CP VIOLATION (B-factories)

P. Pakhlov (ITEP)

2

Plan of the lectures

I lecture: Discrete symmetries and their breaking.

II lecture: Observation of CP violation at B factories.

III lecture: Other CP study and rare decays. Physics at Super-B-factories

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Parity inversionParity: sign flip of all three spatial coordinates

1 zyx uuu 1 zyx uuu

equivalent to mirror reflection

P

Parity invariance:Physics laws are invariant with respect to a P transformation; For any given physical system, the mirror-symmetric system is equally probable;Nature does not know the difference between Right and Left.

y

x

z

x

y

z Change the sign of the scalar triple product (triple product is pseudoscalar)

x

y

z Rotation

x

y

z

Physical quantaties under P transformation

4

P violation in macro world

Coriolis effect

Pond-skater feels P-violation

F

(force which always acts to the right)

v water

Coriolis forces (if considered locally) violateP-symmetry:

• Pond-skater (living in the pond in northern hemisphere) concludes that there is a P-violation in its world: independent on the direction of moving the path is twisted to the right• Coriolis flow meter is rotating in the same direction with opposite direction of water flow

However, if we look at the Earth from the space, the P-symmetry is restored

• cyclones are clockwise in the northern hemisphere and counterclockwise in the south

5

P violation in macro worldAll toys produced by industry have the spin direction clockwise. I guess that this is due to the technical standards maintained by Council for Standardization, Metrology and Certification.

This is an example of law that violates parity (but it is technical, rather than physical )

spinning top

F

aIf we put this toy inside the black box (the box should have “top”-”bottom” marks) , tightly lock it and make experiments with the box, we conclude that this object does not obey P-invariance.

Consider now, that there are many such boxes and they are so tiny that we

could not open them and look inside…

6

Problems

Do you know any observable, which is a pseudoscalar? Why in the two previous examples the ignorance about

rotation of macro or micro object leads to a wrong conclusion of P-violation?

We can check that there is no P-violation in classical mechanics and electromagnetism, e.g. because Lorentz force should be true vector, we can check that the same relations are derived from Column and Faraday’s laws. HHEE

,

Why do some classical rules rely on “right hand grip rule”?

7

P violation in living world Biological objects (and their products) are not invariant

under mirror reflection! Sugar solution polarizes light. Screws are left (to be convenient for screwing with right

hand). Snail’s shells are curled clockwise P-violating book by L.Caroll “Through the Looking-Glass

and What Alice found There”

Do not eat!

The existence of non invariant objects does not contradict to the conservation law, but P-invariance suggests that the probability

to construct by means of physical processes both object itself and its mirror image are equal!

Why there is no mirror living world???

Defective

Rarity

Only one molecule was once constructed, that is self reproducible?

The probability of its creation is tiny and we are accidentally here?

Or its creation changed the environments and mirror-twin just could not be produced?

Behind mirror

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Parity in particle physics P-invariance is checked in classic physics. In nonrelativistic quantum theory

there is no extra terms that can add parity violation. However, in relativistic quantum field theory particles can appear and

disappear: e.g. a+b a+b+c. Introduce internal parity for particles P() = .

For some particles internal parities can be measured if the particle can be produced individually or in a pair with particle of know parity.

For some particles it is a question of convention (e.g. for ground state fermions): we agreed that for matter particles P = +1 and for antimatter P = –1.

Then we should check that in all processes that can be seen in nature our definition of internal parities are not ambiguios.

The parity conservation in strong and electromagnetic interactions is checked (Tanner):

p + 19F 20Ne* 16O + ? JP(20Ne*)=1+; JP(16O)=0+; JP()=0+ JP(16O ) = 0+, 1–, 2+ evidence for this chain

means parity violation! It was not observed Now parity is measured to be conserved in strong and EM interactions at a

very high level of accuracy (up to the level of influence of weak interactions).

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P-violation in weak decays - paradox: +→ +0 and + ++–

With the same mass (within ~ 0.3% accuracy) With the same lifetime (within ~ 5% accuracy)

+→ +0: JP= 0+, 1–, 2+ …

+→ ++– more complicated: P = (1)ℓ+ (–1) (–1)ℓ– = (-1) (ℓ+ + ℓ– +1); ℓ+= angular momentum in ++ system;

ℓ– = angular momentum between (++) and –;

ℓ+& ℓ– seems to be = 0 from the experimental study of the Dalitz plot

???

and may be the same particle

« Existing experiments do indicate parity conservation in strong and electromagnetic interactions to a high degree of accuracy.»« Past experiments on the weak interactions had actually no bearing on the question of parity conservation. »

R. Dalitz

T.D. Lee & C.N. Yang (1956)

600 events are distributed uniformly

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Wu experiment

parity violates0 0.4~ , ) cos 1( aaaR

Angular momentum L is axial vector; momentum P is true vector If P-conserved, any processes can not depend on pseudoscalar product (L●P)

Lee and Yang suggested possible experimental tests of parity conservation:•π and μ decay•β-decay of the Cobalt 60

Parity violation is big effect ~ 1

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π+ μ+ + ν decay

Parity invariance requires that the two cases

+

spin

spin“A”

+

spin

spin“B”

are produced with equal probabilities (i.e. the emitted μ+ is not polarized)

Experiments find that the + has full polarization opposite tothe momentum direction State “A” does not exist MAXIMAL VIOLATION OF PARITY INVARIANCE

+ beam μ+

energydegrader

B

μ+ magnetic moment parallel to μ+ spin sμ precesses in magnetic field.

s

Decay electron detector

Method to measure the μ+ polarization (R.L. Garwin, 1957)

Pion decay

&

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Two component neutrinos

Franz Kafka “The top”

Do particle physicists resemble the Kafka’s philosopher from “The top”?

The two-component neutrino theory (Lee & Yang, Salam, Landau 1957):

The observed maximum parity violation in leptonic weak processes could be accommodated if neutrinos are massless (and hence helicity and chirality eigenstates). Only lefthanded neutrinos and righthanded antineutrinos are needed.

ν ν~

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PV in macroworld due to weak interactions

With external B parallel to the light direction Faraday effect

Bismuth vapor have optical activity. E1 and M1 (opposite parity) transitions are mixed due to Z-boson exchange between nucleus and electrons.

The effect is similar to the polarization of light in sugar solution, but sugar has two modifications “left” and “right” while any atom has only one. In case of sugar the parity violation is induced by predominance of “left” isomer. In case of bismuth – by weak interaction contribution

β ~ 10–8

Parity violation (by neutral currents) leads to optical rotation in atoms (Ya. B. Zeldovich, 1959). Yes! Zeldovich had suggested neutral analogue of beta-decay 10 years before the Standard Model predicted existence of Z0.

PV observed in heavy atoms (L.V. Barkov, M.S. Zolotarev, 1978) + many experiments later

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T-transformation

There are three types of lie: ordinary lie, blatant lie and statistics…

All (classical) physics laws are T-invariant.

But it is difficult to find an example in macroworld with exact T-symmetry …

It seems only equations (that pretends to describe the real world), but not the real world itself respect T-symmetry.

Physicists usually says: “That’s statistics. The classical laws are good to describe the interactions of two bodies, but when we talk about 1024 bodies, we should use Statistical mechanics”

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- What about “two”?- No, “two” is not “many”.- And “nine”?- Yes, “nine” is many.

- “One” is “many”?- No, “one” is not “many”.- And “ten” is many?- Yes, “ten” is many.

- OK, and “six”?

- “Six”? I do not know. You have totally confused me…

The Second Law of Thermodynamics

Start with order

In few seconds get disorder

Anti-Second Law of Thermodynamics

I can play another game: start with disorder of 10 molecules; stop experiment when all 10 molecules gather in one half of the box (I need to wait < 15 minutes). If I report about my experiment to theoretician, he derives a

- I have said not all the truth to theoretician?- Ten molecules is not many enough? Where is phase transition?

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T-violation in particle physics

Excellent way to search for new sources of CP-

violation SM EDMs are strongly suppressed Theories beyond the SM predict EDMs

many orders of magnitude larger!

Theory de (e cm)

Std. Mdl. < 10-38

SUSY 10-28 - 10-26

Multi-Higgs 10-28 - 10-26

Left-right 10-28 - 10-26

Best limit on atomic EDM (Seattle, 2001):cm100.40)0.49(1.06Hg)d( -28199 e

Electric dipole moments (EDM) violate parity (P) and time-reversal (T)

CPLEAR measure rate difference for K0(t0) →K0(t1) and K0(t0) →K0(t1) (t1>t0)

3106.16.6 TA)()(

)()(0000

0000

KKRKKR

KKRKKRAT

and one more T-violating effect in

K0 →ππee

Asymmetry = (13.6 ± 2.5 ± 1.2)%

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Dirac’s equation: a relativistic wave equation for the electron

Two surprising results: Motion of an electron in an electromagnetic field: presence of a term describing (for slow electrons) the potential energy of a magnetic dipole moment in a magnetic field existence of an intrinsic electron magnetic dipole moment opposite to spin

Antimatter discovered “theoretically” (1928)

P.A.M. Dirac

electron spin

electron magnetic dipole moment μe e

e m

e

2

Generic solutions of Dirac’s equation: complex wave functions (r , t)For each negative-energy solution the complex conjugate wave function * is a positive-energy solution of Dirac’s equation for an opposite charge electron.

The equations have two possible solutions, both are mathematically equally valid (just like √1 = ±1). But only one solution makes sense for ordinary matter (positive energy moving forwards in time)!What is the physical meaning of these “negative energy” solutions?`

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Dirac’s assumptions: nearly all electron negative-energy states are occupied and are not observable. electron transitions from a positive-energy to an occupied negative-energy state are forbidden by Pauli’s exclusion principle. electron transitions from a positive-energy state to an empty negative-energy state are allowed: electron disappears, but the empty negative-energy state disappears as well. To conserve electric charge, a positive electron (positron) must disappear e+e– annihilation. electron transitions from a negative-energy state to an empty positive-energy state are also allowed electron appearance. To conserve electric charge, a positron must appear creation of an e+e– pair.

empty electron negative-energy states describe positive energy states of the positron

Antimatter remained amathematical curiosity for few years.In 1932, Anderson discoveredanti-electrons (“positrons”)produced in a cloud chamber bycosmic rays.

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Charge conjuagtionThe mathematical transformation that turns a particle into its antiparticle is called “charge conjugation” (C).

Every fundamental particle has its own antiparticle

although some particles are ≡ their own antiparticles,e.g. the photon.

Most intrinsic properties of a particle and its antiparticle are the same (mass, spin, …). The exceptions are properties that depend on the direction of time such as charge. Therefore, a particle that is its own antiparticle must be neutral (but not vice-versa: ν)

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C-violation in macro world?

+

p-type

n-type

electrons

hole

e–

LED diode distinguish polarities

γ

e+e+Consider LED diode as a black box (we are so ignorant that do not know that it is produced of matter) producing photons (charge conjugation eigen state).

The beam of electrons through the coil results in light flash

The beam of positrons does not

However if apply both C and P transformations the tableau works again.

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C-violation in weak decay B.L. Ioffe and A.P. Rudik (1956): the way of P-violation suggested by Lee-

Yang leads to C-violation: Pseudoscalar product (L●P) is invariant under T, therefore by CPT-

theorem while T is conserved, C-parity have to be violated together with P.

Based on C-invariance in weak interactions Gell Mann and Pais (1952) predicted the existence of KL (which had been observed recently).

Does this mean that Lee and Yang suggested obviously wrong idea (Wu’s experiment was not yes finished that time)?

L.B. Okun suggested that existence of KL is explained

by T- rather than C- symmetry.

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CP-tranformation Introduced by L.D. Landau as a mean to restore

broken C and P symmetries. The idea of exact CP-symmetry supports the idea of

two-component massless neutrinos

exists in nature

exists in nature

not found in nature

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Observation of CP violation in KL 1964 Kronin, Fitch, Cristenson & Turlay Small rate for pure KL beam

K2π+π–

Effect is tiny: about 2/1000

5001

KK

S

L

Background

Signal

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Tiny effect BIG RESULT

Does not matter

Matter

Antimatter

Need:

CP violation + baryon number

nonconservation + thermal

nonequilibrium A.D. Sakharov 1968

… otherwise, the universe would be completely empty of both matter (stars, planets, people) and antimatter!

Big Bang all matterno antimatter

matter-antimattersymmetric

no matterno antimatter

CP violated CP conserved

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Classification of CPV in kaons

CP violation in the decay amplitute

CP eigenstates ≠ mass eigenstates

CP violation from interference of “DIRECT and MIXING”

Direct Indirect or mixing

Interference

Direct CP-violation

firmly established after more than 30 years

εKRe(ε’/ε)

CP-violation

Indirect

Direct

No CP violation

Re(ε’/ε) = (16.7 ± 2.3) × 10-4

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How to incorporate CPV in QFT?

qq

W+

g

CP ( ) =

CP operator:“charges” should be different g g*

W–q

g*mirrorq

However, even if g complex, in the rate calculations its phase is cancelled out:

qq

W+

g

| |2= |

W–q

g*mirrorq

|2

as |g| = |g*|

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What about a process with two competing amplitudes (with different phases)?

A BA+B

still

|A+B| = |A+B|

A

B

A+BA B

A+B

AB

A+B

|A+B| ≠ |A+B|

need a reference phase difference that is not changed under CP

A-real; B=|B| eiφ

A=A; B=|B| e–iφ

A-real; B=|B| ei(δ+φ)

A=A; B=|B| ei(δ–φ)

δφ

Strong interaction can provide this phase δ

We have done half of the job, but we still do not know how to make weak phase

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Flavor mixing

GF

Gd

Gs

d→u s→uGd 0.98GF Gs 0.2GF

du

W–

α GF

W–s

uβ GF+

d’uGF

=W–

d’ = α d + β s

Problem: Different weak charges for leptons and quarks:

Cabibbo solution:

Unitarity:

with α2 + β2 =1

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Quark mixing Fourth c-quark is predicted to explain K0

→ ℓ+ ℓ– cancellation (GIM mechanism, 1970). In order GIM mechanism works c-quark should couple to s’, orthogonal to d’. Can we make Cabbibo matrix complex?

Before answer this question let’s understand where the Cabbibo matrix originates from.

α β

–β* α*

2

2

Why are they not diagonal?

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I have two answers, both are impolite (sorry for my answer by another question):

1) Why should they be diagonal?

2) Do you like the Λ-hyperon to be stable?

… and one polite:

Because this is only way to accommodate the experimental results (the flavor mixing) in the SM.

Quark mixing Fourth c-quark is predicted to explain K0 →

ℓ+ ℓ– cancellation (GIM mechanism, 1970). In order GIM mechanism works c-quark should couple to s’, orthogonal to d’.

Can we make Cabbibo matrix complex? Before answer this question let’s understand

where the Cabbibo matrix originates from.

α β

–β* α*

2

2

Why are they not diagonal?

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Mass basis

diagonal

Quark masses can be diagonalized by unitary transformations

Then, charged weak interactions become non-diagonal

Problem: Why these manipulations do not lead to FCNC?

u c

Z0

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If apply transformations: “α” can become real, while all other terms in Lagrangian remain unchanged. Then remove phase in “γ” (which changed after d-rotation) . Finally, we can make “δ” to be real by .

Do not touch “u” trying to correct “β”, otherwise you introduce another phase to “α”! Just check that “β” automatically becomes real. WHY?

CPV with two quark generations

d

s d’s’

θC≈13º

2×2 matrix = 8 real parameters – 4 unitarity conditions – 3 free quark phases = 1 – Cabibbo angle

2×2 matrix is REAL! – not enough freedom to introduce imaginary part

α β

γ δ

d → eiξ1 d

c → eiξ2 c

s → eiξ3 s

cosθ sinθ

–sinθ cosθ

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Kobayashi-Maskawa idea Try 3×3 matrix: 18 parameters – 9 unitarity

conditions – 5 free quark phases = 4 = 3 Eiler angles + 1 complex phase

This may be helpful!To-pu &

Bo-to-mu

lead to CP violation and

Nobel prize to Kobayashi &

Maskawa

2008, Stockholm

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CPV in the Standard Model

Requirements for CPV

Where JCP = Jarlskog determinant

Using parameterizations

CPV is small in the Standard Model

0

222222

222222

CPdsdbsb

ucutct

Jmmmmmm

mmmmmm

,Im ** jiVVVVJ jijiCP

519.020.0

26132312231312 1005.3sin

AcccsssJCP

Why all quarks should have different masses?

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History since KM till B-factories

1974 charm (4th) quark discovered 1978 beauty/bottom (5th) quark discovered 1983 B-mesons explicitly reconstructed 1988 Vcb,Vtd,Vub measured:

Unitarity triangle is not squashed CKM matrix is really complex!

1995 truth/top (6th) quark discovered 1999 direct CP violation is observed in kaon system 1999 B-factories (Belle and BaBar) start operation

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CKM matrix in Wolfenstein parameterizationWolfenstein parameterization (expansion on a small parameter λ)

Reflects hierarchy of strengths of quark transitions2312

13

2312

13212

231212

sincos8.023.0sin

ss

s

ss

s

s

sAs

Charge –1/3 Charge +2/3

d

s

b

u

c

t

O(1)

O()

O(2)

O(3)

4

23

22

32

1121

21

O

AiA

A

iA

VCKM

CPV phases are in the corners

t

Vtd

W+

d

b

Vub

W–

*u

37

Unitarity triangle

6 orthogonality conditions (i≠k) can be represented as 6 triangles in the complex plane:

Unitarity triangle

All six triangles have the same area = ½ Jarlskog determinant

Only in two triangles all three sides of the same order O(λ3)

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One (the most important) Unitarity Triangle

1

2

3

Vud Vub*

Vcd Vcb*

Vtd Vtb*

phase of Vtdphase of

Vub

VudVub* VcdVcb+ + VtdVtb = 0**

Convenient to normalize all sides to the base of the triangle (VcdV*cb = Aλ3).

Vcd Vcb*0 1

(ρ,η)

Coordinate of the Upper apex becomes Wolfenstein parameters (ρ , η).

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Summary Lecture ICP violation was discovered in 1964 in K meson decays.

The K system remained the only place CP violation had been observed until 2001 when the first observation of CP violation in the B system was reported by the B factory experiments (BaBar and Belle).

The B system provides a laboratory where theoretical predictions can be precisely compared with experimental results.

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The neutral current remains the same since the CKM matrix VCKM is unitary