1. Today’s plan
Collect homework
QCD leftovers
Weak Interaction

2. Why is the singlet discarded ?
Gluons carry color –anti color combinations
The singlet is symmetric and colorless and would couple to baryons.
Tata, Griffiths….
In SU(3)QCD combine a color triplet (R,G,B) and an anti-triplet
There are 8 gluons

3. Before QCD in the 1960’s: String Theory of Hadrons
Perkins
Some problems with full theory: seems to predict a massless tensor particle
Note the string is relativistic and rotating !

4. “String Theory” derivation
Perkins:
“String Theory” derivation
Here r0 is the half-length of the string.
Perkins 5th edition

5. String Theory of Hadrons: J vs M2
mesons
baryons
Tullio Regge
baryons

6. Neutron β decay is the first weak interaction studied in detail.
Enrico Fermi proposed an accurate theory for the weak interaction in 1933 before quarks, Feynman diagrams, W bosons, QFT etc.
The weak vector bosons, which mediate the weak interaction have masses of O(100 GeV) (“the weak scale”), and hence at low energies the two vertices in the Feynman diagram appear to be merged and the interaction is point-like.
Question: How do the weak interaction propagators compare to those for QED or QCD ?
1938 Nobel Prize for discoveries related to neutrons and nuclear physics (not weak interaction).

7. There are two broad classes of weak interactions called the charged current (CC) and neutral current (NC).
Question: Which one is the NC reaction ?
Ans c), mediated by a virtual Z0
Question: How would one detect a NC decay or reaction ?
Ans: observe the electron recoil in the case of c).

8. Question: What are the three types of weak interaction processes
Question: What are the three types of weak interaction processes ? (Are they all decays or is scattering also possible ?)
Ans: (1) leptonic, (2) semileptonic (3) hadronic. For (3) only weak decays are possible.

9. Muon decay
Effectively a point-like interaction with coupling strength “G Fermi”
Here g is the weak charge.

10. Dimensional Analysis of GF
[GF] ~ 1/[E]2 . However, [E]~[1/L]

11. Muon lifetime
Effectively a point-like interaction with coupling strength “G Fermi”
Here g is the weak charge.
Question:
In natural units, what are the dimensions of GF and m
Ans: 1/E4 and E5 but Gamma is 1/T or E

12. Leptonic τ decays
Let’s compare the widths for different types of leptonic tau decay.

13. Leptonic τ decays
Experimentally, let’s also compare the widths for different types of leptonic tau decay.
Lepton universality in the weak interaction

14. Is this a general result ?
Let’s compare muon and tau decays (which have these Feynman diagrams.
Question: What are the Feynman diagrams for muon and tau semi-electronic decay ? Show the weak charges explicitly.
Ans: it decays 100% of the time to an electron
Question: Why don’t we have a BF term for the muon ?

15. Is this a general result ?
Let’s compare muon and tau decays (which have these Feynman diagrams.
Mass measurements from BES (Beijing)
Solve for ratio of g’s

16. Lepton Universality in the weak interaction is nearly perfect.
Question: What about hadronic couplings of the weak interaction ? Are they universal ?

17. Neutrino weak cross-sections
Question: What is the Feynman diagram for muon-neutrino electron scattering ?
Question: Suppose the neutrino has energy Eν and the electron is initially at rest, what is s ?
Question: In NU, can we check the dimensions ?
Ans: [L]2 ~1/E2 however, GF~1/E2 and s~E2
Question: Does the cross-section rise for all E ?

18. Hadronic weak currents
Vus
Vud
Here the coupling is GF x Vij where the Vij are elements of the CKM (Cabibbo Kobayashi Maskawa) matrix. The values may be complex numbers !

19. Eigenstates
The rotation angle is the “Cabibbo angle”.
Weak interaction quark eigenstates (d’-type) are rotated from strong interaction quark eigenstates (d-type).
Cabibbo did not share in the 2008 Nobel Prize for Kobayashi and Maskawa