Transcript A CP - Indico

The Violation of Symmetry between
Matter and Antimatter
Andreas Höcker
B. Cahn
Laboratoire de l’Accélérateur Linéaire and Université de Paris-Sud
CERN Summer Student Lectures, June 5-9, 2005
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
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CP Violation through the History of
Particle Physics
Discovery of strange particles (Rochester, Butler)
(1946, ‘47)
Neutral kaons can mix (Gell-Mann, Pais)
(1952)
KL discovery (Lederman et al.)
(1956)
P violation: possible explanation
(Lee, Yang)
P violation found in  decay (Wu et al.)
(1956)
(1957)
later: maximum P and C violation, but CP invariance
Cabibbo-Theory
(1963)
CP violation (CPV) discovered (Cronin, Fitch et al.)
(1964)
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CP Violation is a Family History of Quarks
GIM-Mechanism
(Glashow, Illiopolous, Maiani)
CPV phase requires 3 families
J/ resonance: c quarks
(1970)
(Kobayashi-Maskawa)
(1973)
(Ting, Richter)
(1974)
Discovery of  lepton: 3rd family (Perl et al.)
(1975)
 resonance: b quarks
(1977)
(Lederman et al.)
Broad (4S) (CLEO)
(1980)
B mesons live long (|Vcb| small)
B mesons oscillate
t-quark discovery
’/  0
(MAC, MARK II)
(ARGUS)
(1983)
(1987)
(CDF)
(NA31, NA48, KTeV)
(1995)
(1999)
Start of B Factories: BABAR (PEP II), Belle (KEKB)
(1999)
CPV in B system : sin(2)  0 (BABAR, Belle)
(2001)
Direct CPV in B system : ACP(K+–)  0 (BABAR, Belle)
(2004)
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Evolution of working conditions (example BABAR) :
Discovery of CP violation:
V.L. Fitch
R. Turlay
J.W. Cronin
J.H. Christenson
PRL 13, 138 (1964) [cited: 1067 times]
… 623 physicists (in early 2005).
BABAR: PRL 87, 091801 (2001) [cited: 308 times]
Belle:
CERN Summer Student Lectures 2005
PRL 87, 091802 (2001) [cited: 319 times]
A. Höcker: The Violation of Symmetry between Matter and Antimatter
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USA
[38/311]
INFN, Perugia & Univ
INFN, Roma & Univ "La Sapienza"
INFN, Torino & Univ
INFN, Trieste & Univ
The BABAR
Collaboration
California Institute of Technology
UC, Irvine
UC, Los Angeles
UC, Riverside
UC, San Diego
UC, Santa Barbara
UC, Santa Cruz
U of Cincinnati
U of Colorado
Stanford U
Colorado State
U of Tennessee
Harvard U
U of Texas at Austin
U of Iowa
U of Texas at Dallas
Iowa State U
Vanderbilt
LBNL
U of Wisconsin
LLNL
Yale
U of Louisville
U of Maryland
Canada
[4/24]
U of Massachusetts, Amherst
MIT
U of British Columbia
U of Mississippi
McGill U
Mount Holyoke College
U de Montréal
SUNY, Albany
U of Victoria
U of Notre Dame
Ohio State U
China
[1/5]
U of Oregon
Inst. of High Energy Physics, Beijing
U of Pennsylvania
Prairie View A&M U
France
[5/53]
Princeton U
LAPP, Annecy
SLAC
LAL Orsay
U of South Carolina
11 Countries
80 Institutions
623 Physicists
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The Netherlands [1/4]
NIKHEF, Amsterdam
Norway
[1/3]
U of Bergen
LPNHE des Universités Paris
VI et VII
Ecole Polytechnique, Laboratoire
Leprince-Ringuet
CEA, DAPNIA, CE-Saclay
Germany [5/24]
Ruhr U Bochum
U Dortmund
Technische U Dresden
U Heidelberg
U Rostock
Italy
[12/99]
INFN, Bari
INFN, Ferrara
Lab. Nazionali di Frascati dell' INFN
INFN, Genova & Univ
INFN, Milano & Univ
INFN, Napoli & Univ
INFN, Padova & Univ
INFN, Pisa & Univ &
ScuolaNormaleSuperiore
Russia
[1/13]
Budker Institute, Novosibirsk
Spain
[2/3]
IFAE-Barcelona
IFIC-Valencia
United Kingdom [11/75]
U of Birmingham
U of Bristol
Brunel U
U of Edinburgh
U of Liverpool
Imperial College
Queen Mary , U of London
U of London, Royal Holloway
U of Manchester
Rutherford Appleton Laboratory
U of Warwick
A. Höcker: The Violation of Symmetry between Matter and Antimatter
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To start with … a Motivation
nbaryon
1. The Universe is empty* !
2. The Universe is almost empty* !
n

nbaryon  nbaryon
n
~ O 1010 
Bigi, Sanda, “CP Violation” (2000)
Initial condition ? Would this be possible ?
Dynamically generated ?
Sakharov conditions (1967) for Baryogenesis
1.
2.
Baryon number violation
C and CP violation
3.
Withdrawal from thermodynamic equilibrium (non-stationary system)
So, if we believe to have understood CPV in the quark sector, what does it signify ?
A sheer accident of nature ?
What would be the consequence of a different CKM phase ?
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Today, the study of CP Violation is
the Search for New Physics
Since the precise measurement of CP violation in K and B decays (in perfect agreement
with the SM), there is considerable effort at the B Factories towards the search for specific
signs of New Physics (NP). WHY ?
The gauge hierarchy Problem (Higgs sector, scale ~ 1 TeV)
Baryogenesis (CKM CPV too small)
The strong CP Problem (why is  ~ 0 ?)
Grand Unification of the gauge couplings
Neutrino masses, dark matter, ... many more
Conflict between New Physics limits from flavor physics:  1 TeV (e.g., K0, D0, B0 mixing),
and the expected NP scale (1 TeV)  NP cannot have a generic flavor structure
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QCD and CP Violation
as seen by A. Roodman (SLAC)
Theoretical errors
Experimental
Difficulty
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but, wait :
What is CP Violation ?
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Lecture Themes
I.
Introduction
Antimatter
Symmetries
II.
CP Violation
Electric and weak dipole moments
The strong CP problem
The discovery of CP violation in the kaon system
III.
CP Violation in the Standard Model
The CKM matrix and the Unitarity Triangle
B Factories
CP violation in the B-meson system and a global CKM fit
Penguins
IV.
CP Violation and the Genesis of a Matter World
Baryogenesis and CP violation
Models for Baryogenesis
The experimental future in the quest for new physics
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Through the
Looking
Glass
What’s the
Matter with
Antimatter ?
David Kirkby, APS, 2003
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Paul Dirac
Combining quantum mechanics with special relativity,
and the wish to linearize /t, leads Dirac to the equation
i     x,t   m  x,t   0
Solutions with negative energy appear
Dirac, imagining holes and seas
Vacuum represents a “sea” of such negative-energy
particles (fully filled to satisfy Pauli principle)
Energy
E 
me
these holes were protons, despite their large difference in mass,
because he thought “positrons” would have been discovered already)
0
me
s  1/ 2
Dirac identified holes in this sea as “antiparticles” with
opposite charge to particles … (however, he conjectured that
E
s  1/ 2
This picture fails for bosons !
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An electron with energy E can fill this hole, emitting an
energy 2E and leaving the vacuum (hence, the hole
has effectively the charge +e and positive energy).
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Positron – Antiparticle of the Electron
Discovered in cosmic rays by Carl Anderson in 1932
Has the same mass as the electron but positive charge
Anderson saw a track in a cloud
chamber left by “something
positively charged, and with the
same mass as an electron”
History of antiparticle discoveries:
1955: antiproton
1960: antineutron
1965: anti-deuteron
1995: anti-hydrogen atom (by now millions produced at CERN !)
Every particle has an antiparticle
Some particles (e.g., the photon) are their own antiparticles !
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Particles and Antiparticles Annihilate
What happens if we bring particles and antiparticles together ?
A particle can annihilate with its
antiparticle to form gamma rays
An example whereby matter is
converted into pure energy by
Einstein’s formula E = mc2
Conversely, gamma rays with
sufficiently high energy can turn
into a particle-antiparticle pair
Particle-antiparticle tracks in a
bubble chamber
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Symmetries
A symmetry is a change of something that leaves
the physical description of the system unchanged.
1.
Physical symmetries:
people are approximately bilaterally symmetric
spheres have rotational symmetries
2.
Laws of nature are symmetric with respect to mathematical operations
pollen of the hollyhock exhibits spherical
symmetry (magnification x 100,000)
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Continuous Symmetries and Conservation Laws
In classical mechanics we have leaned that to each continuous symmetry
transformation, which leaves the scalar Lagrange density invariant, can be
attributed a conservation law and a constant of movement (E. Noether, 1915)
Continuous symmetry transformations lead to additive conservation laws
Symmetry
Invariance under
movement in time
Homogeneity of
space
Isotropy of space
Transformation
Translation in time
Translation in
space
Rotation in space
Conserved
quantity
Energy
Linear momentum
Angular
momentum
No evidence for violation of these symmetries seen so far
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digression: Symmetry of Reference Systems
Another type of symmetry has to do with reference frames moving with respect
to one in which the laws of physics are valid (inertial reference frames):
Physical laws are unchanged when viewed in any reference frame
moving at constant velocity with respect to one in which the laws are valid
Note that while laws are unchanged between reference frames, quantities are not
The fact that the laws of motion are unchanged between frames, plus the fact that
the speed of light is always the same lead to the theory of special relativity with two
consequences
Two events that are simultaneous in one reference frame are not
necessarily simultaneous in a reference frame moving with respect to it
There are some quantities (called Lorentz scalars) that have values
independent of the reference frame in which their value is calculated
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Continuous Symmetries and Conservation Laws
In general, if U is a symmetry of the Hamiltonian H, one has: H,U   0  H  U †HU
f  H i   f U †HU i  f H i
Accordingly, the Standard Model Lagrangian satisfies local gauge symmetries
(the physics must not depend on local (and global) phases that cannot be observed):
U(1) gauge transformation

electromagnetic interaction
SU(2) gauge transformation

weak interaction
SU(3)C gauge transformation

strong interaction (QCD)
Conserved additive quantum numbers:
electric charge (processes can move charge between quantum fields, but the sum of all charges is constant)
similarly, color charge of quarks and gluons, and the weak charge
quark (baryon) and lepton numbers (however, no theory for these, therefore believed to be only
approximate asymmetries)  evidence for lepton flavor violation in “neutrino oscillation”
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Discrete Symmetries
Discrete symmetry transformations lead to multiplicative conservation laws
The following discrete transformations are fundamental in particle physics:
Parity P (“handedness”):
reflection of space around an arbitrary center;
P invariance  physics does not distinguish right and left
Particle-antiparticle transformation C :
change of all additive quantum numbers (for example the
electrical charge) in its opposite (“charge conjugation”)
P eL  eR
P 0   0
P n  n
C eL  eL
Cu  u
Time reversal T :
the time arrow is reversed in the equations;
T invariance  if a movement is allowed by a the physics law, the movement in
the opposite direction is also allowed
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In particle physics:
Cd  d
C 0   0
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Conservation of Discrete Symmetries
Invariance under the discrete transformations requires:
P:
f ( x,t ) H i ( x,t )  f (  x ,t ) H i (  x,t )
C:
f ( x,t ) H i ( x,t )  f ( x ,t ) H i ( x,t )
T :
f ( x,t ) H i ( x,t )  f ( x, t ) H i ( x, t )
Remarks:
These are interesting because it is not obvious whether the laws of nature should look the
same for any of these transformations, and the answer was surprising when these symmetries
were first tested.
Time reversal symmetry (invariance under change of time direction) is not obvious at all in
the macroscopic world. See, e.g., the Billiard table at the beginning of the game: it would strike
our common sense if we could hit the balls so that they all move in just the directions and
speeds necessary for them to collect and form a perfect triangle at rest, with the cue ball
moving away. This lack of time reversal invariance is due to the laws of thermodynamics
(statistics). For the individual processes we are interested in thermodynamics is not important.
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C, P, T Transformations and the CPT Theorem
Quantity
P
C
T
–x
x
x
t
t
–t
–p
p
–p
s
s
–s
electrical field
–E
–E
E
magnetic field
B
–B
–B
space vector
time
momentum
spin
The CPT theorem (1954): “Any quantum field theory is invariant under the
successive application of C, P and T ”  implied by Lorentz invariance
G. Lüders, W. Pauli; J. Schwinger
Fundamental consequences:
relation between spin and statistics: fields with integer spin (“bosons”) commute and
fields with half-numbered spin (“fermions”) anticommute  Pauli exclusion principle
particles and antiparticles have equal mass and lifetime, equal magnetic moments
with opposite sign, and opposite quantum numbers
Best experimental test:
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m
K
0
 mK 0  / mK 0  1018
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If CPT is Conserved, how about P, C and T ?
Parity is often violated in the macroscopic world:
Strongly Left-sided
Strongly Right-sided
Mixed Sided
Handedness
5%
72%
22%
Footedness
4%
46%
50% (?)
Eyedness
5%
54%
41%
Earedness
15%
35%
60%
Porac C & Coren S. Lateral preferences and human behavior. New York: Springer-Verlag, 1981
About 25% of the population drives on the
left side: why ?
 in ancient societies people walked (rode) on the left to have their
sword closer to the middle of the street (for a right-handed man) !?
The DNA is an oriented double helix
two right-handed
polynucleotide
chains that are
coiled about the
same axis:
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Not so in the microscopic World ?
Electromagnetic and strong interactions are C, P and T invariant
Example: neutral pion decays via electromagnetic (EM) interaction : 0   but not 0  
0 
1
uu  dd 
L 0,S 0
2
C  B, E  B, E
, C  0    0
, C    
the initial (0) and final states () are C even: hence, C is conserved !
Generalization: P qq   1
L1
qq , C qq   1
LS
qq , G uu (d )   1
L S I
uu (d )
Experimental tests of P and C invariance of the EM interaction:
C -invariance: BR  0  3   3.1 108
P -invariance: BR   4 0   6.9  107
Experimental tests of C invariance of strong interaction: compare rates of positive and
negative particles in reactions like: pp     X , K K  X
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And … the Surprise in Weak Interaction !
T.D. Lee and C.N. Yang pointed out in 1956 (to explain the observation
of the decays K+  3 and 2) that P invariance had not been tested
for weak interaction  Madame C.S. Wu performed in 1957 the
experiment they suggested and observed parity violation
It was found that parity is even maximally
violated in weak interactions !
Angular distribution of electron intensity:
I ( )  1  
where:
  Pe
Ee
 1 
v
cos 
c
 - spin vector of electron
helicity
Pe - electron momentum
Ee - electron energy
 1 for electron
 1 for positron

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TCO ~ 0.01 K
polarized in
magnetic field
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P and C Violation in Weak Interaction
Goldhaber et al. demonstrated in 1958 that in the  decay of the nucleus, the
neutrino is left-handed, while the antineutrino is right-handed:
Particle :
e
Helicity :  v / c
e
+v / c


1
1
(  C violation ! )
In the Dirac theory, fermions are described as 4-component spinor wave
functions upon which 44 Operators i apply, which are classified according
to their space reflection properties :
   † 0 , scalar (S )
 5 , pseudoscalar (P )
  4  4  current
Lorentz-covariant bilinear
  , vector (V )
  5 , axial vector (A)
          , tensor (T )
2i 
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P and C Violation in Weak Interaction
Let’s consider the  reaction: n    e   p
General ansatz for the current-current
constants
matrix element :
G
 p i n   e i Ci   5Ci  v 
M

2 i S,...
Use the helicity projection operators for Dirac spinors: uL / R 
u u  uL  uR    uL  uR   uL uL  uR uR
so that one has for a V interaction:
while for a scalar interaction:
uL uR 
u L uR 
1
1  5  u
2
 at high energies, the EM interaction
conserves the helicity of the scattered fermions
1 
u (1   52 )u  0
4
1
and similar for A
1
u (1   5 )u  0
2
and similar for P, T
Now, consider the weak neutrino-electron current in the relativistic limit:
ue V  A  u  ue 
1
1   5  u  ue,L  ue,R   u ,L  ue,L u ,L
2
It projects upon the left handed helicities, and hence violates P maximally, as required !
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P and C Violation in Weak Interaction
Weak interaction violates both C and P symmetries

 e      e
Consider the decay of a polarized muon: polarized
P
The preferred emission
direction of an electron
is opposite to the muon
polarization.
handedness of the electron:
C
suppressed
P transformation (i.e.
reversing all three
directions in space)
yields constellation that
is suppressed in nature.
Similar situation for C
transformation (i.e.
replace all particles with
their antiparticles).
suppressed
handedness of the positron:
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B. Cahn, LBL
Applying CP, the resulting
reaction—in which an
antimuon preferentially
emits a positron in the
same direction as the
polarization—is observed.
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CP Violation
CP Symmetry requires that processes and
antiprocesses have the same rates
1.
Due to the CPT theorem, CP symmetry also requires T symmetry
2.
CP violation would enable us to distinguish between particles and
antiparticles, and between past and future in an absolute way(*) !
(*)Imagine
two worlds that are far away want to gather together: if one were made of matter, and the other one of
antimatter, the spaceship of the one that landed on the planet of the other would lead to a disastrous annihilation.
This could be prevented by measuring a CP violation parameter (if exists) by both worlds and comparing the results.
stolen from Gino Isidori’s homepage
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Dipole moments
Can there be CP violation in the electromagnetic or neutral weak current ?
Let’s modify the Standard Model Lagrangian to allow for CP violation through
electromagnetic and weak dipole moments:
LCP  
i
   5  d EM (q 2 )F  d weak (q 2 )Z  
2
where F and Z are electric and weak field strength tensors.
In the nonrelativistic limit one obtains the Pauli equation with the additional terms:
LCP  d EM E  d weak Z
But…. why do these dipole moments violate CP symmetry ?
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Dipole Moments and CP Violation
Spin is the only explicit “direction” of an elementary particle. Hence the dipole moment
must be proportional to it:
d s
The electric dipole moment is the average of a charge density distribution (polar vector):
d   d 3 x   (x)  x
spin
The spin has the form of an angular momentum (axial vector):
s r p
Parity transformation gives:
Pd  d , Ps  s
dipole
moment

d 0
+
–
P
–
+
P invariance
Time reversal transformation gives: Td  d , Ts  s

d 0
T invariance
Hence, the electric or weak dipole moments can be only nonvanishing in presence of a P- and T-violating (and thus CP-violating)
interaction
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T
+
–
+
–
30
Experimental Limit on dEM (e.cm)
d(muon)  7×10–19
neutron:
electron:
10-20
10-20
10-22
10-22
10-24
10-24
10-26
Multi
Higgs
Electromagnetic
d(proton)  6×10–23
d(neutron)  6×10–
SUSY
26
d(electron)  1.6×10–
27
10-28
Left-Right
present experimental limits
10-30
10-30
none of this seen yet, why ???
1960 1970 1980 1990 2000
10-32
The Measurement of EDMs:
History of the experimental
progress
10-34
Standard Model
10-36
10-38
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CP Violation in the QCD Lagrangian
It was found in 1976 that the perturbative QCD Lagrangian was missing a term L
LQCD 

LpQCD
perturbative QCD
L ,
where:
L  
P ,T -violating
s
8
a
G
G  ,a
, and G  ,a 
Gluon field tensors
1
  G ,a
2
dual field tensor
that breaks through an axial triangle anomaly diagram the U(1)A symmetry of LpQCD , which
is not observed in nature
when classical symmetries are broken on
the quantum level, it is denoted an anomaly
a
 ,a
a
The term G
is P-and T-odd, since:
G ,a contained in LpQCD is CP-even, while G G

GG   Ea  Ba
a

2
GG   Ea  Ba
a

2

 E
P,T


2
a
a

P,T

   Ea  Ba
a
 Ba
2


Relativistic invariants,
similar to electric field
tensors: F F  , F F 
  F   j  ,   F   0
color electric and magnetic fields
Maxwell equations
This CP-violating term contributes to the EDM of the neutron:
dn
  5  1016 ecm, so that  tiny or zero
"Strong CP (finetuning) Problem"
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
32
The Strong CP Problem
Remarks:
If at least one quark were massless, L could be made vanish; if all quarks are massive,
one has uncorrelated contributions, which have no reason to disappear
Peccei-Quinn suggested a new global, chiral UPQ(1) symmetry that is broken, with the
“axion” as pseudoscalar Goldstone boson; the axion field, a ,compensates the contribution
from L :

   a  ,a
axion coupling to SM particles is
L     a  s G
G
suppressed by symmetry-breaking
fa  8

scale (= decay constant)
QCD nonperturbative effects (“instantons”) induce a potential for a with minimum at a =  fa
The axion mass depends on the UPQ(1) symmetry-breaking scale fa
 107 GeV 
ma  
  0.62 eV ,
f
(GeV)
 a

and axion coupling strength: ga  ma
If fa of the order of the EW scale (v), ma~250 keV  excluded by collider experiments
CERN Summer Student Lectures 2005
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33
The Search for Axions (the axion is a dark matter candidate)
The axion can be made “invisible” by leaving scale and coupling free, so that one has:
ma ~ 10–12 eV up to 1 MeV  18 orders of magnitude !
Axion scale and mass, together
with the exclusion ranges from
experimental non-observation

Axion decays to 2, just as for the
0,
or in a static magnetic field:
a
f

Schematic view of
CAST experiment
at CERN:
Axion source
CERN Summer Student Lectures 2005
Axion detection (LHC magnet)
A. Höcker: The Violation of Symmetry between Matter and Antimatter
34
The Discovery of CP Violation
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
35
CP Violation in Particle Reactions
General signature: rate differences between CP-conjugated processes:
 i  f


  i  f

It necessarily involves interference of amplitudes contributing to the processes.
To obtain interference, we need phases that change sign under CP
Example: if the decay amplitudes are given by: a1,2 ,1,2 

Example for so-called “direct CP violation”,
i2 i2

A  or
i 
f  precisely:
 a1e i1e i1 CP
a2eviolation
e
more
in the decay j


A i  f

a e
1
i1
e  i1  a2e i2 e  i2

alters sign under CP
(“weak phase”)
j
e 2i (i f )
CP invariant
(“strong phase”)
unphysical phase
where:
 i  f

 A i  f

2
and

 i  f


 A i  f

2
We can define the following CP asymmetry ACP:
ACP


 i
 i  f
CERN Summer Student Lectures 2005
 f
   i
   i
 f
 f


 a
2a1a2 sin 1   2  sin 1  2 
2
2
1  a2  2a1a2 cos 1   2  cos 1  2 
A. Höcker: The Violation of Symmetry between Matter and Antimatter
36
Strange Particles
Strange mesons have an “s” valence quark
Non-strange particles: ( ,  , )I 1 : ud , (uu  dd ) / 2
(,, )I 0 : (uu  dd ) / 2 
neutral particles are
eigenstates of C operator
(K ,K , )I 1/ 2 : K   us , K   us, K 0  ds , K 0  ds
Strange particles:
neutral strange particles are
not eigenstate of C operator
Production of strange particles via strong or electromagnetic interaction has to respect
conservation of the S (“strangeness”) quantum number (they are “eigenstates” of these interactions)





S  0 S  0 S 0
p

S  0 S  0 S 0
p
   S 1KS01 
S 0
  pS 0KS1KS01 
S 0
 pS 0 pS 0 S 0   S0KS1KS01 S 0 ,  S0KS1KS01 S 0
e



S 0 S 0 S 0
e
 S 0   KS01KS01 
S 0
The C operator changes S by |ΔS| = 2, for |S| = 1 strange particles.
CERN Summer Student Lectures 2005
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37
The Discovery of CP Violation
Empirically (in the experiment) one does however not observe the neutral “flavor
0
eigenstates” K and K 0 but rather long- and short-lived neutral states: KL and KS
Their observed pionic decays are: KS   
and it was believed that: CP KS   KS
0
and K L   
0
Larger phase space of
2 decay:
and CP KL   KL
  KL /  KS
580
However, Cronin, Fitch et al. discovered in 1964 the CP-violating decay: K L    
Jim Cronin
Measurement of opening angle of pion
tracks and their invariant mass:
+ –
KL    events
Today’s most precise
measurement for amplitude ratio:
 
A  K L     
A  KS     
  2.282  0.017   10 3
Val Fitch
CERN Summer Student Lectures 2005
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38
Observing CP Violation at the  Factory
The KLOE experiment at the  Factory DANE (Frascati, Italy) can detect single CPviolating decays, since due to angular momentum conservation and Bose symmetry:
  K 0K 0
and equivalently:
KS   

  KS K L

K L    
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
Note that the
quantum
coherence is
broken after the
decay of one of
the two K0’s
39
The Discovery of CP Violation in
the Charged Weak Current
To understand the observed CP violation from the flavor perspective, let us construct CP
eigenstates with CP eigenvalues ±1:




1
0
K

 K 0antiparticles
,
1
CP ! They
K1 and K12 are notKmutual
2
have different decay modes, different lifetimes
1
0
K 2 and different
K 0  Kmasses
,
CP  1
2
While the flavor eigenstates are distinguished by their production mechanism, the CP
eigenstates are distinguished by their decay into an even and odd number of pions.
Since there is CP violation, the physical states (“mass eigenstates”) are not exactly the
same as the CP eigenstates:
 KS 
1


2
K 
1 
 L 
where: q / p  1    / 1   
CERN Summer Student Lectures 2005
 K1   K 2

  K  K
1
2

0
  p q  K 



  q p   K 0 



0.995  1 (!)
A. Höcker: The Violation of Symmetry between Matter and Antimatter
40
CP Violation and Neutral Kaon Mixing
CPLEAR (CERN) measured the rates of K 0 ,K 0 (t )     as a function of the decay
time, t, and finds quite a surprise:
after acceptance correction
and background subtraction
rates are different for the
two flavor states
K 0    
K 0    
there is a non-exponential
component (?)
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
41
Neutral Kaon Mixing
Neutral kaons can “mix” through the charged weak current, which does not conserve
strangeness, and neither P nor C. Weak interaction cannot distinguish K 0 from K 0
Simple picture: they mix through common virtual states:
 
0
K0
K0
 
0
A priori, mixing has nothing to do with
CP violation !
Because Δm(K) = m(KL) – m(KS) = 3.5 10–12 MeV > 0, a K 0 will change with time into
a
and
K 0 vice versa
These oscillations are described in QCD by ΔS = 2 Feynman “box” diagrams:
[S=2]
s
K
0
t,c
d
d
W
W
t ,c
s
K0
matrix element calculated numerically
using Lattice gauge theory
CERN Summer Student Lectures 2005
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42
Neutral Kaon Mixing
An initially pure K0 state, will evolve into a superposition of states:
K (t )  g(t ) K 0  h(t ) K 0
The time dependence is obtained by solving the time-dependent Schrödinger equation:
 K 0 (t )
d
i  0
dt  K (t )


 K 0 (t )
 M i  
 0
2
 

 K (t )







with 22 matrices M, , of which the offdiagonals  Δm, Δ govern the mixing
The respective time-dependent intensities
are found to be (neglecting CP violation):
I (T ) / I (0)
K0
IK 0 t   e Lt  2e Lt / 2 cos  m  t 
IK 0 t   e
Lt
 2e
Lt / 2
K L0
cos  m  t 
K0
After several KS lifetimes, only KL are left
T  t /S
CERN Summer Student Lectures 2005
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43
Neutral Kaon Mixing and CP Violation
Since KS and KL are not CP eigenstates, the time dependence has to be slightly modified
by the size of , giving rise to an additional sine term.
 +K 0–         K 0     
Let’s get backAto
the  0 decay
rates: 0
  sin  m  t 
Asymmetry:
 
 
  K        K     
Neglecting other sources of
CP violation, and assuming
arg() = /4.
CPLEAR 1999
dominated by KS+–
K 0    
A
N(KS+–) ~ N(KL+–amplitude
)
 ||
 Large interference with opposite sign
K 0    
CERN Summer Student Lectures 2005
dominated by KL+–
A. Höcker: The Violation of Symmetry between Matter and Antimatter
44
There are in Fact Four Meson Systems with Mixing
Pairs of self-conjugate mesons that can be transformed to each other via flavor changing
weak interaction transitions are:
K 0  sd
Bd0  bd
D0  cu
Bs0  bs
They have very different oscillation properties that can be understood from the “CKM
couplings” (see later in this lecture) occurring in the box diagrams
N(T ) / N0
for
for the
the plot
plot
xxDs = 15
0.02
yyDs = 0.10
0
Ds = 0
Bs0  Bs0
00
00
0
B
B
K

K
00 
s
s
D

D
Bd
Bd0
mixing probability:
 ~~
=210
18%–6
50%
K L0
Bd0  Bd0K 0  K 0
T
CERN Summer Student Lectures 2005
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45
Three Types of CP Violation
The CP violation discovered by Cronin, Fitch et al. involves two types of CPV:
CP Violation in mixing :
Prob(K 0  K 0 )  Prob(K 0  K 0 )
CP Violation in interference between decays with and without mixing :
also called:
“indirect CPV”
Prob(K 0 (t )     )  Prob(K 0 (t )     )
However, there is yet another, conceptually “simpler” type of CP violation yet to discover:
CP Violation in the decay:
Prob(K  f )  Prob(K  f )
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
also called:
“direct CPV”
46
CP Violation in the Decay
We have seen that at least two amplitudes with different CP-violating (weak) and conserving (strong) phases have to contribute to the decay for direct CPV. This suppresses this
type of CPV, so that the observable effect should be small compared to .
To allow for (small) direct CPV, we need to slightly modify our previous definitions:
   
2
  K L     
  KS   



and use also:
  2  
2
  KL   0 0 
  KS   0 0 
“Clebsch-Gordon isospin” factor when
passing from charged to neutral pions
If the observed CP violation is different in the two decay modes, we have a prove for a
contribution from direct CP violation. From the measurement of the ratio of these decayrate ratios we can determine  ’
The observable
  KL   0 0 
  KS   0 0 
  KL     
  KS     
  2 

  
2
 
 
1  6  Re  
 
First order Taylor expansion
CERN Summer Student Lectures 2005
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47
The Discovery of CP Violation in the Decay
Due to the smallness of the effect, it took several experiments and over 30 years of
effort to establish the existence of direct CPV
Feynman graphs:
K0
“Tree”
(born-level)
amplitudes
K
0
s
d
s
d
W
u
d
u
d

W
u
u
d
d

Experimental average
Indeed, a very small effect !

0
0
(16.7 ± 2.3)10–4
Interference
W
“Penguin”
(loop-level)
amplitude
s
K
0
d
CERN Summer Student Lectures 2005
t, c,u
g
d
u
u
d


A. Höcker: The Violation of Symmetry between Matter and Antimatter
48
And the Theory ?
Direct CP violation is in general very hard to calculate due to its sensitivity to the
relative size and phase of different amplitudes of similar size…
Many theoretical groups have put serious efforts into this. All agree that the effect is
much smaller than the indirect CPV (which is a success for the Standard Model !),
but the theory uncertainties are much larger than the measurement errors:
Theoretical
pre(post)dictions
plot not updated !
...the ball is on
the theory side
courtesy:
G. Hamel de Monchenault
e n d
CERN Summer Student Lectures 2005
o f
L e c t u r e
1&2
A. Höcker: The Violation of Symmetry between Matter and Antimatter
49
Conclusions of the first two Lectures
No CP violation without antimatter !
P, C, T are good symmetries of electromagnetic and strong interactions
P, C are maximally violated in weak interaction
CP, T are not good symmetries of weak interaction
no other source of CP violation has been found so far (EDM’s)
CP violation has been first discovered in the kaon system, and both,
Cartoon
shownCP
by N.violation
Cabibbo in 1966…
then,
there was tremendous
direct and
indirect
havesince
been
observed
progress in the understanding (better: description) of CP violation  next lecture !
CERN Summer Student Lectures 2005
A. Höcker: The Violation of Symmetry between Matter and Antimatter
50