7. Weak Interaction Phenomena

Question 1

What does the parity operator P do?

Answer 1

Changes signs of all the components of the three vectors in the system

Question 2

What is a consequence of a system being symmetrical under parity wrt its handedness?

Answer 2

If it is symmetrical under P, you cannot distinguish between the LH and RH coordinate systems
- The equations governing the system are the same in either coord system and vv

Question 3

What are the eigenvalues of the parity operator P and when is it conserved?

Answer 3

Eigenvalues of +1 and -1
It is conserved when the description is symmetrical

Question 4

What does the charge conjugation operator C do?

Answer 4

Interchanges particles with anti particles

Question 5

What is a consequence of a system being symmetrical under charge conjugation

Answer 5

Cannot distinguish between particles and anti particles and vv

Question 6

What are the eigenvalues of the charge conjugation operator C and when is it conserved?

Answer 6

Eigenvalues of +1 and -1
It is conserved when the description is symmetrical

Question 7

Which fundamental forces are conserved by the C and P operators?

Answer 7

Strong and EM conserve C and P
Weak does not due to its V-A structure

Question 8

Describe what was observed in the experiment which exhibited the weak interaction violating parity

Answer 8

Used a polarised sample of cobalt and in beta decay, the electrons were emitted preferentially in teh direction opposite to the spin polarisation
- Maximally violated

Question 9

Describe what is meant by maximal parity violation, and how this is calculated

Answer 9

Calculates N(↓) - N(↑) / N(↓) + N(↑)
- N(↓) is the number of electrons emitted in the opposite direction of polarisation
- N(↑) is the number of electrons emitted in the parallel direction of polarisation
- Calcualted to be +1 for the WI parity violation which is the max number

Question 10

What does the C symmetry imply about the decay rate

Answer 10

The particle decay rate is equal to the anti particle decay rate

Question 11

What does the CP symmetry imply about the total rate of a process

Answer 11

The total rate for a process (decay or interaction) is equal to the total rate of the anti process

Question 12

What does CP violation allow you to distinguish between

Answer 12

Matter and anti matter and LH and RH

Question 13

What is the CP symmetry of the universe?

Answer 13

CP asymmetric as the observed universe is made of matter

Question 14

How is CP related to the BB

Answer 14

It is thought that the U contained equal amounts of matter and anti matter
- CP would have been necessary to eliminate all the anti matter while retaining a tiny portion of matter

Question 14

How is CP related to the BB

Answer 14

It is thought that the U contained equal amounts of matter and anti matter
- CP would have been necessary to eliminate all the anti matter while retaining a tiny portion of matter

Question 15

What are the three Sakharov conditions

Answer 15

1. A baryon number violating process existed, so the total U baryon number could change
2. C and CP violating processes were taking place. This means the baryon number violating process affects baryons and anti baryons at different rates
3. Processes forwards wouldn’t equal processes backwards as the U is out of thermal equilibrium

Question 16

Which of the C,P,T operators are unitary?

Answer 16

C and P are
T is not

Question 17

Describe what the T operator does and how it is different to the C and P operators

Answer 17

The T operators reverses the time direction of the theory
- As it is not unitary it does not result in a conservation law

Question 18

Describe what happens to parameters under the T operator

Answer 18

Momenta, spins change sign
- complex scalars in the Lagrangian or Hamiltonian become complex conjugated

Question 19

What is the CPT theorem and state the two consequences of it?

Answer 19

CPT symmetry is respected in any QFT which is local, unitary and Lorentz invariant
- Consequences are that mass and lifetime of a given particle is equal to the antiparticle

Question 20

Describe how we can test for CP and T symmetry violations

Answer 20

Neutral meson oscillations
- The probability of a meson to oscillate into its antiparticle and reverse process are related by both CP and T symmetries
- They have different probabilities

Question 21

What are penguin diagrams?

Answer 21

A one loop process where a quark temporarily changes flavour and this quark engages in a tree interaction

Question 22

Describe why we can see FCNCs in penguin diagrams

Answer 22

They are forbidden in tree diagrams, but can appear rarely in loop diagrams, such as penguin diagrams

Question 23

What are box diagrams?

Answer 23

Second order weak interaction (flavour changes by 2 units)
- Transitions between meson particles and anti particles

Question 24

Does strangeness commute with the Hamiltonian?

Answer 24

No as it does not conserve flavour

Question 25

What is the intrinsic parity of a pion?

Answer 25

-1