1. Nuclear Physics Curve of Binding Energy
The “mass defect” is the difference between the nuclei’s mass and the sum of the masses of its neutron and proton constitutents
Binding energy is the energy required to separate a nucleus into individual protons and neutrons. The strong nuclear force is responsible for this binding.

2. Odd-even nuclei are found to be less stable than even-even nuclei
Question: What uranium isotope is most abundant ?

3. Today’s plan Posted Chapter 7 homework assignment
More on the weak interaction: CKM matrix
Quiz on QCD

4. The CKM rotation matrix
Parameter counting: a complex 3 x 3 unitarity matrix has 9 independent elements.
Rephasing invariance
In the end, there are three rotation angles and one irreducible complex phase factor eiδ

5. This result is quite clear in the Wolfenstein parameterization of the CKM matrix.
Lincoln Wolfenstein
In the end, there are three rotation angles and one complex phase factor eiδ
Question: What are the three real parameters and phase in the Wolfenstein parameterization ?
Ans: A, λ, ρ and η

6. Last time: CKM weak interaction exampleb
Cabibbo favored: VcsVud
Singly Cabibbo suppressed: VcsVus c d
Singly Cabibbo suppressed: VcdVud
Doubly Cabibbo suppressed: VcdVus

7. CKM weak interaction Question:
Hint: What is the valence quark content in the two reactions ? (ρ- = ubar d)
Hint: Draw the Feynman diagrams for the two reactions.

8. CKM example

9. How are the magnitudes of the CKM matrix elements experimentally determined ?
For example, |Vud| comes from measurement of allowed 0+ 0+ β decays, the neutron lifetime and pion semileptonic decay. (all methods agree at the 0.1% level)
This is a rather rare decay mode with a branching ratio of O(10-8). Need 1014 pion decays to do this. Experiment at PSI (Paul Scherrer Institute) in Switzerland.
Question: Can you draw the Feynman diagram for this decay and indicate the couplings at each vertex ?

10. Diagrams for πe3 decay
Note the strong interactions of the spectator quark.
Introduced the hadronic form factor f+(q2), which is evaluated at q2=0 since the energy release is so small.
Can be obtained from data using isospin symmetry

11. Here Δ is the Q value for the decay, δEM , is a small radiative (electromagnetic) correction and f is the Fermi function, ε~ 10-2
Question: Does the above formula remind you of any other calculation in the weak interaction chapter ? What is the same and what is different ?

13. Question: Why are there two diagrams shown here ?
The best experiment is done at the KLOE experiment in Frascati, Italy.
To measure Vus:
Question: Can you draw the diagrams for this decay ? Show the weak couplings.
Question: Why are there two diagrams shown here ?
Ans: The Kshort weak eigenstate is the a linear combination of the K0 and anti-K0 strong interaction eigenstates.

14. Question: Does this look familiar ?
Covers a range in q2 2%
0.5%
Question: Does this look familiar ?
Question: what is q2 in this case ?

15. KLOE experiment at Frascati, Italy