1. Lecture 7
Parity
Charge conjugation
G-parity CP
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2. Already done a lot to understand the basic particles of nature
Strong, weak,em ?
Lepton universality
Isospin singlets
175000
Isospin multiplets
small
small
small
Neutrino oscillations/mass
Quark composition
Decay modes
Symmetry and QM demands much of what is observed!
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3. Transforming under parity1
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4. Ways of thinking about parity
Possible.
Not possible. v
ms=-1/2
ms=1/2 +
real
”virtual”
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5. Intrinsic Parity
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6. Intrinsic Parity
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7. Calculating parity Particle Parity (P) -1
Pseudoscalar mesons (s=0) p,K,h,D,B -1
Vector mesons (s=1) K*,w,f
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8. Parity of the photon
Dl=+-1 g
Atomic energy levels
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9. Parity of the electron
positronium
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10. Intrinsic parity Particle Parity (P) +1 -1 Electron, muon, tau
Positron,antimuon,antitau -1
Quark
Antiquark
Photon
Pseudoscalar mesons (s=0,l=0) p,K,h,D,B..
Vector mesons (s=1,l=0) K*,w,f
Ground state baryons (l=0) p,n,S..
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11. Question
Before Wu’s experiment the t and q particles were observed with the same spin, mass, charge. They were thought to be different particles because they decayed into states with different parities
Calculate the parity of the pion system from the second decay. Assume no orbital angular momentum in the final pion system.
State which particle t and q is.
Which of the decays violates parity ?
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12. Charge conjugation: C
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13. Question
Show, with the example of a neutrino, that charge conjugation is not a symmetry of the weak force.
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14. C-parity (C)
Same game as for parity! We’ve found a symmetry of the em and strong forces, but not of the weak.
Find a quantity conserved in strong and em processes.
Most particles are not eigenstates of
Particles which are eigenstates are their own particles, eg p0,g,r0
Can also construct eigenstates using particle-antiparticle pairs, eg
Particles or multiparticle states have eigen value known as an intrinsic C-parity quantum number, eg g has C=-1
C is a multiplicative quantum number like parity.
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15. Calculating C C for the lowest mass hadron states (l=0 )
Unless otherwise stated, we will be dealing in this lecture with systems of particles for which l=0.
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16. Question
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17. Pseudoscalar mesons (s=0) p,K,h,D,B
C and P
Particle P C
Pseudoscalar mesons (s=0) p,K,h,D,B -1 +1
Vector mesons
(s=1) K*,w,f
Photon
Ground state baryons
N/A
Charged Leptons 1
Charged anti- leptons
C value only applicable
for particles which are
their own anti-particles
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18. Formalism A particle is characterised by the form JPC, eg 1--
J=total angular momentum, P=parity(+ = +1,- = -1), C=charge conjugation number (+ = +1, - = -1)
In certain situations C is not a useful quantum number – most particles are not eigenstates of C:
JP is used.
P= ”even” parity, P= ”odd” parity
C= ”even” C-parity, C= ”odd” C-parity
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19. G-parity
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20. Particles for which G-parity is relevant
(7.34)
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21. Some decays explained with G-parity
,ppp
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22. Conserved quantities/symmetries
Quantity
Strong
Weak
Electromagnetic
Energy 
Linear momentum
Angular momentum
Baryon number
Lepton number
Isospin -
Flavour (S,C,B)
Charges (em, strong and weak forces)
Parity (P)
C-parity (C)
G-parity (G) CP T
CPT
Coming up
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23. CP  X  C and P are not separately respected in weak decays
What about CP ?
Original and CP-transformed decays occur with same rate. CP symmetry is respected in many weak processes.  X 
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24. FK7003

25. Neutral kaons
We define a neutral K0 by its quark content (sd), mass (498 MeV), spin (0), isospin (I=1/2,I3=-1/2) - a normal particle !
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26. Strategy
Test the hypothesis that CP is a good symmetry of the weak force.
Try to form CP eigenstates from K0 and K0 and check they decay in CP-conserving ways (recall p gg and C conservation.)
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28. Neutral Kaons and Strangeness Oscillations
Consider in the kaon rest frame and allow a decay
Consider a particle produced at t=0 as a K0 . Amplitude that it is still a K0 at a later time t:
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29. Probability that it is still a K0 at a later time t:
Strangeness oscillation!!
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30. Kaon oscillations (Niebergall et al., 1974) Intensity 2 4 6 8
Time in K0 rest frame (x10-10 s)
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31. Question
To measure the oscillations of a beam of neutral kaons of energy 10 GeV how large should an experiment be ?
(Niebergall et al., 1974)
Intensity
Time in K0 rest frame (x10-10 s)
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32. Some interpretation and comparisons
|DS|=2
Strangeness violated
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33. Summary Discrete symmetries Next lecture – CP violation Parity (P)
Charge conjugation (C-parity)
G-parity
Fundamental symmetries of nature constrain the behaviour of particles CP
Neutral kaons
Strangeness oscillations
Next lecture – CP violation
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