Countries that signed the nuclear arms treaty with Iran

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. p.91 Intrinsic Parities of fermions and anti-fermions are opposite

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-

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

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 ?

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 ?

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

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

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

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

Question: But why are muons and electrons different ? Answer: the ratio of the masses 106 MeV (muon) versus 0.511 MeV (electron) The V-A nature of the weak interaction explains the ml2 dependence of the decay rate.

Baryon number

Lepton flavor and lepton number

Isospin

The spin ½ baryons

The pseudoscalor mesons

The sum of two isospins; the product of two representations