1. Countries that signed the nuclear arms treaty with Iran

2. Intrinsic parities of fermions and bosons
Intrinsic parity can be defined if a particle is at rest.
For scalars (spin 0), vectors (spin 1) and tensors, parity is equivalent to a rotation by 2π
P2=1 so P= ±1
Subtle point: Bosons have well-defined parity but fermions (spin ½) are spinors and produced in pairs. So one can define relative parity of fermions and anti-fermions that satisfy the Dirac equation. In addition, the parity of Dirac fermions can be real or imaginary. By convention, we choose it to be real.
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Intrinsic Parities of fermions and anti-fermions are opposite

3. Intrinsic parities of fermions and bosons (continued)
Question: What is the JP for the photon ?
Answer: 1-
Question: What is the JP for a pion (and an anti-pion) ?
Answer: O-

4. Example of parity of a two-body system with relative orbital angular momentum l
Here P1 and P2 are the intrinsic parities of the two particles.
The derivation closely follows the example that we did for the hydrogen atom last time.
Question: What is the parity of two pions in a p-wave (l=1) state ?
Answer: P(pion)P(pion)(-1) = -1
Question: What is the parity of a proton and anti-proton in an orbital angular momentum state l?
Ans: These are fermions (spin ½) so they have opposite intrinsic parities. (1)(-1)l = (-1)l+1

5. Question: What are the possible values of JP for a spin ½ particle and its anti-particle if they are in a S-wave state or a P-wave state (an example in atomic physics is positronium)
Hint: addition of angular momentum in QM
Do you understand the spectroscopic notation ? What is the left superscript ?

6. Charge conjugation (continued) C eigenvalues of the photon and π0
Question: What is the charge conjugation of the π0 ?
Ans: it is the charge conjugation of two photons ? (-1)(-1) = +1
Question: What does the charge conjugation operator do to a charged pion ?

7. Charge conjugation (continued)
Question: What is the charge conjugation of a charged meson-antimeson pair with relative orbital angular momentum l ? (Do two cases: when the mesons are spin zero and when they have non-zero spin)
Hint: M+  M- and M- and M+ under C.
Now let’s try spin 1 mesons (spin 0, 1, 2). What is the symmetry of spin 0, 2 ?
So there is an extra factor of (-1)s

9. Time reversal and CPT
There is a theorem from QFT (Quantum Field Theory) called the CPT theorem, which states if a local theory of interacting fields is invariant under the proper Lorentz group, it will also be invariant under the combination of C (particle-anti particle conjugation), space inversion (P) and time reversal (T).
Consequences: if CP is violated then T is violated (and the theory is not invariant under the reversal of the direction of time)
particle
Anti-particle

10. ASACUSA (low energy anti-proton experiment at CERN)
2003
PDG

11. Mystery of charged pion decay
But the ratio of phase space volume goes like p(electron)/p(muon) as discussed in Chapter 1.
Question: How can we the four order of magnitude discrepancy ?
Two body decay kinematics

13. Question: But why are muons and electrons different ?
Answer: the ratio of the masses 106 MeV (muon) versus MeV (electron)
The V-A nature of the weak interaction explains the ml2 dependence of the decay rate.

14. Baryon number

15. Lepton flavor and lepton number

16. Isospin

17. The spin ½ baryons

18. The pseudoscalor mesons

19. The sum of two isospins; the product of two representations