3. Quark + Hadron Masses + Decays

Question 1

What can be deduced about the masses of the up and down quark from the proton and neutron mass?

Answer 1

As the proton and neutron mass differ very slightly, the up and down quark mass must also differ very slightly

Question 2

Describe what makes it difficult to measure quark mass and explain

Answer 2

Different mesons can have very different masses
- The effects related to the alignment of spins of the quark and antiquark of the meson can have a large effect on the masses
- Called hyperfine splitting effects

Question 3

What derives the mass of the quarks?

Answer 3

The couplings of the quarks to the Higgs

Question 4

What is important to remember when looking at the size of the quark masses

Answer 4

They are scale dependent
- i.e a function of the energy scale on which they are measured

Question 5

What have measurements revealed about the distribution of momentum on a nucleon?

Answer 5

• Roughly 50% of the of the momentum is carried by the valence quarks
• The other 50% is carried by its quark and gluon sea

Question 6

Why is the mass of hadrons larger than the sum of their constituents?

Answer 6

Due to the Fermi motion of the constituents

Question 7

How is the number of states in each multiplet related to the isospin

Answer 7

Number of states = 2I + 1

Question 8

What does a combination of a doublet and antidoublet give

Answer 8

A triplet and a singlet

Question 9

State how pions decay

Answer 9

They are the lightest mesons so are stable vs the strong interaction
- Decay via weak and EM

Question 10

When do transitions to the ground state occur electromagnetically, and explain what this is

Answer 10

They emit one or more photons
- Will be the dominant or only transition if the strong decay is suppressed or forbidden

Question 11

How does the ground state decay, and explain why

Answer 11

Decays weakly because flavour is conserved in the strong interaction
- The decay of any lightest flavoured meson results in a flavour change
- The lightest hadrons of each flavour are long lived

Question 12

What does the combination of a triplet and an antitriplet give

Answer 12

An octet and a singlet

Question 13

Why can the top quark not form hadrons

Answer 13

It is so large that it decays weakly very quickly due to its large phase space
- Has a very short lifetime

Question 14

What are quarkonia states

Answer 14

Bound states of a quark and anti quark with the same flavour

Question 15

How are quarkonia states and mesons different?

Answer 15

Quarkonia ground states are not limited to weak decays only
- Can also have OZI suppressed transitions

Question 16

What is the colour of mesons and hadrons

Answer 16

0 - They are colourless states

Question 17

What are branching fractions?

Answer 17

The probability of the different decay channels

Question 18

What is the total decay rate equal to?

Answer 18

The sum of the individual decay rates

Question 19

What is an exclusive decay?

Answer 19

One where all the final state particles are defined

Question 20

What is an inclusive decay?

Answer 20

One where all the final state particles aren’t defined

Question 21

What is a hadronic decay?

Answer 21

Where the final state particles are all hadrons
- Hadronic decay of hadrons can be through the weak or strong interaction

Question 22

What is a leptonic decay?

Answer 22

Where the final state particles are all leptons
- Leptonic decays of hadrons are always weak where flavour is not conserved

Question 23

What is a semi leptonic decay

Answer 23

When the final state contains hadrons and leptons

Question 24

What is a radiative decay?

Answer 24

When a photon is emitted usually through the EM interaction, but it could also be weak

Question 25

How are two body decays for particles with spin and without spin different

Answer 25

Particles without spin decay isotropically
Particles with spin have an orientation of their final state which represents the polarisation of the initial state

Question 26

What does it mean if a particle is “on mass shell”

Answer 26

It is a real particle and obeys Einstein’s energy-momentum relationship
- It has 3 degrees of freedom rather than 4

Question 27

What is a Dalitz plot

Answer 27

a scatter plot of one pairwise invariant mass squared against another
- Allows the two left over degrees of freedom of the 3 body decay to be visualised

Question 28

How many degrees of freedom does the 3 body decay have

Answer 28

Has 9 (3 for each particle)
- Can subtract 4 as the total 4 momentum is conserved
- Left with 3 angular degrees of freedom (or 0 if spin 0) and 2 magnitude degrees of freedom

Question 29

Describe how biased and unbiased distributions appear on a Dalitz plot

Answer 29

Unbiased would be uniformly distributed across the plane
Biased would have the characteristic right angled triangle with rounded edges