1. Shu-Yu Ho Date : 2010/9/20 QFT study group
CP Violation ” Introduction to elementary particles” by David Griffiths Chapter 4
Shu-Yu Ho
Date : 2010/9/20
QFT study group

2. Outline Introduction Parity (P) Charge Conjugation (C) CP symmetry
Neutral Kaons
CP Violation (CPV)
CPT Theorem

3. Introduction
Parity

4. Introduction Parity Parity invariance
The mirror image of any physical process also represents
a perfectly possible physical process.
Physicist held the mirror symmetry of the laws of nature to be self-evident.
But in 1956 , Lee and Yang discovered that although there
was ample evidence for parity invariance in strong and
electromagnetic processes , there was no confirmation in the
case of weak interactions.

5. Introduction
Parity
Lee and Yang proposed a test , which was carried out later
that year by Wu .
In this famous experiment radioactive cobalt 60 nuclei were
carefully aligned , so that their spins pointed in same direction.
Cobalt 60 undergoes beta decay and
Wu recorded the direction of the emitted electrons.
What she found was that most of them came out in the “southerly” direction , opposite to the nuclear spin.

6. Introduction
Parity
Parity is not an invariance of weak interactions.
If it were, the electrons in Wu’s experiment would have to
come out in equal numbers , ‛north’ and ‛south’. P

7. Introduction Parity Helicity : h = +1 right-handed h = -1 left-handed
For massive particle , helicity is not Lorentz-invariant.
For massless particle , helicity is Lorentz-invariant.
By experiment ,
photons have right-handed and left-handed ;
neutrinos are left-handed ;
antineutrinos are right-handed.

8. Introduction
Parity

9. Parity is a multiplicative quantum number
Introduction
Parity
According to QFT , the parity of fermion must opposite to
that of the corresponding antiparticle , while the parity of a
boson is the same as its antiparticle.
We take the quarks to have positive intrinsic parity , so the
antiquarks are negative.
Parity is a multiplicative quantum number

10. Introduction Parity Tau-theta puzzle
Two strange mesons , called at the time θ and τ , appeared
to be identical in every respect - same mass, same spin (0) ,
same charge , and so on – expect that one of them decayed
into two pions and the other into three pions .
Lee and Yang suggested that θ and τ are really same particle
( now known as the ) , and parity is simply not conserved
in one of the decays.

11. Introduction Charge Conjugation
Classical electrodynamics is invariant under change in the
sign of all electric charges , we introduce an operation that
generalizes this notion of changing the sign of the charge.
It is called charge conjugation (C) , and it converts each
particle into its antiparticle.
Charge conjugation changes the sign of all the “ internal "
quantum numbers (charge , baryon number , lepton number,
strangeness , charm , ······ ) while leaving mass , momentum
and spin untouched.

12. Introduction
Charge Conjugation

13. Introduction
Charge Conjugation

14. Introduction Charge Conjugation
Charge conjugation is a " multiplicative " quantum number ,
it is conserved in the strong and electromagnetic interactions.
For example , the pion decays into two photons but never decays into three photons.

15. Introduction
Charge Conjugation

16. Introduction
Charge Conjugation

17. Introduction C Charge Conjugation
Charge conjugation is not a symmetry of the weak
interactions : when applied to a neutrino(left-handed),
C gives a left-handed antineutrino. C

18. Introduction C P CP symmetry
Physicists then expect CP to be a good symmetry.

19. Introduction
Neutral Kaons

20. Introduction
Neutral Kaons

21. Introduction
Neutral Kaons

22. Introduction
Neutral Kaons

23. Introduction
Neutral Kaons

24. Introduction
Neutral Kaons

25. Introduction

26. Introduction CP violation
In 1964 , Cronin and Fitch was reported an experiment. At
the end of a beam 57 feet long , they counted 45 two pion
events in a total of decays . That’s a tiny fraction , but
unmistakable evidence of CP violation.

27. Introduction
CP violation

28. Introduction CP violation
Parity is maximally violated in the weak interaction . By
contrast , CP violation is a small effect by any measure .
Within Standard Model , it can be accommodated by
including an empirical phase factor (δ) in CKM matrix ,
provided that there are three generations of quarks.

29. Introduction CP violation
32% of all KH’s decay by 3π mode we have discussed ,
41% go to
CP takes (a) into (b) , so if CP were conserved , and KL
were a pure eigenstate , (a) and (b) would be equally
probable. But experiment show that KH decays more often
into positron than into an electron.
CP violation is a necessary condition for matter-antimatter asymmetry!

30. Introduction CP violation
In 1981, Carter and Sanda pointed out that the violation
should also occur with the neutral B mesons.
A B-Factory is a machine created by particle physicists to produce large numbers of B mesons. Currently there are two B-Factories running: BaBar at SLAC in California, and Belle at KEK in Japan respectively.

31. Introduction CP violation
By 2001 , their detector had recorded evidence of CP violation in neutral B decays.
CP violation of B meson decays is larger effct than K meson decays.

32. Introduction ? Is T a good symmetry ? CPT theorem T-reversal :
Strong and Electromagnetic interaction
→ T invariance .
Weak interaction → expect not T invariance ,
but experiments are tough to do.
Is T a good symmetry ?

33. Introduction CPT theorem
CPT theorem states that the combined operations of time
reversal (T) , charge conjugation (C) , and parity (P) is an
exactly symmetry of any interaction .
Here are two reason to support this theorem :
All observations indicate that CPT is indeed a symmetry of nature.
It is impossible to construct a Lorentz-invariant QFT with a Hermitian
Hamitonian that violates CPT .

34. ? Introduction CPT theorem
MINOS ( Main Injector Neutrino Oscillation Search)
νμ Disappearance –
Oscillation Parameters Contour New at Neutrino 2010 ?