Transcript CP VIOLATION (B-factories)
CP VIOLATION (B-factories)
P. Pakhlov (ITEP)
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
2
Parity inversion
Parity: sign flip of all three spatial coordinates
y
u x
u y
u z
1
x x z
u x
u y
u z
1
z x
equivalent to mirror reflection
y Rotation P z y Change the sign of the scalar triple product (triple product is pseudoscalar) Physical quantaties under P transformation 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.
3
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 Pond-skater feels P-violation v water F Coriolis effect (force which always acts to the right) 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 4
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. F
This is an example of law that violates parity (but it is technical, rather than physical )
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. spinning top
Consider now, that there are many such boxes and they are so tiny that we could not open them and look inside…
5
Problems
We can check that there is no P-violation in classical mechanics and
E
E
H
should be true vector, we can check that the same relations are derived from Column and Faraday’s 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”? 6
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”
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???
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?
Rarity Behind mirror Do not eat!
Defective
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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 + 19 F
20 Ne *
16 O +
?
J P ( 20 Ne * )=1 + ; J P ( 16 O)=0 + ; J P (
)=0 + J P ( 16 O
) = 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 :
J P
= 0 + , 1 – , 2 + …
+ →
+
+
– more complicated: P = (1) ℓ+ (–1) (–1) ℓ– = (-1) (ℓ + + ℓ – +1) ;
ℓ
+ = angular momentum in
+
+
ℓ
– system; = angular momentum between (
+
+ ) and
– ;
ℓ
+ & ℓ –
???
seems to be = 0 from the experimental study of the Dalitz plot T.D. Lee & C.N. Yang (1956) R. Dalitz
600 events are distributed uniformly
« 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 9
Wu experiment
Lee and Yang suggested possible experimental tests of parity conservation:
•
π and μ decay
•
β-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)
R
( 1
a
cos ) ,
a
~ 0.4
a
0 violates parity
Parity violation is big effect ~ 1 10
Pion decay
π +
μ + + ν decay Parity invariance requires that the two cases
+
+
+
+
spin
“A”
spin
&
spin
“B”
spin are produced with equal probabilities (i.e. the emitted μ
+
is not polarized) B
Method to measure the μ + polarization (R.L. Garwin, 1957)
+ beam
μ + s
μ +
magnetic moment parallel to μ
+
spin s μ precesses in magnetic field.
energy degrader Decay electron detector Experiments find that the
+ the momentum direction
has full polarization opposite to State “A” does not exist
MAXIMAL VIOLATION OF PARITY INVARIANCE 11
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” ν ν~ Do particle physicists resemble the Kafka’s philosopher from “The top”?
12
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 Z 0 .
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 β ~ 10 –8 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 13
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: “That’s statistics. The classical laws are good to describe the interactions of two bodies, but when we talk about 10 24 bodies, we should use Statistical mechanics”
There are three types of lie: ordinary lie, blatant lie and statistics
14
…
The Second Law of Thermodynamics
- “One” is “many”?
- No, “one” is not “many”.
- And “ten” is many?
- Yes, “ten” is many.
Start with order 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 < 15 minutes). If I report about my experiment to theoretician, he derives a
- What about “two”?
- No, “two” is not “many”.
- And “nine”?
- Yes, “nine” is many.
Anti-Second Law of Thermodynamics - I have said not all the truth to theoretician?
- Ten molecules is not many enough?
Where is phase transition?
- OK, and “six”?
- “Six”? I do not know. You have totally confused me…
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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!
Best limit on atomic EDM (Seattle, 2001):
d( 199 Hg) (1.06
0.49
0.40) 10 -28
e
cm
Theory Std. Mdl.
SUSY Multi-Higgs Left-right d e (e cm) < 10 -38 10 -28 - 10 -26 10 -28 - 10 -26 10 -28 - 10 -26 CPLEAR measure rate difference for K 0 (t 0 ) →K 0 (t 1 ) and K 0 (t 0 ) →K 0 (t 1 ) (t 1 >t 0 )
A T
R
(
K R
(
K
0 0
K
0 )
K
0 ) +
R
(
K
0
R
(
K
0
K K A
0 0
T
) ) 6 .
6 1 .
6 10 3
and one more T-violating effect in K 0 →ππee Asymmetry = (13.6 ± 2.5 ± 1.2)% 16
Antimatter
discovered “theoretically” (1928) 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
electron spin
P.A.M. Dirac
electron magnetic dipole moment μ e
e
e
2
m e
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?` Generic solutions of Dirac’s equation: complex wave functions
(r , t) For each negative-energy solution the complex conjugate wave function
* positive-energy solution of Dirac’s equation for an opposite charge electron.
is a 17
Dirac’s assumptions:
nearly all electron negative-energy states are occupied and are not observable.
forbidden by Pauli’s exclusion principle.
electron transitions from a positive-energy to an occupied negative-energy state are 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 a mathematical curiosity for few years.
In 1932, Anderson discovered anti-electrons (“positrons”) produced in a cloud chamber by cosmic 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: ν) 19
C-violation in macro world?
LED diode distinguish polarities p-type n-type
e + + e –
hole electrons
γ
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 K L (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 K L 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 not found in nature exists in nature 22
Observation of CP violation in K
L 1964 Kronin, Fitch, Cristenson & Turlay Small rate for pure K L beam
K 2
π + π –
Effect is tiny: about 2/1000
Background Signal
K L K S + + 1 500
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Tiny effect
BIG RESULT
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!
no matter no antimatter all matter no antimatter matter-antimatter symmetric
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Classification of CPV in kaons
Direct CP violation in the decay amplitute Re(ε’/ε) Indirect or mixing CP eigenstates ≠ mass eigenstates No CP violation Interference CP violation from interference of “DIRECT and MIXING” ε K Indirect Direct CP-violation Direct
CP-violation
firmly established after more than 30 years Re(ε’/ε) = (16.7 ± 2.3) × 10 -4 25
How to incorporate CPV in QFT?
“charges” should be different g
g*
CP operator:
g CP
(
q q
W +
)
= q
g*
q
mirror W –
However, even if g complex, in the rate calculations its phase is cancelled out:
|
g
q
W
q
+
| 2
=
|
q
g*
q
mirror W –
| 2
as |g| = |g*| 26
A-real; B=|B| e A=A; B=|B| e What about a process with two competing amplitudes iφ –iφ (with different phases)?
A A+B B A B still A+B |A+B| = |A+B| need a reference phase difference that is not changed under CP A-real; B=|B| e i(δ+φ) A A=A; B=|B| e i(δ–φ) B A+B A B φ
δ
A+B Strong interaction can provide this phase δ |A+B| ≠ |A+B| We have done half of the job, but we still do not know how to make weak phase 27
Flavor mixing
Problem: Different weak charges for leptons and quarks: d→u G d
0.98G
F G s
s→u 0.2G
F Cabibbo solution: d’ = α d + β s Unitarity: d’ G F W – u = d α G F u + β s W – with α 2 + β 2 =1 G F W – u G F G G s d 28
Quark mixing
Fourth c-quark is predicted to explain K 0 → 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.
2 2
α –β * β α * Why are they not diagonal?
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Quark mixing
Fourth c-quark is predicted to explain K 0 → 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 I have two answers, both are impolite (sorry for my answer
2
by another question): * 1) 2) 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 30
Quark masses can be diagonalized by unitary transformations Mass basis Then, charged weak interactions become non-diagonal diagonal Problem: Why these manipulations do not lead to FCNC? u c
Z 0
31
CPV with two quark generations
d
α ” can become real, while all other terms in Lagrangian remain unchanged. Then remove phase in “ γ ” Finally, we can make “ δ c → e iξ 2
c
s → e iξ 3
s
Do not touch “u” trying to correct “ β ”, otherwise you introduce another phase to “ α ”! Just check that “ β ” automatically becomes real. WHY?
β δ
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
s’ s d’
θ C ≈13º
d
32
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 33
CPV in the Standard Model
Requirements for CPV
m t
2
m b
2
m c
2
m s
2
m t
2
m b
2
m u
2
m
2
d
m c
2
m s
2
m u
2
m d
2
Why all quarks should have different masses?
J CP
0
Where J CP = Jarlskog determinant
J CP
Im
V i
V j
V i
*
V j
*
i
j
,
Using parameterizations
J CP
s
12
s
13
s
23
c
12
c
23
c
13 sin 6
A
2 3 .
05 + 0 0 .
.
19 20 10 5
CPV is small in the Standard Model 34
History since KM till B-factories
1974 charm (4 th ) quark discovered 1978 beauty/bottom (5 th ) quark discovered 1983 B-mesons explicitly reconstructed 1988 V cb ,V td ,V ub
measured: Unitarity triangle is not squashed
CKM matrix is really complex!
1995 truth/top (6 th ) quark discovered 1999 direct CP violation is observed in kaon system 1999 B-factories (Belle and BaBar) start operation 35
CKM matrix in Wolfenstein parameterization
Wolfenstein parameterization (expansion on a small parameter λ)
s
12 sin 12 0 .
23
A
s
23
s
2 12 0 .
8
s
13 cos
s
12
s
23
s
13 sin
s
12
s
23
Reflects hierarchy of strengths of quark transitions d u s b
Charge –1/3
t V td W + d t c
Charge +2/3
V CKM
1 2
A
3 1 2
i
1 2
A
2 2
O(1) O(
) O(
2 ) O(
3 )
CPV phases are in the corners
V
*
ub
A
3
A
2
i
+
O
b
1
W – u 36
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(λ 3 ) 37
One (the most important) Unitarity Triangle
*
V ud V ub + V
*
cd V cb + V
*
td V tb = 0 Convenient to normalize all sides to the base of the triangle (V cd V * cb = Aλ 3 ).
(ρ,η)
V * ud V ub
2
* V td V tb
phase of
V ub
0
3
g
V cd V cb
1
1 phase of
V td
Coordinate of the Upper apex becomes Wolfenstein parameters (ρ , η).
38
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.
39
The neutral current remains the same since the CKM matrix
V CKM
is unitary 40