Symmetry and Symmetry Violation in Particle Physics 违反对称

Lecture 3 March 21, 2008

Summary Lecture 2

• Antimatter predicted by Dirac & discovered by Chao & Anderson– 1933 Nobel prize Dirac– 1936 Nobel prize Anderson (but not Chao)

• Electron & positron have opposite parity

• Charge “reversal” Charge “conjugation”– Particle Antiparticle (not just charge)

• C=+1 even # of ’s; C=-1 odd # of ’s

• and K mesons = qq with L=0, S=0 & P=-1

Summary Lecture 2 (pg 2)

• + = ++- & +0 puzzle led Lee & Yang to question L-R symmetry of nature

• C.S. Wu discovered P viol. in Co60Ni60 e-– 1957 Nobel Prize to Lee & Yang (but not Wu)

• + and + are the same particle, the K+ meson

• C & P violation differences seen in -/+ decay

– But CP seems okay

• Large matter vs antimatter asymmetry in the

present-day Universe implies CP is violated.• K0K0 transitions possible @ 2nd-order W.I.

C, P & CP for and K mesons

Particle P C CP|+

|0|-

-1

-1

-1

-1

+|- -|-+|0 -|0

+|+ -|+

+|K0

|K+|K0

|K0|K-

-1

-1

-1

+|K+ -|K+

-|K-+|K--|K0 +|K0-|K0

Reminder

My tentative plan for this class is as follows:

Lecture 1. Definition of symmetry, why they are important in physics. Symmetries of the laws of nature. Relation of symmetry and conservation laws. Discrete symmetries C, P & T. Violation of parity (P) in beta-decay

Lecture 2. Antimatter, and matter-antimatter symmetry. Quark content of hadrons & discrete symmetries of hadrons. Violation of parity (P) and charge conjugation (C ) symmetry in beta-decay Particle- antiparticle mixing.

Lecture 3. K0K0 mixing. CP violation in K decay. Difficulties with incorporating CP violation into a physics theory. KM 6-quark model for CP violation. Role of B mesons in the theory

Lecture 4. Studying CP violation in the B meson system. Experimental techniques and results. What is left for the future.

Lecture 5. Exam

Discovery of CP violation in the neutral K meson system

• Neutral K meson decay mechanisms

• K0 – K0 mixing KS and KL mesons

• Discovery of KL+-

• CP violation in KLe-/e+ decays

• “Direct” CP violation in KL decays

outline

K0 +- decays via weak interaction

d

W.I.

u

W+

u

d

s

d

K0

-

+

S=-1

K0 also decays to +-

S W.I.

u

W- u

d

d

d

K0

+

-

S=1

K0 K0 possible as a 2nd orderweak interaction process

S W.I.

u

W- u

d

dd

K0

+

-

W.I.

W+

s

dK0

This is a so-called “long-range” process. It occurs on a size scale determined by the mesons: ~ 10-15m

1 fermi

S|=2

K0 K0 in short-range quark

S W.I.u

W-

c td

u

K0W.I.

W+

s

d

K0

This is a so-called “short-range” process. It occurs on a size scale determined by the t-quark: ~ 10-18 m

W.I.

c tW.I.

10-3 fermi

S|=2

What happens when two identical systems are coupled?

Energy transfersback-and-forthbetween the two oscillators

Steady-state “normal modes”

Shrodinger Equation: H = E

0

0

0

0

0

0

K

KE

K

K

H

00

00

:

:

KK

KK

..

* If CP symmetry holds:

Eigenvalues and Eigenstates

0

0

Find the eigenvalues

and eigenvectors for:

001

001

0

KKaK

KKK

E

L

S

Answer

Homework: Please check that these answers are correct

特征值

In standard (textbook) notation

0*

12

120

0*12

120

0

0

2

i

MM

MM

00

00

122

KqKpK

KqKpK

MMMM

L

S

SL

1

2

22

1221

12

*122

1*12

12

qp

M

M

p

q

LS

If CP symmetry is good: 2

1pq

00

21

2

00

21

1

KKKK

KKKK

L

S

CP of K1 and K2

00

00

KKCP

KKCP

Recall:

CP = +1

100

1 12

1KKKKCP

00002

2

1

2

1KKKKKCP

21 KCP = -1

1decays

1 CP= (-1)x(-1) = +1

CP = (-1)x(-1)x(-1) = -1

CP +1

CP= +1 OK

NG 1

2decays

2 CP= (-1)x(-1) = +1

CP = (-1)x(-1)x(-1) = -1

CP -1

CP= -1 NG

OK 2

K1 & K2 lifetimes

1has more phase space

QK1 = MK – 2M 215 MeV

2has little phase space

QK2 = MK – 3M 80 MeV

Easier for K1 to decayK1<<K2

相空间

1956: Search for long-lived K0

Brookhaven-Columbia Expt

Can you see it?

KS & KL mesons

Two neutral K mesons were discovered:

KS +- KS 0.1 nanosecs (10-10s)

KL +-0 KS 50 nanosecs (5x10-8s)

(Are they the CP eigenstates K1 and K2?)

500x bigger

e+ e-510MeV

510MeV

pL = 110 MeV<> = 3.4m

pS = 110 MeV<> = 6mm +

-

+

0

-

= ssM() = 1020 MeV

KL = K-long

KS = K-short

KL & KS mesons in e+e- annihilation

KLOEExperiment

in Italy2m

K L

KS

In this event the KL

only travels ~1m before it decays

Usually, the KL traverses to entire 2m radius of the drift chamber

KKLL “crash”“crash”

= 0.22 (TOF)= 0.22 (TOF)

KKSS ee

2m

KL “crash”

KS

Neutral K mesons “Basis” sets

K0-K0

Flavor States

K1-K2

CP eigenstates

KS-KL

Mass eigenstsate

These are theParticles that exist in Nature

These have awell defined

quark structure

are these the same?

Does KS=K1 & KL=K2?(i.e. is CP conserved?)

00

00

KqKpK

KqKpK

L

S

00

21

2

00

21

1

KKK

KKK

express them in terms of K1 and K2:

These are theparticles thatare observed

in nature

00

21

2

00

21

1

KKK

KKK

212

10

21210

KKK

KKK

invert

222

12KqpKqp

212121 KKqKKpKS

212121 KKqKKpKL

121

12

KKKL

211

12 KKKS

If CV is conserved: =0, KS=K1 & KL=K2

Does KL +- ?

121

12

KKKL

Forbidden(?)

211

12

KKKS

Forbidden(?)

2

2

1

1

K

K

K

K

S

L

if CP is conserved

Remember,+- has CP=+1

Christenson-Cronin-Fitch-Turlay Experiment (1964)

KL

+

-

2

2

4

2

c

pp

c

EEM

M(+-)<M(KL)

M(+-)>M(KL)

M(+-)=M(KL)

KL

-

+

+

cos

+- “invariant mass”

4x10-6

small,but not 0

CP is violated!!

1980 Nobel Prize for Physics No prizes for Christenson or Turlay

James Cronin Val Fitch

Flavor-non specific K0 (K0) decays

00

If you see +-, you don’t know if it was from a K0 or a K0

00

Decays that are equally likely for K0 and K0

Same for +-0, (& & )

特定

Flavor specific K0 (K0) decays

If you see -e+,you know it must befrom a K0, not K0

Decays that can only come from a K0 or K0, but not both

d

W.I.

W+

u

d

s

e+

K0

-

S=-1Q=-1

0eIf you see +e-,you know it must befrom a K0, not K0

s W.I.

e-W-

d

ud

K0

+

S=+1Q=+1

0eonlyS=Q

Rule:

特定

K0 & K0 in terms of KS & KL

00

00

KqKpK

KqKpK

L

S

invert

LS

LS

KKK

KKK

0

0

Start with a K0 at t=0

00

00

KqKpK

KqKpK

L

S

using

ttiML

ttiMS

LL

SS eKKeKKKtKK 22 0000 )(

0

1

00

00

KK

KK

and

ttiMttiM LL

SS eeptKK 22)(00

LS KKK 0

KS & KL havedifferent

t-dependence

ttiML

ttiMS

LL

SS eKeKtK 22)(0

ttiMttiM LL

SS eeptKK 22)(00

ttiMttiM LL

SS eeqtKK 22)(00

MteeeptKKIeP ttt LSLS cos2)()( )(2200

021

Similarly:

MteeeqtKKIeP ttt LSLS cos2)()( )(2200

021

)( SL MMM

K0K0 Oscillations

)(

)cos4)(()(

)(2221

tt

ttt

LS

LSLS

ee

MteeeqptA

)()(

)()(

)()(

)()()(

00

00

ePeP

ePeP

KNKN

KNKNtA

K0

K0

t/(“proper time”)

)(tA

Expt NA48 (CERN)

3102)( tA

S>>L (S500xL)

CP is violated in KLe-/e+ decays

)(

)cos4()(

)(21

tt

ttt

LS

LSLS

ee

MteeetA

22

221

qp

qp

Search for direct CPV in KL

121

12

KKKL

Forbidden(?)

CP violation from|S|=2 transition

Mass MatrixIs this true?

Can there be a“direct” CP violation

in |S|=1 K2?

In 2002,after 20 yr searches, NA48 (CERN) & KTeV (Fermilab)

found direct |S|=1 CPV in

K2

= ’ 1.6 x 10-3 x Small, but establishesexistence of “direct” |S|=1 CP violation.

CPV in neutral K meson systemsummary

• Neutral K mesons mix: K0 K0

• CP is violated in the K0-K0 mass-mixing matrix– scale 2x10-3

• CPV is seen in flavor non-specific & flavor specific modes– KL (CPV 4x10-6)

– KL +e- / -e+ (CPV = 2x10-3)

• Direct CP is seen in KL decays– scale = ’ = 1.6 x 10-3

CP is violated in the Weak Interactions

Observation of both Mass-Matrix CPV (|S|=2)

& direct CPV (|S|=1) rule out theorieswhere CPV comes from a previously

unknown “fifth” force characterized by |S|=2

Force C P CPGravity √ √ √Electro-magnetic √ √ √Strong-nuclear √ √ √Weak-Interaction ╳ ╳ OK?

C P and the forces of NatureSlide from last weak

Force C P CPGravity √ √ √Electro-magnetic √ √ √Strong-nuclear √ √ √Weak-Interaction ╳ ╳ ╳

Next:

• How are CP-violating asymmetries generated in QM?

• How does CP violation fit into the Standard Model for particle physics?– Brief review of flavor mixing/GIM-mechanism– Kobayashi 6-quark model

Generating CPV asymmetries in QM

CP: matter

qq

W

gCP( ) =

For CPV: g g* (charge has to be complex)

CP operator:“charge”

antimatter

W†q

g* q’

mirrorsome basic process

QM: processes go as |A|2

• Phases tend to cancel out in rate calculations

qJ

g q’=

2

matter- symmetry is ~“automatic”

even for g* = g (i.e with CPV)

J†

2

q

g* q’

mirror

antimatter

gg* g*g

Phase measurements in QM: need interference

• need a process with 2 competing mechanisms:

• Amplitudes should have similar magnitudes:

A & Bei:

2|A|B|cos

|A|2+|B|2if |A|>>|B|

2|B|

|A|cos

Small numberRelative size of theinterference effect

|A+B|2=|A|2+|B|2+2|A|B|cos

phase

angle

干扰

Even this doesn’t work for CPV!!

A

BA+B

A+B

A

B

|A+B| |A+B|=

matterantimattersymmetric

still!

need a “common phase” between A & B

eg A=real: B = |B|eii & B = |B|ei-

i

A

BA+B

A

BA+B

|A+B| |A+B|=

matterantimatterdifference

same sign合用

CP violating asymmetries in QM

• Even if CP is violated, generating matter-antimatter differences is hard– need a CP-violating phase ()– need 2 (or more) interfering

amplitudes

– + a non-zero “common” phase () (often called a “strong” phase)

Common and weak phases“Common” (strong) phase (): same sign for

matter & antimatter CP conserving

Weak phase (): opposite sign for matter& antimatter CP violating

BA+B

A

BA+B

|B|eiiB = |B|ei-i

How does CPV fit into the Standard model?

Clue: CPV is seen in strangeness-changing weak decays.

It must have something to do with flavor-changing Weak Interactions

Flavor mixing&

CP Violation

3 quarks:

d

u

s

q=2/3

q=1/3

4 leptons:

~

e

e

Weak interactions

Brief review of weak int’s in the 3-quark era1964--1974

|S|=1

Problems Problem 1: Different weak interaction “charges” for leptonshadrons:

np

K

0

GF

GdGs

suGs 0.21GF

d

u

s

u

du

Gd 0.98GF

Fermi Constant

Cabibbo’s sol’n: flavor mixing

d = d + s

Weak Int flavor state

Flavor mass eigenstates

Unitarity: |2 + |2 = 1

du

W

GF

Ws

uGF

=cos c; = sin c

+d’

uGF =

c=“Cabibbo angle”

W

=cosc=0.98=sinc=0.21

Missing neutral currents Problem 2: no flavor-changing “neutral currents” seen.

flavor-preserving neutral currents (e.g. NX) are

allowed

flavor-changing neutral currents (e.g. K l+l) are strongly supressed

Discovered

At CERN

GN

d,u d,uK

d

s

GIM sol’n: Introduce 4th quark

2 quark doublets:

s

c

d

u

'' s

c

d

u

charmed quark

Weak eigenstates

Mass eigenstates

d’ & s’ are mixed d & s

Weak eigenstates

Mass eigenstates

s

d

s

d

'

'

4-quarkflavor-mixing

matrix

Mixing matrix must be Unitary

U

UU† = 1

= 1 & =0

10

01**

**

Charged currents (u-quark)

d(s)

u(c)

W

GF

Ws(d)

u(c)

GF

31

31

32

sd

u

GF modified by GF modified by

|S|=1

Charged currents (c-quark)

dc

W

GF

Ws

cGF

31

31

32

sd

c

GF modified by GF modified by

|C|=1|S|=1

|C|=1|S|=0

Flavor preserving Neutral Current

d,(S)GN

=1

OK

dss

sdsddd **

sdd

ssdssddd 2*2

*

=1

=0 =0

22

d,(s)Z

=1

=1

From Unitarity

Flavor changing Neutral Current

From Unitarity

=1

dss

sddsds **

sdd

=0 =0

sdddssds 2*2*

=1

**

FCNC forbidden by Unitarity

s(d)

d(s)

Z

GN

=0

=0

GIM- Mechanism

GIM Mechanism

FCNC forbidden by Unitarityif quarks come in pairs of 2

GIM: Glashow Iliopoulis Maiani

Glashow won 1979Physics Nobel prize

No prize forIliopoulis & Maiani

Next Friday: Incorporating CPV into flavor mixing

Summary Lecture 3

• CP is violated Weak-Interactions – Mass-matrix induced; scale 2x10-3

– Direct CPV; scale = ’ = 1.6 x 10-3 • Observing CPV requires:

– Two interfering amplitudes– One with a CP-violating weak phase – Another “common” or “strong” phase

• In the W.I., the d and s quark mix d’ & s’– d’ =coscd +sin s; s’ =-sincd +coscs– c 120 is the “Cabibbo angle

• If all quarks are in pairs, FCNC = 0 by Unitarity – (GIM Mechanism)