Matter,
Antimatter and
CP violation
Aurelio Bay
Institut de Physique
des Hautes Energies
Séminaire Uni Neuchâtel 27-I-2003
The Cosmic
Onion
QUARKS
NEUTRON
PROTON
} 10-15 m
NOYAU
ELECTRON
ATOM
10 -10 m
1m
10-5 m
The cosmic
onion 2
107 m
1m
1020 m
.
1011 m
Universe
1022-24 m
Matter Antimatter and CP violation
The Standard Model of particles (and antiparticles)
Symmetries
Parity (P),
Charge Conjugation (C)
and Time reversal (T)
P and C violation
Baryogenesis
CP & T violation
Experiments
Conclusion
The
Standard
Model
MATTER
INTERACTIONS
Charge [e]
0
ne
nm
nt
-1
e-
m-
t-
2/3
u
-1/3
d
c
Quarks
s
t
b
Spin 1/2
Weak : W+ W- Z
E.M. :
photon
Strong : gluons
Spin 1
The SM incorporates:
QED: photon exchange between charged particles
Weak (Flavour-Dynamics): exchange of W and Z
QCD: gluon exchange between quarks
SM is based on the gauge group:
SU(3) c  SU(2) L  U(1) Y
QCD
Electro-weak Theory
do not forget
antiparticles... !
Antiparticles
Paul A. M. Dirac theory of relativistic
quantum mechanics in 1927
m
(i   m - m)  0
correctly describes spin 1/2 particle
but with a "double" of negative energy...
Oppenheimer, Stückelberg, Feynman suggest
to replace E<0 particles with other
(anti)particles of opposite charge and E>0
 describes spin 1/2 particle & antiparticle
Positrons observation
Positrons were observed at CAL-Tech by
C. D. Anderson in 1932.
e+
e-
B
Pair creation
Symmetries
Amalie (Emmy) Noether
In 1915 she links the invariance
properties of a Lagrangian to
conservation laws
Invariance under:
Translation
Rotation
Gauge
Momentum conserved
Angular mom. conserved
Charge conserved
Symmetries in particle physics
Non-observables
symmetry transformations
difference between
permutation
identical particles
absolute position
r r+d
absolute time
tr+t
absolute spatial direction
rotation r  r'
absolute velocity
Lorentz transf.
absolute right (or left)
r  -r
sign of electric charge
q  -q
relative phase between states with
different charge q
y  eiqq y
different baryon nbr B
y  eiBq y
different lepton nbr L
y  eiLq y
difference between
p
 p
   U 
coherent mixture of (p,n)
n
n
 
 
conservation law
/ selection rules
B.E. / F.D. statis.
p conserved
E conserved
J conserved
generators L. group
Parity
Charge conjugation
charge conserved
B conserved
L conserved
isospin
Some symmetries might have a deep reason to exist
... other not.
... suddenly we discover that we can observe a "non - observable".
A
symmetry violation
is discovered.
The Right-Left symmetry (Parity) was considered an
exact symmetry  1956
Discrete symmetries P, C,...
P: (x,y,z) -> (-x,-y,-z).
C: charge -> -charge.

P:x
-x
P :p
-p
P:J
J
C:x
x
C:e
-e
C : A,V
e.m. interactions
are P & C invariant

VCoulomb (r ) ~
-A,-V
qQ
r
P : VCoulomb (r )
VCoulomb (-r )  VCoulomb (r )
C : VCoulomb (r )
VCoulomb (r )
What about T ?
If x(t) is solution of F = m d2x/dt2 then x(-t) is also a
solution (ex.: billiard balls)
T: x
x
T:t
-t
T:p
-p
T: J
-J
Ok with electrodynamics:
E T : B -B
F  q(E + v  B)  T : F
T:E
F
Parity: (x,y,z)  (-x,-y,-z)
1848 L. Pasteur discovers the property of optical isomerism.
H
Mirror symmetry
M
OH
H3C
COOH
H
OH
COOH
H3C
The synthesis of the lactic acid in the lab gives a "racemic" mixture:
Nleft molecules = Nright molecules (within statistic fluctuations)
N right - N left
0
Asymmetry =
N right + N left
This reflects the fact that e.m. interaction is M (and P) invariant
Parity violation in biology
Humans are mostly right handed:
Asymmetry  A = (NR-NL)/(NR+NL) ≈ 0.9
 “90% Parity violation"
Lemmon and orange flavours
are produced by the
two "enantiomers"
of the same molecule.
100% P violation in DNA
Too much symmetry...
LR
LL
RR
? Bacchus, Arianna ?
QuickTime™ et un décompresseur
Cinepak sont requis pour visualiser
cette image.
MUSEE ROMAIN DE NYON
P conserved in e.m. and strong
1924 O. Laporte classified the wavefunctions of an atom as
either even or odd, parity +1 or -1.
In e.m. atomic transitions a photon of parity -1 is emitted.
The atomic wavefunction must change to keep the overall
symmetry constant (Eugene Wigner, 1927) :
Parity is conserved in e.m. transitions
This is also true for e.m. nuclear or sub-nuclear processes
(within uncertainties).
H(strong) and H(e.m.) are considered parity conserving.
Parity in weak interactions
6
Fermi, 1949 model of W interactions: P conservation assumed
C.F. Powell,... observation of two apparently identical particles
"tau" and "theta" weakly decaying
tau  3 pions
theta  2 pions
which indicates P(tau) = -1 and P(theta) = + 1
If Parity holds "tau" and "theta" cannot be the same particle.
6
HEP conf. Rochester 1956 Tsung Dao Lee and Chen Ning Yang
suggest that some particles can appear as parity doublets.
Feynman brought up the question of non-conservation of parity
(but bets 50 $ that P is conserved). Wigner suggests P is violated
in weak interactions.
6
Parity in weak interactions .2
Lee and Yang make a careful study of all known experiments
involving weak interactions. They conclude
"Past experiments on the weak interactions had
actually no bearing on the question of parity conservation"
Question of Parity Conservation in Weak Interactions
T. D. Lee Columbia University, New York, New York
C. N. Yang Brookhaven National Laboratory, Upton, New York
The question of parity conservation in beta decays and in hyperon and meson
decays is examined. Possible experiments are suggested which might test
parity conservation in these interactions.
Phys. Rev. 104, 254–258 (1956)
Co 60
1956 C. S. Wu et al. execute one of the
experiments proposed by Lee and Yang.
Co60 at 0.01 K in a B field.
Observables:
a "vector" : momentum p of beta particles
an "axial-vector" : spin J of nucleus (from B).
Compute
m = <Jp>
In a P reversed Word: P: Jp a - Jp
P symmetry implies m = 0
m was found  0  P is violated
J
p
Co
p
152 Sm
Measurement of neutrino helicity
(Goldhaber et al. 1958)
A=152
Z=63Eu
n
+ e-
152 Sm
152
Sm
62

+n+
Counter
NaI
Polarimeter: selects  of defined helicity
Result: neutrinos are only left-handed
Parity P and
neutrino helicity
P
n left
n right
P symmetry violated at (NL-NR)/(NL+NR) = 100%
Charge conjugation C
C transforms particles  antiparticle
C
n left
n left
C symmetry violated at 100%
Last chance:
combine C and P !
P
n left
gauche
Is our Universe
CP symmetric ?
CP
C

right
n droit
(A)symmetry in the Universe
matter
Big Bang
antimatter
time
Big Bang produced an
equal amount of matter
and antimatter
Today: we live
in a matter dominated
Universe
Baryo
genesis
I
Big Bang models are matter/antimatter symmetric
Where is ANTIMATTER today?
1) Anti-Hydrogen has been produced at CERN:
antimatter can exist.
2) Moon is made with matter. Idem for the Sun
and all the planet.
3) In cosmics we observe e+ and antiprotons, but
rate is compatible with secondary production.
4) No sign of significant of e+e- annihilation in
Local Cluster.
5) Assuming Big Bang models OK, statistical
fluctuations cannot be invoked to justify
observations. No known mechanism to
separate matter and antimatter at very large
scale
e+e- annihilation in the Galaxy
AMS
QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture.
sensitivity
(0.5 - 20 GeV):
He/He ~10-9
C/C ~10-8
Baryo
genesis
II
Today (age of Univers 10-20 10 9 years),
no antimatter around:
the visible Universe contains essentially
protons, electrons and photons.
The N of photons is very large compared to p and e :
2.5 10-10
Nprotons
Nphotons
 5 10-8
3
This suggests a Big
Bang
annihilation3phase
kT
2
N2.7  1.202 2 ( )  412 photons/cm
ch
in which matter +pantimatter
was transformed
-6 GeV/cm3  10-6 p/cm3
=0.1
=1
10
r
r
C
matter
into photons...
Baryo
genesis
III
Scenario:
At a certain point of the history of the Big Bang,
we need the following conditions:
N(quarks ) > N (antiquarks)
and
N(e-) > N(e+ )
time
quarks
antiquarks
e+
et e-
annihilation
gives photons
Hydrogen
plus photons
To get the correct baryon/photon ratio, we need an
asymmetry of the order:
N(q)
N(q)

3 1010 + 1
3 1010
Baryo
genesis
IV
Starting from a perfectly symmetric
Universe: 3 rules to induce asymmetry
during evolution
1) $ processes which violate baryonic
number conservation:
B(t=0) = 0
B(today)>0
B violation is unavoidable in GUT.
Andrej Sakarov
1967
2) Interactions must violate C and CP.
C violated in Weak Interactions.
.
CP violation observed in K and B decays
3) System must be out of thermal equilibrium
OK : Universe expands.
Baryogenesis V
q
1027
°K
ou
q
X
q
e+
{
q
X
q
Prob(Xqq) = a
- -qq)
- =b
Prob(X
ou
CP
mirror
q
e-
- +) = (1-a)
Prob(Xqe
Prob(Xqe-) = (1-b)
Requirement: a > b...
... forbidden by CP symmetry !
CP
- qq
--  a  b
X  qq
X
CP violation
July 1964: J. H. Christenson, J. W. Cronin, V. L. Fitch et R. Turlay
find a small CP violation with K0 mesons !!!
S. Bennet, D. Nygren, H. Saal, J. Steinberg, J. Sunderland (1967):
p+ e - n
K0L
{MIRROR
CP
p- e+ n
K0L
K0L is its own antiparticle
CP symmetry implies identical rates. Instead...
N
p- e+ n
N
p- e+ n
+
N p+ e- n
N p+ e- n
provides
an absolute
definition
of + charge
 0.3 %
CP violation
experiment
KL0 production and
measurement of the decay in
pp ,e
, e• and neutrino
p and electron
IDentification
(Cherenkov)
20 m
Target
Vacuum Helium
p
Protons
Collimators
Magnet for neutral
particle selection
N(e+) - N(e-)
d
N(e+) + N(e-)
K0S
KL0
n
e
Magnetic spectrometer
S. Bennet et al (1967):
C. Geweniger et al (1974):
(2.370.42) 10-3
(3.410.18) 10-3
+
-
+
-
K p p
0
CPLear
CP
K p p
0
Processes should be
identical but CPLear
finds that
neutral kaon
decay time distribution
K0
K0

anti-neutral kaon
decay time distribution
Other experiments: NA48, KTeV, KLOE f factory in Frascati, ...
NA48 decay channel
The Kaon decay channel of the NA48 experiment at CERN
- the latest study to provide a precision measurement of CP violation.
CPT
Schwinger-Lüders-Pauli show in the '50 that a theory with
locality,
Lorentz invariance
spins-statistics
is also CPT invariant.
Consequences:
* Consider particle y at rest. Its mass is related to:
y H 0 y  y CPT) H 0 CPT) y  anti - y H 0 anti - y
+

 particle and antiparticle have same mass (and
also same life time, charge and magnetic moment)
* If a system violates CP  T must be violated,...
K0 - K 0
T from CPLear
K0
s
d
W
oscillations
t
t
W
d
K0
s
(6.61.6)10-3
0
AT
K

(t) 
0
 K )- K  K
0
0
+
0
)(t)
pp  K 0K-p +
K 0  e +p - n
pp  K 0K +p-
K 0  e-p + n
Electric Dipole Moments
Energy shift for a particle with EDM d in a weak electric field E
is linear in E: DE = E d . d can be calculated from
d =  ri qi
which is left unchanged by T:
qaq
T: r a r
Consider a neutron at rest.
The only vector which characterize the neutron is its spin J.
If a non-zero EDM exists in the neutron: d = k J
Under time reversal T: J a -J
This implies k = 0 if T is a good symmetry:  d = 0
EDM 2
expt [e cm]
proton
neutron
electron
muon
129-Xe
199-Hg
( - 4  6 ) 10-23
< 0.63 10-25 ( 95% CL)
( 0.07  0.07 ) 10-26
( 3.7  3.4 ) 10-19
<10-27
<10-28
SM prediction
10-31
10-31
10-38
10-35
muon measurement in future "neutrino factories"  10-24
No signal of T violation "beyond the Standard Model" so far !
CP & T violation only in
K0 system ???
Since 1964, CP and or T violation was searched for in other
systems than K0, other particles decays, EDM...
No other signal until 2001...
BaBar (SLAC) and Belle (KEK)
in 2001: observation of CP violation in the B meson
system, using "asymmetric collider" B factories.
KEKB machine:
8 GeV
electrons
3.5GeV positron
 production of
(4s) (10.58GeV/c2)
b = 0.425
(4s)  B0 B0
 B+ B-
BaBar and Belle
Study of the time dependent asymmetry in decay rates of
B0 and anti-B0
N(B 0  J / KS ) - N(B0  J / KS )
ACP (t) 
(t)  S sin Dm t )
+
CP violated  S ≠ 0
Dm = mass difference of "mass eigenstates" ~ 0.49 1012 h/s
CP measurements at Belle
Difficult: B0 mean life 1.54 10-12 s
Δz  cβγΔt ~ 200 mm at Belle
B0 and anti-B0 oscillate coherently (QM untangled state).
When the first decays, the other is known to be of the opposite
flavour  use the other side to infer the flavour, B0 or anti-B0,
of the fCP parent
e +  B0
e 0
e  B
(4s)
n
J/
D
Ks
region of
 Dz
B0 & B0
coherent
evolution
z1
z2
fCP
z
Belle
Silicon Vertex Detector SVD
Impact parameter resolution
 55mm for p=1GeV/c at normal incidence
Central Drift Chamber CDC
(Pt/Pt)2 = (0.0019 Pt)2 + (0.0030)2
K/p separation :
dE/dx in CDC dE/dx =6.9%
TOF
TOF = 95ps
Aerogel Cerenkov ACC
Efficiency = ~90%,
Fake rate = ~6% 3.5GeV/c
, e : CsI crystals ECL
ACC
E/E ~ 1.8% @ E=1GeV
e : efficiency > 90%
~0.3% fake for p > 1GeV/c
KL and m : KLM (RPC)
m : efficiency > 90%
<2% fake at p > 1GeV/c
-1
Ldt

103
fb

108 B pairs
~8m
Belle micro-vertex detector
spatial resolution Blepton + X
z (lepton) ~ 100 mm
Belle event
CP is violated
in
the B0 system
CP
N(B 0  J / KS ) - N(B0  J / KS )
ACP (t) 
(t)  S sin Dm t )
+
Origin of CP violation
Hamiltonian H = H0 + HCP with HCP responsible for CP violation.
Let's take HCP = gH + g*H†
where g is some coupling.
The second term is required by hermiticity.
If under CP: H  H†
that is
CP H CP† = H†
then
CP HCP CP† = CP (gH + g*H†) CP† = gH† + g*H
CP invariance : HCP = CP HCP CP†

gH + g*H† = gH† + g*H
The conclusion is that CP is violated if g  g* i.e. g non real
CP violation is associated to the existence of phases in the
hamiltonian.
Standard Model and CP violation
The transitions
s
quark(i)  quark(j)
are described by parameters Vij ,
introduced by N. Cabibbo for i,j=u, d, s
... try to get some of the Vij to be complex !
W
Vus
u
In the '60 only u, d, s quarks were known. c was introduced in
1970 (Glashow, Iliopoulos, Maiani), discovered in 1974.
In 1972 Kobayashi & Maskawa show that, in order to generate
CP violation, V must be (at least) a 3x3 matrix 
they predict the three quark families of the SM:
(u, d), (c, s), (t, b)
The last quark, t, was observed 25 years later !
CP violation
and SM
Up type quark
spinor field
Q = 2/3
u
c
t
SM with 3 families can
accommodate CP violation
in the weak interactions
through the complex
Cabibbo-Kobayashi-Maskawa
quark mixing matrix VCKM,
with 4 parameters.
Down type quark
spinor field
Q = -1/3
I
II
III
d
s
b
but SM does
not predict these
parameters...
... and there is another (cosmic) problem...!
CP violation in
the K and B meson decays
can be "explained" by
the Standard Model.
Universe:
SM provides:
CP violation in
the Universe
(baryogenesis)
cannot
NB - NB_
NB + NB_
NB - NB_
NB + NB_
-9
 10 ~ 10
 ~ 10
-10
-20
New source for CP beyond the Standard Model?
New source(s) of CP violation ?
q
Complex coupling  CP violation
X
X: Super Symmetric Particles,
Multi-Higgs doublets,
etc.
q
complex
coupling
constant
Search for unexpected effects in CP violation,
study rare decays (<10-6)
in Bu, Bd, Bs, Bc and b-baryons...
At LHC
over-constrain the SM parameters
p
7 TeV
p
7 TeV
14 TeV
Rate(bb)  105 sec-1 !
L = 2 1032 cm-2s-1
bb=500 mb
LHCb detector
B mesons production rate ~100 times larger
than in B factories  high precision in CP
and door open to study rare decays
The
1y yield
experiment
particle
identification

vertexing
N scientists ~560
N Institutions 47
Cost ~ 76 MCHF
B0  p + p -
27k
B0  K + p -
115k
B0s  D-s p +
72k
B0s  J y f
130k
Underground experimental hall
Pillar
Pillar
POINT 8 - UX85 - Headwall
(ex DELPHI area)
March 2002
Conclusion
CP & T violation has been observed in the K and B systems.
SM parameterizes CP violation but cannot explain its origin.
The amount of CP violation in SM cannot describe baryogenesis.
High precision studies of discrete symmetries violation
needed to probe the physics beyond the Standard Model
and to understand the Big Bang.
The domain is under heavy theoretical and experimental attack:
K and B factories, EDM measurements, anti-H, neutrinos,
double beta, g-2, ...
LHC will provide a huge statistics of B's (and other particles)
to shed light on this domain of fundamental physics and cosmology,
"curiosity driven".
Bibliography
I.I. Bigi and A. I. Sanda: CP violation
Cambridge U. Press, 2000
G. C. Branco, L.Lavoura, J.P. Silva: CP violation
Oxford U. Press, 1999
T. Nakada: CP Violation, status and future prospect
XXXth ITEP Winter school of physics
www-iphe.unil.ch IPHE 2002-011