Countries that signed the nuclear arms treaty with Iran - PowerPoint Presentation

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Countries that signed the nuclear arms treaty with Iran Slide2

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

P

2=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 oppositeSlide3

Intrinsic parities of fermions and bosons (continued)

Question: What is the J

P

for the photon ?

Answer: 1

-

Question: What is the J

P for a pion (and an anti-pion) ?Answer: O-Slide4

Example of parity of a two-body system with relative orbital angular

momentum l

The derivation closely follows the example that we did for the hydrogen atom last time.

Here P

1

and P

2 are the intrinsic parities of the two particles.

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+1Slide5

Question: What are the possible values of J

P

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 ?Slide6

Charge conjugation (continued)

C eigenvalues of the photon and π

0

Question: What is the charge conjugation of the π

0

?

Ans

: it is the charge conjugation of two photons ? (-1)(-1) = +1

Question: What does the charge conjugation operator do to a charged pion ?Slide7

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)

sSlide8
Slide9

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-particleSlide10

ASACUSA (low energy anti-proton experiment at CERN)

2003Slide11

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 kinematicsSlide12
Slide13

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 m

l2

(mass-squared) dependence of the decay rate.