The Standard Model of Elementary Particles

The Structure of Matter

The Standard Model of Elementary Particles:

Particles and Antiparticles

Composite Particles:

Examples:

In the 1950s and 1960s, hundreds of other particles were discovered, many of which are very unstable and so are not found in ordinary matter.

Elementary Particles: particles not made out of any smaller component particles; 2 elementary particles of the same kind are completely identical.

3 Classes of Elementary Particles:

a)b)c)

Antiparticles –

All antiparticles are denoted with a line above the symbol

Examples:

If a particle has zero electric charge, the antiparticle can still be distinguished because of other quantum numbers

Example:

Some particles are their own antiparticle and must be electrically neutral

Example:

Antimatter –

What happens when antimatter comes into contact with matter?

Which is predominant in today’s universe, matter or antimatter?

Quantum numbers:

Examples:

Quarks

Quarks:

There is solid experimental evidence for the existence of 6 types or “flavours” of quarks

Quark flavour / Symbol / Electric Charge (e) / Rest Mass (MeV c-2) / Spin
(h/2π)
Up
Down
Strange
Charmed
Bottom
Top

Note: A particle’s “spin” is a quantum property that isanalogous to, but not actually, angular momentum (L=mvr). All known particles have spin, which must beeither an integral or half-integral multiple of the quantity h/(2π).

Bosons:

Fermions:

So all quarks are….

Hadrons –

Meson –

Baryon –

The proton is a baryon made out of….

The neutron is a baryon made out of….

1. Show that the charge of a proton is 1.

1. Show that the charge of a neutron is 0.

1. What is the quark content and the charge of an antiproton?

1. What is the quark content and the charge of an antineutron?

Baryon number (B): Baryons are assigned a quantum number

What is the baryon number for:

protons and neutrons?antiprotons and antineutrons?

quarks? antiquarks?

So how does B of an antiparticle compare to B of the particle?

Law of Conservation of Baryon Number: Baryon number is conserved in ALL reactions.

_

Example: n + p  n + p + p + p

1. Show that the reaction below cannot occur; if it did, the law of conservation of baryon number would be violated.

--

p + p π0 + π0 + n

Leptons

Leptons:the electron and its neutrino, the muon and its neutrino, and the tau and its neutrino, as well as all of their antiparticles

There is solid experimental evidence for the existence of 6 types of leptons

Lepton / Symbol / Electric Charge (e) / Rest Mass (MeV c-2) / Spin
(h/2π)
Electron
Electron neutrino
Muon
Muon neutrino
Tau
Tau neutrino

Because of their spin, all leptons are…..

The leptons of each family or generation are assigned a lepton number. Since there are 3 families, there are 3 lepton numbers

Lepton number (L):

Type of Leptons and Lepton numbers: electron, muon, and tau lepton with numbers, Le, Lμ, and Lτ

The 3 kinds of lepton number are individually conserved in all reactions as is the overall Lepton number.

Le / Lμ / Lτ
Electron, e
Electron neutrino, νe
Muon, μ-
Muon neutrino, νμ
Tau, τ-
Tau neutrino, ντ

1. Show that all lepton numbers are conserved in the following muon decay:

_

μ-  e-+ νe + νμ

1. Do the following reactions conserve lepton number?
2. p+ e+ + π0

1. π0 e+ + μ-

_

1. τ+ π+ + ντ

Exchange Particles

Exchange Particles:associated with interactions or forces; includes the photon (γ), the W and Z bosons (W± and Z0), 8 particles called gluons, and the graviton.

There is solid experimental evidence for the existence of all exchange particles except the graviton.

Gauge bosons: particles that mediate (or transmit) the force between a pair of particles

The 4 fundamental forces have different ranges and a different boson is responsible for each force. The mass of the boson establishes the range of the force. The bosons carry the force between particles.

The Higgs Particle or Higgs boson: a boson-like force mediator, but does not actually mediate any force;

explains the mass of other particles, including the W and Z bosons;

not known if this particle is elementary;

was tentatively confirmed in 2013 to be positively charged and to have zero spin.

Leptons and quarks of the standard model can be arranged into 3 families or generations.

Leptons / Quarks
1st generation / e- / u
νe / d
2nd generation / μ- / s
νμ / c
3rd generation / τ- / b
ντ / T

Conservation Laws

In all reactions, the following quantities are always conserved:

1.

2.

3.

4.

5.

6.

Strangeness (S):

Strange quark has a strangeness of:

Strange antiquark has a strangeness of:

When is strangeness conserved? When strange particles are created in a strong interaction, but it is not conserved when they subsequently decay through the weak interaction.

This is why strange particles are always produced in pairs. If 2 particles interact to produce a strange particle, then a strange antiparticle must also appear.

In the following reactions, determine if Q, B, L, and S are conserved.

_ _

1. uud + ud  ds + uds

_ _ _

1. ds  ud + ud

_

1. uds  ud + uud

Interactions and exchange particles

Basic interaction vertices:

There are 4 fundamental forces or interactions in nature.

Interaction / Interaction acts on / Exchange Particle(s) / Relative Strength
Electromagnetic
Weak (nuclear)
Strong (nuclear)
Gravitational

The electromagnetic and weak nuclear interactions have been combined to form the electroweak interaction.

How does the range of the exchange force relate to the mass of the exchange particle?

The shorter the range of the exchange force, the more massive the exchange particle.

The exchange particles for gravitation and the EM interaction both have infinite range, so must have zero rest masses. Meanwhile the weak interaction has the heaviest boson because its range is the shortest. The strong interaction has an exchange particle of intermediate mass.

At a fundamental level, particle physics views an interaction between 2 elementary particles in terms of interaction vertices.

All interaction vertices should be read from left to right. The left hand side represents BEFORE and the right hand side represents AFTER.

Usually the time axis goes to the right and the space or position axis goes upwards, but they can be reversed.

Because arrows on antiparticles are drawn in the opposite direction to those on particles, we sometimes say that these antiparticles travel backwards in time. This is just an expression! All particles/antiparticles move forwards in time.

The electromagnetic interaction is the exchange of a virtual photon between charged particles. The exchanged photon is not observable. This interaction vertex is show on the left below.

By rotating the arms of the vertices, the following interaction possibilities are generated.

Electric charge, baryon number, and lepton numberare conserved at an interaction vertex. The total Q, B, and L, going into a vertex must equal the total Q, B, and L leaving the vertex.

Feynman Diagrams

Feynman diagrams: pictorial representations or “spacetime diagrams” of particle interactions that uses interaction vertices in order to build up possible physical processes.

Examples: below left is electron-electron scattering (the exchange of a virtual photon in the interaction between electrons), below right is Higgs decay to two photons via top loop;

In this Feynman diagram below, an electron and positron destroy each other, producing a virtual photon which becomes a quark-antiquark pair. Then one radiates a gluon.

Other examples of Feynman diagrams for basic interaction vertices.

To build a Feynman diagram,` the following are needed:

1)

2)

3)

Examples: Draw the Feynman diagram for the following processes:

1. e- + e+ e- + e+

1. e- + e+ γ + γ

1. beta minus decay in which a neutron decays into a proton, an electron, and a neutrino

1. positive beta (positron) decay: p  n + e- + νe

Quark Confinement (or confinement of colour):

Why is this so?

Suppose you wanted to remove a quark from inside a meson. The force between the quark and the antiquark is constant no matter what their separation is. Therefore, the total energy needed to separate the quark from the antiquark gets larger and larger as the separation increases. To free the quark completely would require an infinite amount of energy, and so it is impossible. If you insisted on providing more and more energy in the hope of isolating the quark, all that would happen would be the production of a meson-antimeson pair and not free quarks.

Table of some baryons

Particle
/ Symbol
/ Quark
Content / Mass
MeV/c2 / Mean
lifetime (s) / Decays to
Proton / p / uud / 938.3 / Stable / Unobserved
Neutron / n / ddu / 939.6 / 885.7±0.8 / p + e- + νe
Delta / Δ++ / uuu / 1232 / 6×10-24 / π+ + p
Delta / Δ+ / uud / 1232 / 6×10-24 / π+ + n or π0 + p
Delta / Δ0 / udd / 1232 / 6×10-24 / π0 + n or π- + p
Delta / Δ- / ddd / 1232 / 6×10-24 / π- + n
Lambda / Λ0 / uds / 1115.7 / 2.60×10-10 / π- + p or πo + n
Sigma / Σ+ / uus / 1189.4 / 0.8×10-10 / π0 + p or π+ + n
Sigma / Σ0 / uds / 1192.5 / 6×10-20 / Λ0 + γ
Sigma / Σ- / dds / 1197.4 / 1.5×10-10 / π- + n
Xi / Ξ0 / uss / 1315 / 2.9×10-10 / Λ0 + π0
Xi / Ξ- / dss / 1321 / 1.6×10-10 / Λ0 + π-
Omega / Ω- / sss / 1672 / 0.82×10-10 / Λ0 + K- or Ξ0 + π-

Table of some mesons

Particle
/ Symbol
/ Anti-
particle / Quark
Content / Mass
MeV/c2 / Mean
lifetime (s) / Principal
decays
Charged Pion / π+ / π− / ud / 139.6 / 2.60×10-8 / μ+ + νμ
Neutral Pion / π0 / Self / uu - dd / 135.0 / 0.84×10-16 / 2γ
Charged Kaon / K+ / K− / / 493.7 / 1.24×10-8 / μ+ + νμ or π+ + π0
Neutral Kaon / K0 / K0 / ds / 497.7
Eta / η / Self / uu + dd - 2ss / 547.8 / 5×10-19
Eta Prime / η' / Self / uu + dd + ss / 957.6 / 3×10-21