CP VIOLATION (B-factories)

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CP VIOLATION (B-factories)

• P. Pakhlov (ITEP)

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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 inversion
Parity sign flip of all three spatial
coordinates
x
Change the sign of the scalar triple product
(triple product is pseudoscalar)
z
y
equivalent to mirror reflection
y
Physical quantaties under P transformation
x
Rotation
z
y
x
z
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.
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P violation in macro world

• Coriolis forces (if considered locally) violate
• P-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

water

• 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

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P violation in macro world
All 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 )
F
a
If 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
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Problems
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 Faradays
laws.

• 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?

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

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P violation in living world
Do not eat!

• 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).
• Snails shells are curled clockwise
• P-violating book by L.Caroll Through the
  Looking-Glass and What Alice found There

Defective
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???
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. ab ?
  abc.
• 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
• ? ? ????

R. Dalitz
600 events are distributed uniformly
T.D. Lee C.N. Yang (1956)
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.
? and ? may be the same particle
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Wu experiment

• Lee and Yang suggested possible experimental
  tests of parity conservation
• p and µ decay
• ß-decay of the Cobalt 60

Angular momentum L is axial vector momentum P is
true vector If P-conserved, any processes can
not depend on pseudoscalar product (L?P)
Parity violation is big effect 1
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Pion decay
p ? µ ? decay
Parity invariance requires that the two cases
?
?
?
?
? spin
? spin
? spin
? spin

A
B
are produced with equal probabilities (i.e. the
emitted µ is not polarized)
B
Method to measure the µ polarization (R.L.
Garwin, 1957)
sm
µ
? beam
µ magnetic moment parallel to µ spin sµ
precesses in magnetic field.
energy degrader
Decay electron detector
Experiments find that the ? has full
polarization opposite to the momentum direction
? State A does not exist ? MAXIMAL
VIOLATION OF PARITY INVARIANCE
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Two component neutrinos
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.
Franz Kafka The top

?
?
Do particle physicists resemble the Kafkas
philosopher from The top?
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PV in macroworld due to weak interactions
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
With external B parallel to the light direction ?
Faraday effect
ß 108
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
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T-transformation
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 Thats 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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• - One is many?
• - No, one is not many.
• - And ten is many?
• - Yes, ten is many.

The Second Law of Thermodynamics
Start with order

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

In few seconds get disorder
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 lt 15 minutes). If I report about my
experiment to theoretician, he derives a
Anti-Second Law of Thermodynamics
- I have said not all the truth to theoretician?
- OK, and six? - Six? I do not know. You have
totally confused me
- Ten molecules is not many enough? Where
is phase transition?
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T-violation in particle physics
Electric dipole moments (EDM) violate parity (P)
and time-reversal (T)

• 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. lt 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)
CPLEAR measure rate difference for K0(t0) ?K0(t1)
and K0(t0) ?K0(t1) (t1gtt0)
and one more T-violating effect in K0 ?ppee
Asymmetry (13.6 2.5 1.2)
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Antimatter
discovered theoretically (1928)

• Diracs 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

P.A.M. Dirac

• The equations have two possible solutions, both
  are mathematically equally valid (just like v1
  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?

Generic solutions of Diracs equation complex
wave functions ?(r , t) For each negative-energy
solution the complex conjugate wave function ?
is a positive-energy solution of Diracs equation
for an opposite charge electron.
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• Diracs 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 Paulis 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 ? ee 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 ee pair.

? empty electron negative-energy states
describe positive energy states of the
positron
Antimatter remained amathematical curiosity for
few years.In 1932, Anderson discoveredanti-elect
rons (positrons)produced in a cloud chamber
bycosmic rays.
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Charge conjuagtion
The 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 ?)

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C-violation in macro world?
LED diode distinguish polarities

hole
p-type
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).
?
n-type
The beam of electrons through the coil results in
light flash
The beam of positrons does not
electrons
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 (Wus 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

not found in nature
exists in nature
exists in nature
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Observation of CP violation in KL

• 1964 Kronin, Fitch, Cristenson Turlay
• Small rate for pure KL beam ???

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Tiny effect ? BIG RESULT
Need CP violation baryon number
nonconservation thermal nonequilibrium
Matter
A.D. Sakharov 1968
Antimatter
Does not matter

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

Big Bang
all matter no antimatter
no matter no antimatter
matter-antimatter symmetric
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Classification of CPV in kaons
Direct
Indirect or mixing
CP violation in the decay amplitute
CP eigenstates ? mass eigenstates
Interference
Re(e/e)
eK
CP violation from interference of DIRECT and
MIXING
Direct CP-violation firmly established
after more than 30 years
Re(e/e) (16.7 2.3) 10-4
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How to incorporate CPV in QFT?
charges should be different g ? g
CP operator
CP (
)
g
q?
q?
g
q
mirror
q
W
W
However, even if g complex, in the rate
calculations its phase is cancelled out
g

2
2
q?
q?
g
q
mirror
q
W
W
as g g
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What about a process with two competing
amplitudes (with different phases)?
A-real BB eif
still
need a reference phase difference that is not
changed under CP
A-real BB ei(df)
A
B
AB
f
B
d
A
AB
Strong interaction can provide this phase d
AB ? AB
We have done half of the job, but we still do not
know how to make weak phase
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Flavor mixing
Problem Different weak charges for leptons and
quarks
GF
d?u s?u Gd? 0.98GF
Gs? 0.2GF
Cabibbo solution
Gd
d a d ß s
Unitarity
a GF
ß GF
GF
u
u
u

Gs

d
s
d
W
W
W
with a2 ß2 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 lets understand
  where the Cabbibo matrix originates from.

a ß ß a
2
2
Why are they not diagonal?
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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 lets understand
  where the Cabbibo matrix originates from.

a ß ß a

• I have two answers, both are impolite (sorry for
  my answer by another question)
• Why should they be diagonal?
• Do you like the ?-hyperon to be stable?
• and one polite
• Because this is only way to accommodate the
  experimental results (the flavor mixing) in the
  SM.

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Quark masses can be diagonalized by unitary
transformations
Then, charged weak interactions become
non-diagonal
Problem Why these manipulations do not lead to
FCNC?
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CPV with two quark generations
If apply transformations a
can become real, while all other terms in
Lagrangian remain unchanged. Then remove phase in
? (which changed after d-rotation)
. Finally, we can make d to be real by
. Do not touch u trying to
correct ß, otherwise you introduce another
phase to a! Just check that ß automatically
becomes real. WHY?
a ß ? d
d ? ei?1 d
cos? sin? sin? cos?
c ? ei?2 c
s ? ei?3 s

• 22 matrix 8 real parameters 4 unitarity
  conditions 3 free quark phases 1 Cabibbo
  angle
• 22 matrix is REAL! not enough freedom to
  introduce imaginary part

d
s
s
?C13º
d
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Kobayashi-Maskawa idea

• Try 33 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
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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

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 parameterization

• Wolfenstein parameterization (expansion on a
  small parameter ?)
• Reflects hierarchy of strengths of quark
  transitions

d s b
u c t
O(1) O(?) O(?2) O(?3)
CPV phases are in the corners
Charge 1/3
Charge 2/3
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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(?3)
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One (the most important) Unitarity Triangle
Convenient to normalize all sides to the base of
the triangle (VcdVcb A?3).
(?,?)
?2
(a)
phase of Vtd
?1
?3
(g)
(b)
phase of Vub
0
1
Coordinate of the Upper apex becomes Wolfenstein
parameters (? , ?).
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Summary Lecture I

• CP 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