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**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

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**Outline Introduction Parity (P) Charge Conjugation (C) CP symmetry**

Neutral Kaons CP Violation (CPV) CPT Theorem

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Introduction Parity

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**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.

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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.

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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

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**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.

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Introduction Parity

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**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

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**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.

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**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.

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Introduction Charge Conjugation

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Introduction Charge Conjugation

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**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.

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Introduction Charge Conjugation

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Introduction Charge Conjugation

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**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

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**Introduction C P CP symmetry**

Physicists then expect CP to be a good symmetry.

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Introduction Neutral Kaons

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Introduction Neutral Kaons

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Introduction Neutral Kaons

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Introduction Neutral Kaons

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Introduction Neutral Kaons

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Introduction Neutral Kaons

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Introduction

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**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.

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Introduction CP violation

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**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.

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**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!

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**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.

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**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.

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**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 ?

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**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 .

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**? Introduction CPT theorem**

MINOS ( Main Injector Neutrino Oscillation Search) νμ Disappearance – Oscillation Parameters Contour New at Neutrino 2010 ?

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