mesons are particles made up of a 1 quark and 1 antiquark.



The leptons:You are already familiar with two of the six leptons: the electron and the electron neutrino.

Leptons, unlike quarks, do NOT participate in the strong interaction.


FYIOf course the leptons also have their antiparticles.

THE LEPTONS

Charged Leptons Uncharged Leptons

electron e

muon

tau

electron neutrino emuon neutrino

tau neutrino



The leptons:The leptons interact only via the electromagnetic force carrier, the photon.

Leptons, unlike quarks, do not react to the gluon.

Quarks react to both the gluon and the photon.


FYILeptons and quarks also react to gravitons.



The Higgs particle is another particle that physicists think exists and are in search of.

This particle is the one that gives quarks and leptons their mass.

To date the Higgs particle has not yet been found.


FYICERN and the Large Hadron Collider were developed with the Higgs boson in mind.

The Large Hadron Collider at CERN.


Describe particles in terms of mass and various quantum numbers.


QUARKS u (up) c (charm) t (top)

Charge / e +2/3 +2/3 +2/3

Mass / mp 1/3 1.7 186

d (down) s (strange) b (bottom)

Charge / e -1/3 -1/3 -1/3

Mass / mp 1/3 0.5 4.9

LEPTONS e(electron) (muon) (tau)

Charge / e -1 -1 -1

Mass / mp 0.0005 0.1 1.9

e (e-neutrino) (-neutrino) (-neutrino)

Charge / e 0 0 0

Mass / mp 0 0 0



Quarks have a baryon number of 1/3 and antiquarks have a baryon number of -1/3.


quark (q) or antiquark (q) baryon number B

Quark: B = +1/3Antiquark: B = -1/3

PRACTICE: Find the baryon number of a baryon, a meson, and an electron:SOLUTION:A baryon has three quarks (or three antiquarks): For qqq we have B = +1/3 + +1/3 + +1/3 = +1. For qqq we have B = -1/3 + -1/3 + -1/3 = -1.A meson has a quark and an antiquark: For qq we have B = +1/3 + -1/3 = 0.An electron has no quarks and thus has B = 0.



Leptons have a lepton number of 1 and antileptons have a lepton number of -1.


lepton or antilepton lepton number L

Lepton: L = +1Antilepton: L = -1

PRACTICE: Find the lepton number of an electron, a positron, an anti electron neutrino, and a proton:SOLUTION:An electron has a lepton number of L = +1.A positron is an antiparticle and so has L = -1.An anti electron neutrino has L = -1.A proton is not a lepton and so has L = 0.




Conservation of charge.

Conservation of baryon number.

Conservation of lepton number.




Conservation lepton number violated.

L = 0 L = 0 + 1 = 1.

We need a particle on the right with L = -1 (an antilepton).

01n 1

1p + -10e + e

L : 0 0 1 -1

PRACTICE: Evaluate each reaction as "possible" or "not possible“ considering B, L and Q.

p n + e+ + eB:L:Q:

n p + e- + eB:L:Q:

n + p e+ + eB:L:Q:




1 1 0 00 0 -1 11 0 1 0

POSSIBLE

1 1 0 0 0 0 1 -1 0 1 -1 0

POSSIBLE

1 1 0 0 0 0 -1 -1 0 1 1 0

NOT POSSIBLE


Classify particles according to spin.

A quark (or antiquark) may have spin up (+1/2) or spin down (-1/2).

A baryon is a particle made of three quarks (or three antiquarks) and so it has a spin of

A meson is a particle made of one quark and one antiquark and so it has a spin of

A fermion is a particle having an odd multiple of 1/2 as a spin.A boson is a particle having an integer spin.


baryon spin (qqq) or (qqq) 1/2 or 3/2

quark (q) or antiquark (q) spin

Spin is +1/2Spin down -1/2

meson spin (qq) 0 or 1

fermion

fermion

boson


State what is meant by an antiparticle.

Every particle has an antiparticle which has the same mass but all of its quantum numbers are the opposite.

Thus an antiproton (p) has the same mass as a proton (p), but the opposite charge (-1).

Thus an antielectron (e+ or e) has the same mass as an electron but the opposite charge (+1).


FYIWhen matter meets antimatter both annihilate each other to become energy!

Angels and Demons

Paul Dirac


State the Pauli exclusion principle.

The Pauli exclusion principle states that no two identical fermions may have exactly the same set of quantum numbers.


PRACTICE: Electrons and antielectrons have a spin of 1/2. Are they fermions or bosons? SOLUTION:A fermion is a particle having an odd multiple of 1/2 as a spin. A boson has an integral spin.Thus electron and positrons are fermions (as well as quarks and baryons). Mesons are bosons.

FYIWe first saw Pauli’s exclusion principle when we looked at the orbital structure of the elements. Recall the s, p, d and f suborbitals.

Fundamental interactions

J.1.7 List the fundamental interactions.

J.1.8 Describe the fundamental interactions in terms of exchange particles.

J.1.9 Discuss the uncertainty principle for time-energy in the context of particle creation.


DONE

DONE


Discuss the uncertainty principle for time-energy in the context of particle creation.

Recall the Heisenberg uncertainty principle:

Another way of looking at the time-energy uncertainty principle is this:

“If the time interval is small enough, the uncertainty in the energy can be very large.”

This is a way of saying that the conservation of energy can be violated for very short periods of time!

The consequences are that particles can be randomly created out of the void as long as they annihilate each other in a very short time.


Heisenberg uncertainty principle

∆x∆p h/4 (momentum form)∆E∆t h/4 (energy form)




Heisenberg uncertainty principle

∆x∆p h/4 (momentum form)∆E∆t h/4 (energy form)

EXAMPLE: A proton and an antiproton are created from the void as allowed by the HUP. How much time do they exist before annihilating each other?

SOLUTION: A proton has a mass of 1.6710-27 kg.

From E = mc2 we can calculate the energy of a proton (or an antiproton) to be

∆E = (1.6710-27)(3.00108)2 = 1.5010-10 J.

Since we need both p and p, the energy doubles. ∆t = h/[4∆E] = 6.6310-34 /[4(3.0010-10)]

= 1.7610-25 s.




EXAMPLE: Stephen Hawking proposed that black holes can evaporate because of virtual particle creation. How can this work?

SOLUTION:

At the black hole’s boundary (the Schwarzschild radius) virtual particles are created in matter-antimatter pairs out of the void.

If one of the pair happens to be gobbled up by the hole, and the other has sufficient velocity to escape from the hole, the particles will not annihilate, and the black hole will be lighter by the mass of the one particle!

http://en.wikipedia.org/wiki/File:Stephen_Hawking.StarChild.jpg

Feynman diagrams

J.1.10 Describe what is meant by a Feynman diagram.

J.1.11 Discuss how a Feynman diagram may be used to calculate probabilities for fundamental processes.

J.1.12 Describe what is meant by a virtual particle.

J.1.13 Apply the formula for the range R for interactions involving the exchange of a particle.

J.1.14 Describe pair annihilation and pair production through Feynman diagrams.

J.1.15 Predict particle processes using Feynman diagrams.


Feynman diagrams

Describe what is meant by a Feynman diagram.

Richard Feynman developed a graphic representation of particle interactions that could be used to predict the probabilities of the outcomes of particle collisions.

A typical Feynman diagram consists of two axes: Space and Time:


FYISome books switch the space and time axis. The IB presentation is as shown above.

SP

AC

E

TIME

Feynman diagrams


Consider two electrons approaching one-another from the top and the bottom of the page…

A purely spatial sketch of this interaction would look like this:

But if we also apply a time axis, the sketch would look like this:

The Time axis allows us to draw the reaction in a spread-out way to make it clearer.


e-

e-

The bubble of ignorance

SP

AC

E

TIME

e- e-

e- e-

FYIThe “bubble of ignorance” is the actual place in the plot that exchange particles do their thing.Ingoing and outgoing particles are labeled.

Feynman diagrams


Particles are represented with straight arrows, as were the two electrons in the previous electron-electron interaction.

Exchange particles are represented with either wavy lines (photons, W+, W- and Z0), or curly lines (gluons).


Electromagnetic and weak exchange

Strong exchange

FYIYou may have noticed that the electromagnetic exchange particle and the weak exchange particles all have the same wavy symbol. Indeed, it has been found that the two forces are manifestations of a single ELECTRO-WEAK force.

EXAMPLE:

The complete Feynman diagram showing the repulsion of two electrons looks like this:

EXAMPLE:

Here is a diagram for one electron emitting a photon:

Feynman diagrams

Predict particle processes using Feynman diagrams.


SP

AC

E

TIME

e-

e-

e-e-

SP

AC

E

TIME

e-

e-

EXAMPLE:

In a Feynman diagram, antimatter points backward in time. This diagram represents two positrons repelling each other:

EXAMPLE:

Here is a diagram for one positron emitting a photon:

Feynman diagrams



SP

AC

E

TIME

e+

e+

e+e+

SP

AC

E

TIME

e+

e+

EXAMPLE:

Here is a photon producing an electron-positron pair.

EXAMPLE:

Here is an electron-positron pair annihilating to become a photon:

Feynman diagrams

Describe pair annihilation and pair production through Feynman diagrams.


SP

AC

E

TIME

e-

e+

SP

AC

E

TIME

e-

e+

EXAMPLE:

Here is a diagram of a down quark emitting a W- particle that decays into an electron and an antineutrino:

Feynman diagrams

Discuss how a Feynman diagram may be used to calculate probabilities for fundamental processes.


SP

AC

E

TIME

du

e-

e

W-

FYIOne can use Feynman diagrams to map out complete processes. Using the conservation rules and the exchange particles, you can predict what kind of processes can occur.

EXAMPLE: Explain what has happened in this Feynman diagram.

SOLUTION:

The up quark of a proton (uud) emits a gluon.

The gluon decays into a down quark and an anti-down quark.

Feynman diagrams

Discuss how a Feynman diagram may be used to calculate probabilities for fundamental processes.


SP

AC

E

TIME

u u

d

dg

u ud d

FYIQuarks cannot exist by themselves. Thus the two quarks produced above will quickly annihilate.

Feynman diagrams

Describe what is meant by a virtual particle.

Exchange particles whose range of influence is limited are called virtual particles.

Virtual particles can only exist within their range of influence.


INTERACTION EXCHANGE PARTICLERANGE REST MASS

STRONG GLUON g10-15 m 120 MeV / c2

Electromagnetic PHOTON 0

WEAK W+, W- and Z10-18 m 80 GeV / c2

Gravitation GRAVITON 0

LONG RANGE EXCHANGE PARTICLE

SHORT RANGE EXCHANGE (VIRTUAL) PARTICLE

Feynman diagrams

Apply the formula for the range R for inter-actions involving the exchange of a particle.

We can use Heisenberg’s uncertainty principle to estimate the range R of exchange particles. We use ∆E = mc2 and the assumption that these virtual particles travel at the speed of light c… c = R/∆t (v = d/t)

∆t = R/c

∆E∆t h/4 (HUP)

∆ER/c h/4 (Substitution of ∆t = R/c)

mc2R/c h/4 (∆E = mc2)


particle rangeR h/[4mc]

FYIBe able to do this derivation. IBO requires it.

Feynman diagrams

Apply the formula for the range R for inter-actions involving the exchange of a particle.


particle rangeR h/[4mc]

EXAMPLE: A weak virtual exchange particle called the W+ boson has a mass of 89 protons. What is its approximate range of influence?SOLUTION:

mp = 1.6710-27 kg so that

R h/[4mc] = 6.6310-34/[4(89)(1.6710-27)(3.00108)]

= 1.1810-18 m.

FYIThis is about the size of a quark.

EXAMPLE: Explain what has happened in this Feynman diagram.

SOLUTION:

It is a diagram of a down quark emitting a W- particle that decays into an electron and an antineutrino:

Recall that a neutron consists of an up-down-down quark combo.

Recall that a proton consists of an up-up-down quark combo.

This is non other than the beta decay (-)we talked about a long time ago.

Feynman diagrams



SP

AC

E

TIME

d u

e-

eW-

d du un p

n p + e- + e

EXAMPLE: Write the reaction (including the neutrino) for beta(+) decay.

SOLUTION:

Just know it!

EXAMPLE: Now draw the Feynman diagram for the above + decay:

Feynman diagrams



p n + e+ + e

SP

AC

E

TIME

u d

e+

eW+

d du up n

FYIWhy is the neutrino not an anti-neutrino as in the - decay?

Feynman diagrams

Predict processes using Feynman diagrams.


A virtual particle is a particle that has a very short range of influence.

Look at charge…

-1/3

+2/3

Must b

e -1

-1

0

The particle must be a W-.

Feynman diagrams

Predict processes using Feynman diagrams.


Use R h/[4mc].

m = 1.7810-25 kg.

m = (100109 eV c-2)(1.610-19 J/eV)(1c /3.00108)2

R (6.6310-34)/[4(1.7810-25)(3.00108)]

R 9.8810-19 m.

option j: particle physics j1 particles and interactions

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exchange of particles

particle physicsj1 particles

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compatible particles

strong force particles

option d4 particles

option j

electromagnetic force