4. A Brief Introduction to Particle Physics

Question 1

Fundamental Particles

Answer 1

-fundamental particles are characterised by a set of numerical properties (quantum numbers)

Question 2

Spin

Description

Answer 2

• an important quantum number is spin
• it is the intrinsic angular momentum, i.e. the angular momentum measured in the particles rest frame
• it is analogous to the rotation of the Earth around its own axis , BUT this is just an analogy since fundamental particles have no spatial extent

Question 3

Allowed Values of Spin

Answer 3

√s(s+1) * ћ

-where s is {1/2, 1, 3/2, 2, 5/2, … }

Question 4

Spin-Statistics Theorem

Answer 4

• the behaviour of a particle depends on its s in the allowed values of spin formula
• if s is an integer then the particle is a boson
• if s is a half number {1/2, 3/2, 5/2, …} the particle is a fermion

Question 5

Pauli Exclusion Principle

Answer 5

• fermions obey the Pauli exclusion principle so no two fermions can be in exactly the same state, fermions behave like matter
• bosons do not obey the Pauli exclusion so there can be multiple bosons in the same state, bosons are force carriers

Question 6

Feynman Diagram

Answer 6

• interactions mediated by exchange particles can be represented by Feynman diagrams
• Feynman diagrams arise in quantum field theory as a natural shorthand for numerical factors that give the transition values for particular interactions

Question 7

Classification of Fermions

Answer 7

• there are two types of fundamental fermions, leptons and quarks, they have spin 1/2
• there also composite fermions called baryons

Question 8

Leptons

Answer 8

• fundamental fermions
• not subject to the strong force
• electron, muon, tau, electron neutrino, muon neutrino, tau neutrino

Question 9

Quarks

Answer 9

-fundamental fermions
-subject to the strong force
up, down, strange, charm, top, bottom

Question 10

Baryons

Answer 10

• non-fundamental fermions
• composed of three quarks
• proton, neutron, sigma, lambda

Question 11

Classification of Bosons

Answer 11

• two fundamental types, gauge bosons and higgs

- also non-fundamental bosons, mesons

Question 12

Gauge Bosons

Answer 12

• force carriers
• spin 1
• photons for EM
• W, Z bosons for weak nuclear force
• gluons for the strong force

Question 13

Higgs Bosons

Answer 13

• the standard model’s appendic

- have spin 0

Question 14

Mesons

Answer 14

• composite bosons

- composed of a quark and an antiquark

Question 15

Discovery of Antiparticles

Answer 15

• any attempt to unify quantum mechanics and special relativity leads to ‘too many degrees of freedom
• non relativistically E=p²/2m + V which gives a unique value of E for any momentum
• relativistically E=√(p²c²+m²c^4) which gives a positive and a negative energy for each momentum
• negative energy makes no sense but we can reinterpret a negative energy as a positive energy of an antiparticle where the antiparticle has the same mass and spin but all other quantum numbers are reversed

Question 16

Feynman Diagrams and Probability

Answer 16

• each individual feature of a Feynman diagram (e.g. a vertex, a line etc.) represents some quantity
• we can multiply all of these values together to calculate the probability of a particular event occurring

Question 17

Different Ways of Thinking About Antiparticles

Answer 17

1) antiparticles are the positive-energy degrees of freedom that correspond to the negative-energy degrees of freedom of the corresponding particle
2) because energy and time are conjugate quantities we can also interpret antiparticles as a particle ‘going backwards in time’
3) we can also think of antimatter through Dirac’s ‘hole’ interpretation, BUT this only works for fermions

Question 18

Conservation Laws

Answer 18

• there are various conserved quantum numbers: lepton no., baryon no., charge, strangeness, charm, beauty, truth, etc.
• many quantum numbers are conserved at all vertices in Feyman diagrams e.g. charge
• several quantum numbers are conserved by SOME interactions e.g. S, C, ~B, T
• some are not conserved

Question 19

Quantum Numbers That Are Not Conserved

Answer 19

• mass - energy-mass equivalence means that a difference in mass can be accounted for in kinetic energy
• spin - difference in spin can be accounted for by orbital momentum

Question 20

What do arrows in a Feyman diagram represent?

Answer 20

-arrows on particles in Feynman diagrams depict flow of quantum numbers, not direction of movement

Question 21

Allowed Interactions of the Standard Model

Answer 21

• in the quantum world, everything that is not forbidden must occur, superposition of states
• so if we know which quantities are conserved by which interactions, we can make an exhaustive list of all allowed particle interactions
• likewise if an interaction is never observed we can infer that there is a conserved quantity that would be violated by that interaction

Question 22

Real and Virtual Particles

Answer 22

-if a particle is exchanged between two other particles, then we can never directly observe that photon, since if we did it would never reach the other particles and the interaction wouldn’t complete
-this means that we can only infer its properties indirectly from its effect on the other particles involved
-we call it a virtual particle whereas particles that can be observed are real
-

Question 23

Mass Shell

Answer 23

-since a virtual particle is short lived and travels only a short distance, the uncertainty principle states that the energy and momentum need not be exactly what we would expect
-in fact since the energy and momentum together determine the particles mass:
E² = p²c² + m²c^4
-the virtual particle need not have the ‘correct’ mass that we would measure for a real particle of the same type
-we say that the real particle is on the mass shell, but the virtual particle is off shell

Question 24

Real vs Virtual

Directly Observed

Answer 24

Real - yes

Virtual - no

Question 25

Real vs Virtual

On-Shell

Answer 25

Real - yes

Virtual - no

Question 26

Real vs Virtual

Exchange

Answer 26

Real - no

Virtual - yes

Question 27

Real vs Virtual

Placement in Feynman Diagrams

Answer 27

Real - external

Virtual - internal