CP Violation CP Violation ” ” Introduction to elementary Introduction to elementary

particles”particles”by David Griffithsby David Griffiths

Chapter 4Chapter 4

Shu-Yu HoShu-Yu Ho

Date : 2010/9/20Date : 2010/9/20

QFT study QFT study groupgroup

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

IntroductionIntroduction Parity

IntroductionIntroduction Parity

Parity invarianceThe 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.

IntroductionIntroduction 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.

IntroductionIntroduction 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

IntroductionIntroduction 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.

IntroductionIntroduction Parity

IntroductionIntroduction 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

IntroductionIntroduction 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.

+K

IntroductionIntroduction 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.

IntroductionIntroduction Charge Conjugation

IntroductionIntroduction Charge Conjugation

IntroductionIntroduction 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.

IntroductionIntroduction Charge Conjugation

IntroductionIntroduction Charge Conjugation

IntroductionIntroduction 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

CP symmetry

IntroductionIntroduction

PC

Physicists then expect CP to be a good symmetry.

IntroductionIntroduction Neutral Kaons

IntroductionIntroduction Neutral Kaons

IntroductionIntroduction Neutral Kaons

IntroductionIntroduction Neutral Kaons

IntroductionIntroduction Neutral Kaons

IntroductionIntroduction Neutral Kaons

IntroductionIntroduction

IntroductionIntroduction 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 22700 decays . That’s a tiny fraction , but

unmistakable evidence of CP violation.

IntroductionIntroduction CP violation

IntroductionIntroduction 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.

IntroductionIntroduction 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!

IntroductionIntroduction 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.

IntroductionIntroduction 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.

IntroductionIntroduction CPT theorem

T-reversal :

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Is T a good symmetry ?

• Strong and Electromagnetic interaction → T invariance .• Weak interaction → expect not T invariance , but experiments are tough to do.

IntroductionIntroduction 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 .

IntroductionIntroduction CPT theorem

νμ Disappearance – Oscillation Parameters Contour New at Neutrino 2010

MINOS ( Main Injector Neutrino Oscillation Search)

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