T. D. Lee

A lecture given at the Workshop on Possible Parity Restoration at High Energy, on June 11, 2007, Beijing

(50 years since the discovery of parity nonconservation )

Symmetry and Asymmetry

in Electroweak Interaction

1

• Symmetry Violation : the discovery

Present Status : the complexity

Restoration of P, C, T Symmetries

New Symmetry: A Unified View of

and

2

3

(May 31, 1912 - Feb. 17, 1997)

The initial setups of these two experiments on Co60

decay are exact mirror images, but the final electron distributions are not, as indicated by different readings on the counters.

4

Discovery of Parity Nonconservation 5

…

…

6

7

•TCP invariance √

established by W. Pauli in 1955

•Parity Violation P X

right-left asymmetry

• Charge Conjugation Violation C X

particle-antiparticle asymmetry

both discovered by Wu et. al. in 1957

• Time Reversal Violation T X

• CP Violation CP X

proposed in 1957

discovered by Christenson, Cronin, Fitch and Turlay in 1964

8

Symmetry Violation : the discovery

• Present Status : the complexity

Restoration of P, C, T Symmetries

New Symmetry: A Unified View of

and

9

All known matter ( our kind of matter; i.e.,

, nuclei,

atoms, molecules, DNA, genes, earth, sun, stars,

galaxies, … ) are made of twelve elementary

particles:

10

All known matter ( our kind of matter; i.e.,

, nuclei,

atoms, molecules, DNA, genes, earth, sun, stars,

galaxies, … ) are made of twelve elementary

particles:

11

of these, only were known 50 years ago.

: Cabibbo, Kobayashi, Maskawa

Both and are 3 x 3 unitary matrices. They are two corner stones of particle physics. Yet, they are very different!

12

: neutrino mapping matrix

CKM13

Neutrino Mapping

Very different from !

How can we understand it ?

14

Symmetry Violation : the discovery

Present Status : the complexity

• Restoration of P, C, T Symmetries

New Symmetry: A Unified View of

and

15

Symmetry Violation : the discovery

Present Status : the complexity

• Restoration of P, C, T Symmetries

New Symmetry: A Unified View of

and

15a

• Equation of motion is symmetric, but solutions are not

16

We assume P, C, T asymmetries are all due to

spontaneous Symmetry Breaking Mechanism of spin 0 Higgs Fields .

Without , all spin fields are Symmetry Conserving and of Zero Mass; these include graviton, photon, , quarks and leptons.

17

Consequences

Besides and , there should exist and of heavier masses .

Can ILC be an effective means to

detect and ?

18

Why are Higgs not yet seen?

Because of complex structure,

like Cooper pairs in superconductivity.

19

Symmetry Violation : the discovery

Present Status : the complexity

Restoration of P, C, T Symmetries

• New Symmetry: A Unified View of

and

20

New Symmetry: Neutrino Mass Operator is

invariant under:

21 A Simple Example Friedberg, Lee (HEP & NP 30(2006)591)

In the approximation of T invariance.

Consequence: There exists a zero mass neutrino state.

Neutrino Mass Matrix (in terms of )

22

pf

23

Harrison and Scott, Phys. Lett. B535, 163(2002)

Z. Z. Xing, Phys. Lett. B533, 85(2002)

X. G. He and Z. Zee, Phys. Lett. B560, 87(2003)

Thus, this example of new symmetry in is (approx.) correct ,

24

• This new symmetry assumes T invariance.

Questions and How to Improve

1. In

why (not ) approx. zero mass?

2. How about approx. sym. for

3. Can approx. T invariance be related

to masses of

25

A Unified View of and

• 0th Approx.

• First Approx.

26

R. Friedberg and T.D. Lee

arXiv: 0705.4156[hep-ph]

Hidden Symmetry

• The quarks of charge

and of charge

in

are not mass eigenstates u, c, t and d, s, b

27

• Likewise for leptons

28

both and are unitary.

Likewise,

29

both and are unitary.

Leptons

30

assuming T inv.

Mass Operator in sector (likewise for ) :31

0th approximation: T inv.

all real

New Symmetry: is invariant under

with

and

32

gives

Proof

33

neglecting T violation

With and

34

from particledata group

(1) gives

(1)

consistent with particle data book value

Set

With T violation

Thank you