Symmetry and Symmetry Violation in Particle Physics 违反对称

Lecture 4 March 28, 2008

Summary Lecture 3• CP is violated in Weak-Interactions

– Neutral Kaon mass-matrix induced; scale 2x10-3

– Direct CPV in KL; 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)

CP: matter

qq

W

gCP( ) =

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

CP operator:“charge”

antimatter

W†qg* q’

mirrorsome basic process

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|eii B = |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

CP Violation &

Flavor mixing

d’ & s’ are mixed d & s

Weak eigenstates

Mass eigenstates

4-quarkflavor-mixing

matrix

sd

sd

how about a complex mixing matrix?

-

incorporate CPV by making complex?

(i.e. ≠*?)

not so simple: a 2x2 matrix has 8 parameters

unitarity: 4 conditions

4 quark fields: 3 free phases

# of irreducible parameters: 1

Cabibboangle

suGF

W

controls |S|-1where we see CPV

1001

*

*

2-generation flavor-mixing

-Only 1 free parameter: the Cabibbo angle

C120

not enough degrees of freedom to

incorporate a CPV complex phase d

s d’s’

cosCsinC

sinC cosC

Enter Kobayashi Maskawa a 3x3 matrix has 18 parameters

unitarity: 9 conditions

6 quark fields: 5 free phases

# of irreducible parameters: 4

3 Euler angles +1 complexphase

100010001

UU t

Original KM paper (1973)

From: Prog. of Theor. Phys. Vol. 49 Feb. 2, 1973

CP-violating phase3 Euler angles

3 quarks:

31

32

d

uq=2/3

q=1/3

1964-1974

3x3 matrix 3 generations, i.e. 6 quarks

s1/3

KM paper was in 1973, the 3-quark age

31

32

s

c

Predicted by Glashowbut not discovereduntil Nov.1974

31

32

b

t

These were not evenin our 1973 dreams.4 quarks:

6 quarks:

A little history

• 1963 CP violation seen in K0 system• 1973 KM 6-quark model proposed• 1974 charm (4th ) quark discovered• 1978 beauty/bottom (5th) quark discovered• 1995 truth/top (6th) quark discovered

CKM matrix (in 2008)

bsd

VVVVVVVVV

bsd

tbtstd

cbcscd

ubusud

'''

CPV phases are in the corners

t

d

W+

Vtd

bVub

W+

* u

The challenge

bVub

W+

*

td

W+

Vtd

Measure a complex phase for bu

u

or, even better, both

or in td

The KeyUse B0 mesons

B0 = B0 = bddb

B0/B0 similar to K0/K0

Primer on B mesons 小学课本

• What are B mesons?– B0 = d b B0 = b d

– B = u b B = b u– JPC = 0

– = 1.5 x 10-12 s (cm)• How do they decay?

– usually to charm: |bc|2 |bu|2 100• How are they produced?

– ee (4S) B B is the cleanest process

Lesson 1: Basic properties

u-2/3b+1//3u+2/3 b-1/3

d+1/3b-1/3

b+1//3d-1/3

Lesson 2: “flavor-specific” B decays

In >95% of B0 decays: B0 and B0 are distinguishable by their decay products

X l

X lB0 B0

semileptonic decays:

D X

D XB0 B0

hadronic decays: qC+2/3

D

qC+2/3

D

Lesson 3: B CP eigenstate decaysIn ~1% of B0 decays: final state is equally accessible from B0 and B0

J/KS

J/KL

…

B0 B0

charmonium decays:

K+K

…

B0 B0

charmless decays:

C-2/3C+2/3

J/

JPC=1--

CP=+

Lesson 4: The (4S) resonance

(ee BB) 1nb• B0B0B+B• good S/N: (~1/3)• BB and nothing else• coherent 1-- P-wave

3S bb bound states

(e

e )

had

rons

BBthreshold

e+eqq continuum (u, d, s &c)

10.58GeV

Lesson 5: B0 B0 mixing

V*td

V*td

These have a weak phase: 1

A B0 can become a B0 (and vice versa)

_

u,c,t

u,c,t

b

d

d

b

tb

tb

(only short-distance terms are important)

b u dVub Vud

b c dVcb Vcd

b t dVtb Vtd

* * *bd:

Ά =VubVud f(mu) + VcbVcd f(mc) + VtbVtd f(mt)* * *

GIM: VubVud + VcbVcd + VtbVtd = 0* * *

Ά = 0 if: mu = mc = mt

Large mt overides GIMbut, mt >> mc & mu: GIM cancellation

is ineffective

B0 B0 mixing transition is strong(and this allows us to accesses Vtd)

V*td

V*td

t-quarkdominat

es

Y.H. Zheng, PhD ThesisAlso Y.H. Zheng et al., Phys Rev. D 67 092004 (2003)

N(B

) –

N(B

) N

(B)

+ N

(B)

The large t-quark mass:

mt=174 GeV

What makes B’s interesting?

Neutral meson mixing phenomenology

Neutral B mesons are producedas flavor eigenstates: B0 or B0

B0(t)

B0(t)B0(t)

B0(t)

B1 & B2

|B1> = p |B0> + q |B0>

|B2> = p |B0> - q |B0>

If CPV is small: q ≈ p ≈1/2

Time dependence of B0 (B0) mesons

( pq1/√2 )

|B0 (t)> = ( |B0> (1+eimt)+ |B0>(1-

eimt))e-t

|B0 (t)> = (|B0>(1+eimt)+ |B0>(1-eimt))e-t

common phase

m = m2-m1

Can we measure 1?

two processes: B0fcp & B0 B0 fcp

weak phase: 21

common phase: mt Yes!!

B0

Interfere BfCP with BBfCP

td

td

B0

Vtb

V*

Vcb

KS

J/

J/

KS

V*2

Vtb

V*td

td

Vcb

B0B0

Sanda, Bigi & Carter:

+sin21

eimt

What do we measure?

t z/cβγ

Flavor-tag decay(B0 or B0 ?)

J/

KS

B - B B + B

e

e

more B tagsmore B tags

zt=0

fCP

(tags)

sin21

This is for CP=-1; for CP=+1, the asymmetry is opposite

Asymmetric energies

Requirements for CPV• Many B mesons

– “B-factory” & the ϒ(4S) resonance

• Reconstruct+isolate CP eigenstate decays– Kinematic variables for signal +(cont. bkg suppr+PID).

• “Tag” flavor of the other B

• Measure decay-time difference– Asymmetric beam energies, high precision

vertexing(Δz)– Likelihood fit to the t distributions

PEPII B factory in California

Stanford LinearAccelerator Ctr

BaBar Detector

The PEPII Collider (magnetic separation)

9 x 3.0 GeV; L=(6.5 x 1033)/cm2/sec

On resonance:113 fb-1

Int(L dt)=131 fb-1

Cherenkov Detector (DIRC)[144 quartz bars, 11000 PMTs]

Silicon Vertex Tracker (SVT)[5 layers]

Instrumented Flux Return (IFR) [Iron interleaved with RPCs].

CsI(Tl) Calorimeter (EMC)[6580 crystals].

Superconducting Coil (1.5T)

Drift Chamber [40 stereo lyrs](DCH)

e- (9 GeV)

e+ (3 GeV)

The BaBar Detector

KEK laboratory in JapanTsukuba Mountain

KEK laboratory

KEKB Collider

•Two ringse+ : 3.5 GeV 1.5Ae : 8.0 GeV 1.1A

•ECM : 10.58 GeV•Luminosity:

•target: 1034 cm-2 s-1

•ach’ved: 1034 cm-2 s-1 •(~20 B’s/s

KEKB

elle

A magnetic spectrometer based on a huge superconducting solenoid

Step 2: Select events

B0 J/ Ks event

Tracking chamber only

Drift chamber for tracking & momentum measurement

Drift chamber cell

+

-

-

- -

-

--

E-field

Charged particle track

-

-

---

--

Drift speed 50m/nsecPosition resolution 150 m

16m

m

17mm

Same event in the entire Detector

B0 J/ Ks event

J/

KS

Kinematic variables for the ϒ(4S)

invariant mass:

2/

2 )()2(SKJCMbc ppEm

2/ CMKJB EEEES

e+ e-

in CM:

e+ e-B0

B0

E=Ecm/2

E=Ecm/2

Beam-constrained mass:

J/KS

2/

2/ )()(

SS KJKJB ppEEm

Kinematic variables for the Υ(4S)

Energy difference:

Beam-constrained mass:

2/

2 )()2(SKJCMbc ppEm

2/ CMKJ EEEES

10MeV

2.5 MeV

B0 ψ KL signal event

pB* (cms)

[2332 events with a purity of 0.60]

Event display

J/ KL1399±67 signal

KL “crash”

Step 3: Check the other tracks to see if the other

meson is a B0 or a B0

??

??

??

Flavor-tagging the other B

Inclusive Leptons:high-p l b c l intermed-p l+ s l

Inclusive Hadrons:high-p - B0D(*)+ -, D(*)+ -, etc.intermed-p K- K- X,

low-p + D0 +

Belle: effective efficiency = 30 %

Figure of merit(Q) =ε(1-2 w)2 a.k.a effective tagging efficiency

Distinguishing different particle types dE/dx

Ionization density in the drift

chamber (dE/dx)

Distinguishing different particle types (Cherenkov)

When (=v/c) > 1/n , “cherenkov” light is produced Only particles

with b>0.99count in these

K meson identification fromdE/dx, Cherenkov & TOF

Distinguishing different particle types (time-of-

flight)

Time =

L/v

x

x

ScintillationCounter barrel

TOF measurements of particle mass

Time = L/v = v/c = p/√(p2+m2) m

Mass from TOF measurements

A K- tag event means the other meson is (probably) a B0

(not a B0)

K-

Identify the other tracks in the event

DK- not K+

DK+ not K-

BD >> BD

Silicon detectors measure Δz

(typically ~200 m)

Beam spot: 110 μm x 5 μm x 0.35 cm

Step 4. Find decay time difference

Silicon vertex detector

50m

Silicon detector

E-field

Charged particle track

--++

+

-

position resolution 20 m

300

m

Magnified vertex

Ks+

~7cm

y-z vertices

A Fully-reconstructed EventHuman

hair ~200

Event-by-event Likelihood

background frac

Sidebands & MC

resolution functionB-lifetime studies

f= ±1 for CP=1

PDG

wrong-tag frac.lone free parameter

b-flavor tag

sin2sin211 measurement by Belle measurement by Belle (2003)(2003)

“Raw” asymmetry

BELLE-CONF-0353

5417 evts

Poor tags

Good tags

Results (2007)Belle BaBar

sin21 = 0.681 ± 0.025

CP=-1 CP=+1

CP=-1

CP=+1

1 = 21.50 ± 1.00

The “Unitary Triangle”

100010001

****

***

***

tbtstd

cbcscd

ubusud

tbcbub

tscsus

tdcdudt

VVVVVVVVV

VVVVVVVVV

UU

0*** tbtdcbcdubud VVVVVV

ubudVV *

cbcdVV *

tbtdVV *

Unitary triangle:

ubudVV *

cbcdVV *

tbtdVV *

~1~1

|Vtd| measuredby B0-B0 mixing

|Vub| measured inbuℓ- decay

|Vcb| measured inbcℓ- decay

|Vcd|=sinC

**tdcbcdub VVVV

luckily:

otherwise, the triangle would be flat

Overconstrained!!

Unitary triangle constraints 2007

SM+CKM is verified

CP is violated in B decays• ~70% effect in BJ/ KS decays

– compared to ~0.2% effect in K0 decays• Kobayashi-Maskawa mechanism

verified.

• After 35 years, 3 new quarks &, happily,**

tdcbcdub VVVV

Next Step

Check the Unitary Triangle with Penguins

bs FCNC decayt-quark is

the dominant contributor

Why is heso happy?

SM FCNC:

)( of effectsExpect 2,

2

YX

top

MM

O

i.e.> ~10% for MX,Y accessible @ LHC

t

at leastV

New heavy Particles?2nd-order weak process with t & W

in the loop

New Physics?:X

Y

sin21 with bs penguins (SM)Example:

no CP phase

SM: sin21 sin21 from BJ/ KS (bc c s)eff

Vtd

Vtd

+

1

B B, ’,

1

, ’,

_

*

*

B0 'K0

(bkg subtracted)B0 mass B0 momentum

535MBB

hep-ex/0608039

K0KS K0KL

1421 ± 46 signal evts

454±39 signal evts

TCPV in B0'K0

“sin21” = 0.64 0.11

535MBB

hep-ex/0608039

SM: 0.681±0.025(from BKSJ/)

B0 K0

B0 massB0 momentum

(bkg subtracted)

hep-ex/0608039

535MBB

K0KS

K0KL

307 ± 21 signal evts

114±17 signal evts

TCPV in B0 K0

“sin21” = 0.50 0.22

535MBB

hep-ex/0608039

SM: 0.681±0.025(from BKSJ/)

1 with b s Penguins

Naïve average of all b s modessin2eff = 0.52 ± 0.05

SM: 0.681 ± 0.025

~2.6difference

Hint, but not strong evidence for new physics.

Need more precision (data)

MX,Y > Mtop

Brief summary

得了

• Symmetries are important in:– Life– Art– Nature

• Space time symmetries conservation laws– Space translation symm Conser. of momentum– Rotational symm Conserv of angular momentum– Time translation symm Conserv. of Energy

E. Noether

• Discrete symmetries are important in QM– Parity– Charge Conjugation– Time Reversal

Man P Man

C

• P (and C) are strongly violated in W.I.

• But CP looks OK

e-

e+

CP

“charge conjugate”mirror

•CP is violated in neutral K decay– Small effects:– (KL)/(KS)

= 2 4x10-6

– (KLe+)/(KLe-)

= 2x10-3

M(+-)<M(KL)

M(+-)>M(KL)

M(+-)=M(KL)

cosK0

K0

)(tA

3102)( tA

• Kobayashi Maskawa (1973) 6-quark model– Needs 3 more quarks than are known at the time– Predicts large CP violation in B-meson decays.

• 3 more quarks discovered– c (1974)– b(1978)– t(1995)

bsd

VVVVVVVVV

bsd

tbtstd

cbcscd

ubusud

'''

CP phases go here

• Large CP violation found in B meson decays

– ~70% effect

• KM predictions validated

sin21 = 0.681 ± 0.025

•CP measurements for Penguin (loop) processes can search for new particles at high mass scales

– Even higher than the LHC

New heavy Particles?

XY

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