3. Quark + Hadron Masses + Decays Flashcards
What can be deduced about the masses of the up and down quark from the proton and neutron mass?
As the proton and neutron mass differ very slightly, the up and down quark mass must also differ very slightly
Describe what makes it difficult to measure quark mass and explain
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
What derives the mass of the quarks?
The couplings of the quarks to the Higgs
What is important to remember when looking at the size of the quark masses
They are scale dependent
- i.e a function of the energy scale on which they are measured
What have measurements revealed about the distribution of momentum on a nucleon?
- Roughly 50% of the of the momentum is carried by the valence quarks
- The other 50% is carried by its quark and gluon sea
Why is the mass of hadrons larger than the sum of their constituents?
Due to the Fermi motion of the constituents
How is the number of states in each multiplet related to the isospin
Number of states = 2I + 1
What does a combination of a doublet and antidoublet give
A triplet and a singlet
State how pions decay
They are the lightest mesons so are stable vs the strong interaction
- Decay via weak and EM
When do transitions to the ground state occur electromagnetically, and explain what this is
They emit one or more photons
- Will be the dominant or only transition if the strong decay is suppressed or forbidden
How does the ground state decay, and explain why
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
What does the combination of a triplet and an antitriplet give
An octet and a singlet
Why can the top quark not form hadrons
It is so large that it decays weakly very quickly due to its large phase space
- Has a very short lifetime
What are quarkonia states
Bound states of a quark and anti quark with the same flavour
How are quarkonia states and mesons different?
Quarkonia ground states are not limited to weak decays only
- Can also have OZI suppressed transitions
What is the colour of mesons and hadrons
0 - They are colourless states
What are branching fractions?
The probability of the different decay channels
What is the total decay rate equal to?
The sum of the individual decay rates
What is an exclusive decay?
One where all the final state particles are defined
What is an inclusive decay?
One where all the final state particles aren’t defined
What is a hadronic decay?
Where the final state particles are all hadrons
- Hadronic decay of hadrons can be through the weak or strong interaction
What is a leptonic decay?
Where the final state particles are all leptons
- Leptonic decays of hadrons are always weak where flavour is not conserved
What is a semi leptonic decay
When the final state contains hadrons and leptons
What is a radiative decay?
When a photon is emitted usually through the EM interaction, but it could also be weak
How are two body decays for particles with spin and without spin different
Particles without spin decay isotropically
Particles with spin have an orientation of their final state which represents the polarisation of the initial state
What does it mean if a particle is “on mass shell”
It is a real particle and obeys Einstein’s energy-momentum relationship
- It has 3 degrees of freedom rather than 4
What is a Dalitz plot
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
How many degrees of freedom does the 3 body decay have
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
Describe how biased and unbiased distributions appear on a Dalitz plot
Unbiased would be uniformly distributed across the plane
Biased would have the characteristic right angled triangle with rounded edges
