Italian Physical Society International School of Physics

“Enrico Fermi”

Lecture 4•Life times•Regeneration•Discovery of CP violation•How can we measure the phase?•Final state interaction phase•Watson’s theorem•Other possibilities•Hyperon decays

In this section, we refrain from deriving the expression for ε and ε' etc.

Ｃ ＝

Ｐ ＝

ＣＰ｜ ππ ＞＝＋｜ ππ ＞

and LONG SHORTK K

CP K K

K K K

K K K

CP K K

CP K K

| |

| | |

| | |

| |

| |

112

212

1 1

2 2

K

K1

2

2

3

500

3 420Km MeV

m MeV

K K

K KS

L

1

2

0 01

2LK K K

0 0i ie K e K 0 0( ) ( )i i i iS Le e K e e K

reappears when the beam comes

out of the matterialSK

0 0

0 0

( ) ( ) ( )

( ) ( ) ( )

K t f t g K f t g K

K t f t g K f t g K

1( ) ( )

2L LS S imt timt tf t e e

12

0 0 2 2

- ( ) *

( ( ) ) | | | |

+2e Re( )

1( )

2

L S

L S K

t t

t i M t

I K t K e g e g

e g g

g g g

3102)(

)(

S

L

K

K 3102)(

)(

S

L

K

K

A very good year 1964 (Pais)

The Higgs mechanism The quark modelThe first storage ring for e+e- collisions was built in Frascati. Ω- baryon was found at Brookhaven National Laboratory. CP violation was discovered at the same lab.

†H=ch+c*h † †CP h CP h=

† †CP H CP =ch +c*h

M M12 12

12 12

*

*

| ( ) ( )| ( )|

( )

( )

( )

( )

* *

t a t K b t K

id

dt

a t

b tHa t

b t

H Mi M M

M M

i i

i i

211 2 11 12 2 12

12 2 12 22 2 22

Within our formalism

*

| ( ) ( ) | ( ) |

( ) ( )

( ) ( )

t a t K b t K

a t a tdi H

b t b tdt

MH

M

001

002

*

| | |

| | |

K p K q K

K p K q K

qp

KL

( )

( )| |

K

KL

S

2 610

A tiny violation

00

2 0

( )( ) ( ) 1

( )

q A KA K pA K

p A K

0

0

220

2

( )1

( )

( ) ( ) 1

1 2

A KA K

qK pA K

p

qp

002| | |K p K q K

P F1A (P F)®

2A (P F)®2 2

1 2

2 2 *1 2 1 2

A(P F) A (P F)+A (P F)

A A 2Re(A A )

® = ® ®

= + +

2 2 *1 2 1 2 1 2A A 2| A A | cos( )ff= + + -

† †CP H CP =ch +c*hRemember CP transf ormation: c c*

-ff

Þ

Þ

2 22 *1 2 1 2 1 2

2 22 *1 2 1 2 1 2

| ( )| A A 2| A A | cos( )

| ( )| A A 2| A A | cos( )

A P f

A P f

ff

ff

® = + + -

® = + + - +

1 2Note that A and A have strong phase

i i

i i

A | A |

A | A |

i i

i i

i i

i i

e e

e e

f d

f d-

=

=

P F1A (P F)®

2A (P F)®2 2

1 2

2 2 *1 2 1 2 1 1 2 2

A(P F) A (P F)+A (P F)

A A 2| A A | cos( )f d f d

® = ® ®

= + + + - -

2 2

1 2

2 2 *1 2 1 2 1 1 2 2

A(P F) A (P F)+A (P F)

A A 2| A A | cos( )f d f d

® = ® ®

= + + - + + -

( all) ( all)P P

Br(P F)-Br(P F)Br(P F)+Br(P F)

® ®® ®

1 2 1 2 1 22 2 *

1 2 1 2 1 2 1 2

Br(P F)-Br(P F) 2| A A |sin( )sin( )Br(P F)+Br(P F) A A 2| A A | cos( )cos( )

ff d d

ff d d

® ® - -=

® ® + + - -

1 2 1 2 1 22 2 *

1 2 1 2 1 2 1 2

Br(P F)-Br(P F) 2| A A |sin( )sin( )Br(P F)+Br(P F) A A 2| A A | cos( )cos( )

ff d d

ff d d

® ® - -=

® ® + + - -

K π

π

π

πWie f ie d

( ) | | W Ii ioutI IH K A e ef dpp =

† 1( ) ( ) *out outI IH K T THT T Kpp pp -=

1( ) ( ) *

= ( ) *

out inI I

inI

H K THT K

H K

pp pp

pp

-=

( ) ( ) * *out in out outI I

nH K n n H Kpp pp=å

( ) , (3 )out out outn pp p= 2 3p p®

3 3

0 0C

1

C

C

ff

p p h

= +

= + Þ = +

*1 1 1

2 2 2

3 3 3

C CC

ff f

f h f h f

ff f

æ ö æ ö æ ö÷ ÷ ÷ç ç ç÷ ÷ ÷ç ç ç÷ ÷ ÷ç ç ç÷= ÷ = ÷ç ç ç÷ ÷ ÷ç ç ç÷ ÷ ÷ç ç ç÷ ÷ ÷÷ ÷ ÷ç ç çç ç çè ø è ø è ø1 2 1 2

C i i

C

ff ff

p p±

= + ±

= + m

m

0 C

not eigenstate of C

1 2 1 2; , , , , , , ;n mS out p p p q q q in

¶- ××× = ×××

¶××× = - - ×××- -

h 1 2 3 4 1 2 3 4

1 2 3 4 1 2 3 4

, , , , ; , , , , ;

, , , , ; , , , , ;

i T p p p p out HT p p p p outt

T p p p p out p p p p in

®±¥

é ù¶××× = ×××ê ú

ê ú¶ë ûѶ

××× =- ××× ®- ¥¶

Ѷ××× =- ××× ® +¥

¶

å

å

h

h h

h h

1 2 3 4 1 2 3 4

22

1 2 3 4 1 2 3 4

22

1 2 3 4 1 2 3 4

lim , , , , , , , ,

, , , , ; , , , , ; 2

, , , , ; , , , , ; 2

t

i

i

i

i

i p p p p H p p p pt

i p p p p in p p p p in tt m

i p p p p out p p p p out tt m

- -¶××× = ×××

¶h 1 1

1 2 3 4 1 2 3 4, , , , ; , , , , ;Ti T T p p p p out THT T p p p p outt

( ) ( ) ( ) * ( ) *out in out outI I I IH K H Kpp pp pp pp=

2( ) ( ) ( ) Iiout inI I IS e dpp pp pp= =

isospin I phase shiftId pp=

Iie d Iie d-2 Iie d

2( ) ( ) ( ) Iiout inI I IS e dpp pp pp= =

What happens to 2 state at

500MeV?

I t can not go to 3 state,

not enough energy to go to 4 .

pp pp =( ) ( ) 1out inI I

P

Peiδ ( )A P f

( )A P f

f

1.Mixing exists2.Common final state exists3.There is large δ

1 1 2 2

1 1 2 2

0 11 22

0 11 22

| ( ) | |

| ( ) | |

imt t imt t

imt t imt t

P t e P e P

P t e P e P

0 0 0 01

0 012

0

2

0

| ( ) ( ) | (

| ( ) ( )

| ( ) (| | ) (| |

)

| ( |

)

|

)

L L

L L L LS S S S

S S

imt t imt timt t

imt timt t

imt t

P t

P t e P P e P P

P t e e P e

f t

e

f t P P

P

Within our formalism

*

| ( ) ( ) | ( ) |

( ) ( )

( ) ( )

t a t P b t P

a t a tdi H

b t b tdt

MH

M

001

002

*

| | |

| | |

P p P q P

P p P q P

qp

0 0

0

0

2

0

0

1

| ( ) (

| ( ) ( ) | ( )

)| ( ) |

| ( ) ( )| ( ) |

|L L L LS S S Simt t imt timt t imt t

P t pf t P qf t P

P t pf t P

P t e e P e e P

qf t P

22

22

( ( ) ) ( ) ( ) ( ) ( )

( ( ) ) ( ) ( ) ( ) ( )

qP t f pA P ff t ff t

p

qP t f pA P ff t ff t

p

22

22

( ( ) ) ( ) ( ) ( ) 2Re sin ( )

( ( ) ) ( ) ( ) ( ) 2Re sin ( )

q qP t ff t ff t i Mt f

p p

q qP t ff t ff t i Mt f

p p

**12

*12

tbtd

tbtd

V Vq Mp M V V

t bd

d

B BW W

tsV

tdV

tb

tbV

tdV

NConsider (s ) N(p ,s ) NpLL ®

1/ 2 3/ 21/ 2 3/ 2

* *1/ 2 3/ 21/ 2 3/ 2

1/ 2 3/ 21/ 2 3/ 2

* *1/ 2 3/ 21/ 2 3/ 2

Using

( ) ( )

CPT

( ) ( )

S Si iS SS

P

S Si iS S

Pi iP PP

P Pi

S

iP PP

A

A A e A e

A A e A

A e A e

A A e A e

e

5

5

( , )( ) ( , )

( , )( ) ( , )

N N S P

S PN N

P H u p s A A u p s

P H v p s A A v p s

† 1,0 ,0

,0

*

,0 ,0 ,0

( ) , ; , ( ) , ; , *

( ) , ; , *

( ) , ; ( ) , ' ; ( ) , ' ; , *

I P I P

I P

I P I P I P

P s out H s P s out T THT T s

P s in H s

P s in P s out P s out H s

p p

p

p p p

-L L

L

L

L = L

= - L -

= - L -å

T symmetry implies

,I m 0S PIA

2 SIie

1/ 21/ 2 ( , ) ( , )

SiSN NA e u p s u p s

* * *1/ 21/ 2 ( , ) ( , )

SiSN NA e u p s u p s

'2 ( )', ; , I m ( ) * ( )I IS PiI I

P S P P PP s out H s A A e s s pd dp --L L

é ùL =×××- ´ ×ê úë û

r r r

Correlation can arise not only from CP violation,but also from strong interaction

N N N N

N, N,when

p (s s ) p (s s )

p -p, s -sL L

L L

® ®

´ ® - ´r rr

r r r r

r

r rg g

arg 6.5 3.5PP P

S

AA

† 1,0 ,0

,0

*

,0 ,0 ,0

( ) , ; , ( ) , ; , *

( ) , ; , *

( ) , ; ( ) , ' ; ( ) , ' ;

, *

I P I P

I P

I P I P I P

P s out H s P s out T THT T s

P s in H s

P s in P s out P s out H s

p p

p

p p p

-L L

L

L

L = L

= - L -

= - L -

'2 ( )', ; , I m( ) * ( )I IS PiI I

P S P P PP s out H s A A e s s pd dp -+L L

é ùL =×××- ´ ×ê úë û

r r r

'2 ( )', ; , I m ( ) * ( )I IS PiI I

P S P P PP s out H s A A e s s pd dp --L L

é ùL =×××- ´ ×ê úë û

r r r