Quarks

Question 1

How is charge written in terms of isospin & hypercharge?

Answer 1

Question 2

What is the equation for hypercharge?

Answer 2

Question 3

How do the following symmetry operators act on the following quantum numbers?

Answer 3

Question 4

How are CP eigenstates defined (using mesons as an example)?

Answer 4

Question 5

What is the table of existing mesons relative to quark content?

Answer 5

Question 6

How do the Cabibbo & CKM mixing matrices act on quarks?

Answer 6

Question 7

How does the Wolfenstein parameterisation of the CKM matrix appear (up to 3rd order)?

Answer 7

Question 8

Draw the two box diagrams that cause meson mixing, using neutral kaons as an example.

Answer 8

Question 9

How do we define meson mass eigenstates?
State the condition for CP violation in mixing.

Answer 9

Question 10

What is the function responsible for meson mixing?
Define all terms in the function.
What is the condition for meson mixing to occur?

Answer 10

For meson mixing to occur, either (x) or (y) must be non-zero.

Question 11

What are the following probabilities of meson mixing occuring, in terms of the meson mixing function?

Answer 11

Question 12

What are the following meson average lifetimes?

Answer 12

Question 13

What is the asymmetry term for CP violation in decays (in terms of both decay channels and the strong & weak phases)?

Answer 13

Question 14

What are the decay amplitudes in terms of the leading-order and suppressed amplitudes?
(HINT: define the ratio, strong & weak phases).

Answer 14

Question 15

What diagram represents the impact parameter used in heavy flavour tagging?

Answer 15

Question 16

What diagram represents B-tagging, and what do we measure in opposite/same-side tagging?

Answer 16

• Opposite : follow the b-charge as it decays in leptons or kaons, then trace back to find the root
• Same-side : Search for flavour pairs (e.g. u and ū).
  Note : neutral B-mesons can oscillate & produce false tagging.

Question 17

What are tree-level colour allowed & supressed decay diagrams (use the neutral D-meson as an example)?

Answer 17

Question 18

What is a W-exchange diagram (use netural D-meson decay as an example)?

Answer 18

The leading order diagram where both quarks change flavour.

Question 19

What is a gluonic penguin diagram (use neutral D-meson decay as an example)?

Answer 19

A decay with a W-loop and gluon pair production.

Question 20

What is an electromagentic penguin diagram (use neutral D-meson decay as an example)?

Answer 20

Contains a W-loop and photon/Z-boson pair production.

Question 21

What is a meson annihilation diagram?

Answer 21

Note: heavily colour suppressed.

Question 22

What is the systematic uncertainty mitigation for CP amplitudes?

Answer 22

Question 23

What is the Dalitz plot for finding mass pairs?

Answer 23

It tells you the masses of resonances in decays

Question 24

How do we measure CP violating mixing asymmetrys?

Answer 24

Question 25

What variable do we use evaluate CP violation in the interference of mixing & decays?

Answer 25

Question 26

How does the CP violating interference variable tell us if & where we have CP violations?

Answer 26

Question 27

Construct an example of a unitary triangle from the following unitary relation.

Answer 27

Question 28

What is direct & indirect CP violation?

Answer 28

- **Direct** Occurs when the decay isn't equal to the decay of the CP conjugate. - **Indirect** Occurs when they have the same decay channels, but in different rates (and can mix)

Question 29

How many parameters are there in a NxN mixing matrix?

Answer 29

Question 30

What is the mixing probability graph for neutral kaons?

Answer 30

Question 31

What is the mixing probability graph for neutral D-mesons?

Answer 31

Question 32

What is the mixing probability graph for neutral B-mesons?

Answer 32

Question 33

What is the mixing probability graph of neutral B_s mesons?

Answer 33

Question 34

What are the main differences in methods & purities of flavour tagging of neutral D & B-mesons?

Answer 34

**D-mesons** - Strong decays can be fully reconstructed - Weak decays have high backgrounds, can be partially reconstructed - Shirt lifetimes & slow oscillations, so we need high precisions. **B-meson** - Longer lifetimes,so we can track their paths & find 2nd vertices. Better precision. - Opposite & same-side tagging lets use follow flavours/charges to reconstruct vertices. For purities, think about distinguishing from the backgrounds.

Question 35

How do you tell the spin of particles in a Dalitz plot?

Answer 35

Looking at how many gaps are in the resonance.

Question 36

Name three sources of fake CP asymmetries in meson decays.

Answer 36

- **Production** Heavy quarks get swallowed up by baryons. - **B-field** Opposite charges are sent to different detectors with different efficiencies - **Interaction** Different mesons & decay products have different cross-sections with detectors

Question 37

Draw two examples (flavour & charge) of D-meson tagging.

Answer 37

Question 38

What are the three stages of event selection for flavour experiments?

Answer 38

1. Select candidates via kinematics. 2. Identify possible decay product combinations. 3. Further selection criteria (flight distance, points of origin)

Question 39

What is required for asymmetries in decays, in terms of the strong & weak phases ans the amplitudes? What is the approximate asymmetry for decay?

Answer 39

We require multiple decay amplitudes with different strong & weak phases.

Question 40

What is the PDG parameterisation of the CKM matrix?

Answer 40