1.1 Feynman Diagrams

Question 1

What is a Feynman diagram?

Answer 1

A graphical technique used to calculate the amplitude for transitioning from an initial state i to a final state f

Question 2

What are the three regions of a Feynman diagram?

Answer 2

The initial state
Physics state
Final state

Question 3

What is the mathematical form of a decay and a scatter?

Answer 3

Decay: 1 -> n
Scatter: 2 -> n
Where n >= 2

Question 4

What is a vertex in a Feynman diagram, and why is it important?

Answer 4

Where the particle lines meet, and all conservation laws must be obeyed at every vertex

Question 5

What are Feynman diagram external lines?

Answer 5

Lines representing real particles in the initial and final states
- Observable in detectors

Question 6

What are Feynman diagram internal lines?

Answer 6

Virtual lines that connect verticies inside a diagram

• Represent the transfer of quantum numbers
• Not observable in detectors, do not carry a direction arrow

Question 7

What do we mean by real and virtual lines in relation to FD?

Answer 7

Real lines have a unique rest mass defined by the energy - momentum - mass relationship
Virtual lines do not obey this relationship

Question 8

What is a Feynman diagram vertex?

Answer 8

A point at which quantum numbers are transferred

- Each vertex is associated with a coupling factor that represents the Force strength

Question 9

Why are coupling factors important?

Answer 9

They are used in the amplitude calculation

Question 10

How are particle and antiparticle lines represented on a FD?

Answer 10

Particle lines travel forwards

Antiparticle lines travel “backwards”

Question 11

What do we mean by preserving the “sense” of the arrows in a FD?

Answer 11

You should be able to follow a fermion line from one to another without being stopped at a vertex

Question 12

Describe the hierarchy of the Feyman diagram types

Answer 12

Leading order diagram
Next-to-LO diagram (NLO)
Next-to-next-to-LO diagram

Question 13

Why are the different types of Feyman diagrams improtant?

Answer 13

Because they all possible ways of a particle transitioning from state i to state f must be considered

Question 14

What are the coupling factors for the four fundamental forces?

Answer 14

EM (fine structure constant) = 1/137
Weak = 1/5
Strong and gravity are complicated

Question 15

For the weak and EM interaction, why can we get away with only calculating the LO diagram?

Answer 15

Because the series converges as the coupling factor is &laquo_space;1

Question 16

What are the main steps for drawing a FD?

Answer 16

1. Work out what force(s) can be involved by looking at the initial and final states
2. Analyse the states - what has been destroyed/created?

Question 17

FD Strategy: If a photon is involved, what must the force be?

Answer 17

EM

Question 18

FD Strategy: If neutrinos are involved, what must the force be?

Answer 18

Charged weak W+-

Question 19

FD Strategy: If there is a flavour change, what must the force be?

Answer 19

Charged weak W+-

Question 20

State the heirarchy for choosing the force involved in a FD

Answer 20

Strong -> EM -> Weak

Question 21

How many vertices must be present in order to consider LO, NLO and NNLO diagrams?

Answer 21

2 for LO
4 for NLO
6 for NNLO

Question 22

How can we calculate the amplitude of an interation?

Answer 22

Amplitude is proportional to the coupling factor squared

Question 23

What is a FCNC and why is it important?

Answer 23

There is no flavour changing neutral current that exists in the SM