1. Nuclear Physics: Mossbauer Effect
Problem:
In the Mossbauer effect, the entire crystal lattice absorbs the recoil.
Discovered in 1957 by Rudolf Mossbauer while still a graduate student. Nobel Prize in 1961.

2. Nuclear Physics: Mossbauer Effect

3. Narrowest spectral line known (ΔE/E =10-12)
Mossbauer effect for Al foil. (note the shift from zero).
Mossbauer effect for Fe foil. Splitting due to nuclear magnetic field (NOT an external B field).

4. Application of the Mossbauer Effect.
The Pound Rebka experiment used the Mossbauer effect to test general relativity.

5. Today’s plan Reminder: Final Exam (Friday May 5, time 13:30-15:30).
Chapter 9 material
Reminder: Final Exam
(Friday May 5, time 13:30-15:30).
Schedule for presentations:
Friday April 28
Anirvan (LHCb pentaquark);
Tommy (CPV in the B system);
Makana (discovery of the Higgs)
Monday May 1
Tyler (discovery of the top quark),
James (new detector technology)
Glashow, Salam and Weinberg
1979 Nobel Prize in Physics.

6. Weak Interaction Game Plan
In previous chapters, we studied charged current (CC) weak processes, for which the Standard Model coincides with the four-fermion interaction (Fermi model).
In this chapter, we will examine neutral current (NC) weak processes. For NC processes, the effects of electroweak unification appear directly.
The mediators of the weak interactions (W+, W-, Z0) have direct interactions and a “triple gauge boson coupling”. This was tested at LEP. (Note that we saw an example of triple gauge boson coupling in QCD,
“three gluon vertex”.

7. Weak Isospin, Doublets Let’s introduce weak isospin and hypercharge
In the gauge theory of the electroweak interaction, the symmetry (gauge) group is SU(2) x U(1)
The weak isospin IW corresponds to SU(2)
The hypercharge corresponds to U(1)
N.B. weak isospin has nothing to do with isospin for hadrons

8. Weak Isospin (examples)
Question: Let W=(W1, W2, W3) be the triplet of SU(2) fields, what is IW and Yw for this triplet ?
Ans: IW=1 and YW=0 (since W+- and Z0)
Question: Let B be the gauge field of U(1), what is IW and Yw in this case ?
Ans: Its weak isospin, electric charge and hypercharge are all zero. Note it is a weak isosinglet.
Neutrinos and leptons make weak isospin doublets. These couple with the W.

9. Weak Isospin (more examples)
Question: let’s try some charged leptons next. What is the weak isospin and hypercharge of the tau neutrino and tau lepton ?
Ans: IW=1/2 (doublet) and YW=-1, 1 (2 * Iz).
Quarks form weak isospin doublets but there is a difference (and three for each color)
Note the bottom entry is a rotated version of dL, sL, bL etc.

10. The neutral current couples to right-handed weak isospin singlets
Up to this point, we have covered the charged current (CC) in the weak interaction. In the NC (neutral current) part of the weak interaction, there is an important and interesting difference.
The neutral current couples to right-handed weak isospin singlets
The charged current (CC) does NOT couple to these isospin singlets.
There are no right-handed neutrinos.
N.B. The charged current couples to left-handed leptons and right-handed anti-leptons.

11. Weak Interaction couplings
Ans: L L works but LR does not for W. For Z L L is ok or R R is ok but not R L
Question: Let’s check the hypercharge for one of these reactions e.g. Z0anti-uL+uR

12. Review: Possible weak neutral couplings
Question: Which neutral couplings are allowed ? Why ?
Ans: No flavor –changing neutral currents (FCNC) at 1st order in the Standard Model.

13. Steve Weinberg at University of Texas at Austin
The Weinberg angle is named after him.
Start with the W, B the gauge fields for SU(2) and U(1). End up with the physical fields W±, Z and γ and their couplings to fermions.

14. The couplings to fermions are mediated by weak currents called jμ, which are isovectors made up of 4-vectors.
The physical fields are
Need couplings and weak currents.

15. The angle is called the “Weinberg angle” or weak mixing angle
The angle is called the “Weinberg angle” or weak mixing angle. It expresses the connection between the EM and weak neutral currents. It is not small,a round 290.

16. Question: Can you identify the three pieces in this lagrangian ?
Glashow-Salam-Weinberg Electroweak Theory.
1999 Nobel Prize
Gerard t’Hooft and M. Veltmann
Question: Can you identify the three pieces in this lagrangian ?
CC weak interaction
NC weak interaction
EM interaction
The first equation unifies the weak and EM couplings.

17. NC weak interaction
The weak couplings of the Z are given by this equation.
There are 7 different ways to measure the Weinberg angle. Perhaps the most precise and important uses the masses of the gauge bosons. (p ).

18. Coupling constants for the Z vertex in neutrino scattering to measure θW
Question: Are these identical ?
Ans: for instance, top row has eR and eL contributions.
There are LL and RR contributions.
Question: What is the neutrino energy dependence of these cross-sections
Ans: GF2 me Eν

19. Angular dependence in neutral current scattering.
Question: What is the total spin in the initial and final states in a) and in b) ?
Ans: Spin 0 for a) and Spin 1) for b).
For b) only one Jz state (Jz=-1) is allowed out of the 2J+1 possible states so there is a factor of 1/3 for the b) contribution

20. Question: How is this different from the other ratio of neutrino cross-sections that we have studied ?