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A. Bay Beijng October 2005 1
Summary
1. Some history2. Antiparticles3. Standard Model of Particles (SM) Discrete symmetries, CP violation, Connection with Cosmology Fermionic mass generation mechanism,4. Why do we think that the SM is not the final word ?5. How do we produce particles?6. How do we measure particles ?7. Conclusions
A. Bay Beijng October 2005 2
The Standard
Model
e
e
u c t
d s bQuarks
Strong : gluons
E.M. : photon
Weak : W+ W Z
INTERACTIONSMATTERe.m. charge [e]
0
1
2/3
1/3
The SM incorporates:QED: photon exchange between charged particlesWeak (Flavour-Dynamics): exchange of W and Z QCD: gluon exchange between quarks
123SM is based on the gauge group: SU(3)c × (2)SU L× (1)U YQCD - Electro weak Theory
123
do not forgetantiparticles... !
Spin 1/2 Spin 1
A. Bay Beijng October 2005 3
Summary of this section
SymmetriesParity (P),Charge Conjugation (C) and Time reversal (T)
P and C violationBaryogenesisCP & T violationExperimentsConclusion
A. Bay Beijng October 2005 4
Discrete symmetries
Parity: left
Charge particle antiparticleconjugation
Temporal inversion
right
A. Bay Beijng October 2005 5
Discrete symmetries P and C
e.m. interactionsare P & C invariant
€
VCoulomb(r r ) ~
qQr r
P : VCoulomb(r r ) a VCoulomb(−
r r ) = VCoulomb(
r r )
C : VCoulomb(r r ) a VCoulomb(
r r )
P: (x,y,z) -> (-x,-y,-z).
C: charge -> charge.
€
C :r x a
r x
C : e a −e
C :r A ,V a −
r A ,−V
€
P :r x a −
r x
P :r p a −
r p
P :r J a
r J
angularmomentum,spin.
A. Bay Beijng October 2005 6
What about T ?
If x(t) is solution of F = m d2x/dt2 then x(-t) is also a solution (ex.: billiard balls)
€
T :r E a
r E T :
r B a −
r B
r F = q(
r E +
r v ×
r B ) ⇒ T :
r F a
r F
€
T :r x a
r x
T : t a −t
T :r p a −
r p
T :r J a −
r J
Ok with electrodynamics:
A. Bay Beijng October 2005 7
Parity: (x,y,z) (-x,-y,-z)
1848 L. Pasteur discovers the property of optical isomerism.
H3C COOH
H
OHH3C
H
COOH
OH
M
The synthesis of the lactic acid in the lab gives a "racemic" mixture: Nleft molecules = Nright molecules (within statistic fluctuations)
This reflects the fact that e.m. interaction is M (and P) invariant
Mirror symmetry
Asymmetry =
€
N right − N left
N right + N left
= 0
A. Bay Beijng October 2005 8
Parity violation in biology
Humans are mostly right handed:
Asymmetry A = (NRNL)/(NR+NL) ≈ 0.9
“90% Parity violation"
snif snif
Lemmon and orange flavoursare produced by thetwo "enantiomers" of the same molecule.
A. Bay Beijng October 2005 9
100% P violation in DNA
A. Bay Beijng October 2005 10
Too much symmetry...
LL RR
LR
A. Bay Beijng October 2005 11
Partial R-L symmetry in Rome
QuickTime™ et un décompresseurCinepak sont requis pour visualiser
cette image.
MUSEE ROMAIN DE NYON
? Bacchus, Arianna ?
A. Bay Beijng October 2005 12
Some asymmetry introduces more dynamics
A. Bay Beijng October 2005 13
P conserved in e.m. and strong interacctions
1924 O. Laporte classified the wavefunctions of an atom aseither 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 overallsymmetry 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.
A. Bay Beijng October 2005 14
Parity in weak interactions
* E. 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 pionswhich indicates P(tau) = 1 and P(theta) =1If Parity holds "tau" and "theta" cannot be the same particle.
A. Bay Beijng October 2005 15
Parity in weak interactions .2
Lee and Yang make a careful study of all known experimentsinvolving weak interactions. They conclude
"Past experiments on the weak interactions hadactually no bearing on the question of parity conservation"
Question of Parity Conservation in Weak InteractionsT. D. Lee Columbia University, New York, New YorkC. N. Yang Brookhaven National Laboratory, Upton, New YorkThe question of parity conservation in beta decays and in hyperon and mesondecays is examined. Possible experiments are suggested which might testparity conservation in these interactions. Phys. Rev. 104, 254–258 (1956)
A. Bay Beijng October 2005 16
Co 60
1956 C. S. Wu et al. execute one of the experiments proposed by Lee and Yang.
Observables:a "vector" : momentum p of beta particlesan "axial-vector" : spin J of nucleus (from B).Compute m = <Jp>
In a P reversed Word: P: Jp a JpP symmetry implies m = 0
Co60 at 0.01 K in a B field.
m was found 0 P is violated
Co
J p
p
J
Co
A. Bay Beijng October 2005 17
152 Sm
Eu + e−Z=63A=152 Sγ62
152
Polarimeter: selects γ of defined helicity
152Sm γNaI
Counter
Result: neutrinos are only left-handed
Measurement of neutrino helicity
(Goldhaber et al. 1958)
A. Bay Beijng October 2005 18
Parity P and neutrino helicity
right
left
P
P symmetry violated at (NLNR)/(NLNR) = 100%
A. Bay Beijng October 2005 19
Charge conjugation C
left
C
left
C symmetry violated at 100%
C transforms particles antiparticle
A. Bay Beijng October 2005 20
CPLast chance: combine C and P !
gauche ν droit_
P C
left right
Is our UniverseCP symmetric ?
A. Bay Beijng October 2005 21
(A)symmetry in the Universe
matter
antimatter
Big Bang produced anequal amount of matter and antimatter
Today: we livein a matter dominatedUniverse
time
Big Bang
A. Bay Beijng October 2005 22
Baryo genesis
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 planets. 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
A. Bay Beijng October 2005 23
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
sensitivity (0.5 - 20 GeV):
He/He ~10
C/C ~10
AMS
A. Bay Beijng October 2005 24
Baryogenesis .2 Today (age of Univers 10-20 109 years):
no significant amount of antimatter has been observed.
The visible Universe is maid of
protons, electrons and photonsThe N of photons is very large compared to p and e
matter =0.1C =1 10-6 GeV/cm3 10-6 p/cm3
Nprotons
Nphotons 2511 51
A. Bay Beijng October 2005 25
Baryogenesis .3
N2 122 ( ) = 412 photons/cm 33
kTch
22
This suggests a Big Bang annihilation phasein which matter + antimatter was transformedinto photons...
Sky Temperature observed by COBE~ 2.7K
A. Bay Beijng October 2005 26
Baryogenesis.4
N(q)
N(q)≈
3×11+1
3×11
/ , To get the correct baryon photon ratio we need an :asymmetry of the order
annihilationgives photons
Hydrogenplus photons
quarksantiquarkse+ et e−
time
:Scenario ,At a certain point of the history of the Big Bang :we need the following conditions
( )> ( )N quarks N antiquarksand (N e-)> (N e+)
A. Bay Beijng October 2005 27
Baryogenesis
.5
1) processes which violate baryonic number conservation:
B violation is unavoidable in GUT.
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
Universe expands (but was the change fast enough ?)
Starting from a perfectly symmetric Universe: 3 rules to induce asymmetryduring evolution
Andrej Sakarov 1967
B(t=0) = 0 B(today)>0
A. Bay Beijng October 2005 28
Baryogenesis .6
Prob(Xqq) = Prob(Xqe-) = (1---Prob(Xqq) = Prob(Xqe+) = (1-
Requirement:
q q ouq e+
q q ouq e
X
X
10 27K
... forbidden by CP symmetry !
=
{
Xqq
--- XqqCP
CPmirror
A. Bay Beijng October 2005 29
CP violation
K0L
e
e MIRROR CP{
CP symmetry implies identical rates. Instead...
K0L is its own antiparticle
K0L
S. Bennet, D. Nygren, H. Saal, J. Steinberg, J. Sunderland (1967):
July 1964: J. H. Christenson, J. W. Cronin, V. L. Fitch et R. Turlay
find a small CP violation with K0 mesons !!!
e Ne N e Ne N + 3%
providesan absolutedefinition
of + charge
A. Bay Beijng October 2005 30
CP violation experiment
K0SCollimators
≈2
Protons
Target
Magnet for neutralparticle selection
Helium
K0L
Magnetic spectrometer
ν
Vacuum
π and electronIDentification
π
e
production and measurement of the decay in
π± , e• and neutrino
K0L
N(e+) − N(e−)
N(e+) + N(e−)δ= S. Bennet et al (1967): (2.37±0.42) 10−3
C. Geweniger et al (1974): (3.41±0.18) 10−3
(Cherenkov)
€
±,em
A. Bay Beijng October 2005 31
K0
K0
€
K0 → π +π−
CP b
K 0 → π +π−
Processes should beidentical but CPLearfinds that
neutral kaondecay time distribution
anti-neutral kaon
decay time distribution
CPLear
Other experiments: NA48, KTeV, KLOE factory in Frascati, ...
A. Bay Beijng October 2005 32
CPV in BABAR and BELLE
World average (October 2005): SCP = 0.726 ± 0.037
ACP~ 0, compatible with no direct CPV
SM: SCP = sin(2) => =23or 66.3°)
€
AsymCP (t) =N (B
0→ J / Ψ KS ) − N (B
0→ J / Ψ KS )
+(t)∝ ACP cos Δmd t( ) + SCP sin Δmd t( )
A. Bay Beijng October 2005 33
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 thehamiltonian.
A. Bay Beijng October 2005 34
CKM matrixCPV implies that some of the Vij complex.
In 1972 Kobayashi & Maskawa show that,in order to generate CP violation (i.e. to get a complex phase),the matrix describing the weak decays of the quarksmust be (at least) 3x3 this is a prediction of the three quark families of the SM: (u, d), (c, s), (t, b)
€
VCKMVCKM† =
1 0 00 1 00 0 1
⎛
⎝ ⎜
⎞
⎠ ⎟
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
VCKM=In the SM, with 3 and only 3 families of quarks, the matrix must be unitary
The last quark, t, was observed 25 years later !
Cabibbo
s
uW
Vus
A. Bay Beijng October 2005 35
CKM matrix in the SM
L = L W,Z + L H + L Fermions + L interaction
L Fermions contains the (Yukawa) mass terms:
€
H
vevu L c L t L( )MU
uR
cR
tR
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
+ d L s L b L( )MD
dR
sR
bR
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
⎡
⎣
⎢ ⎢ ⎢
⎤
⎦
⎥ ⎥ ⎥
MU and MD complex matrices, diagonalized by a couple ofnon-singular matrices, to get the physical mass values:
€
ALMUAR−1 =
mu
mc
mt
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
€
BLMDBR−1 =
md
ms
mb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
A. Bay Beijng October 2005 36
CKM matrix .2
€
uR
cR
tR
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟→ AR
−1
uR
cR
tR
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
uL
cL
tL
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟→ AL
−1
uL
cL
tL
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
After the transformation
(idem for D quarks)
e.m. and neutral currents unaffected. The charged currents are modified:
€
Jμch arg ed ∝ d L s L b L( )γμBLA R
−1
uL
cL
tL
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟= d L s L b L( )γμ V
uL
cL
tL
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
"mixing matrix" V unitary
s
uW
Vus
A. Bay Beijng October 2005 37
CKM matrix .3
down strange beauty up 0.97 0.22 0.002charm 0.22 0.97 0.03 top 0.004 0.03 1
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟≈
1− λ2 /2 λ Aλ3 ρ − iη( )
−λ 1− λ2 /2 Aλ2
Aλ3 1− ρ − iη( ) −Aλ2 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟+ O(4)
= sin(Cabibbo) =0.224A=0.83±0.02
phase: changesign under CP
parametrized by 4 real numbers (not predicted by the SM).Need to measure them.
Magnitude ~
Wolfestein (1983)
A. Bay Beijng October 2005 38
CKM matrix .4
down strange beauty up 0.1% 1% 17%charm 7% 15% 5% top 20% ?% 29%
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
Vij)/Vij ~
Today precision from direct measurements, no unitarity imposed:
A. Bay Beijng October 2005 39
CKM matrix .5
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟≈
1− λ2 /2 λ Aλ3 ρ − iη( )
−λ 1− λ2 /2 Aλ2
Aλ3 1− ρ − iη( ) −Aλ2 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
+ O(4)
down strange beauty up 0 0 115°charm 0 0 0 top 25° 0 0
Phase ~ down strange beauty
up 0 0 115°charm 0 0 0 top 25° 0 0
Wolfestein (1983)
A. Bay Beijng October 2005 40
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
CKM Matrix and the Unitary Triangle(s)
SM Unitarity Vji*Vjk=ik VudVub + VcdVcb
+ VtdVtb = 0
V udV ub
Vtd V
tb*
VcdVcb*
*
1
2
γ3
The UnitaryThe Unitary TriangleTriangle
Re
Im
A. Bay Beijng October 2005 41
1
2
γ3
Re
Im
1
CKM Matrix and the Unitary Triangle(s) .2
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟≈
1− λ2 /2 λ Aλ3 ρ − iη( )
−λ 1− λ2 /2 Aλ2
Aλ3 1− ρ − iη( ) −Aλ2 1
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
+ O(4)
SM Unitarity Vji*Vjk=ik VudVub + VcdVcb
+ VtdVtb = 0
The UnitaryThe Unitary TriangleTriangle
afternormalization byVcdVcb*=A3
€
arg(Vtd ) = −β
€
arg(Vub) = −γ
A. Bay Beijng October 2005 42
Experimental program: measure sides and angles
* CP violated in the SM => the area of triangle 0* Any inconsistency could be a signal of the existence of phenomena not included in the SM
γ
~Vub ~Vtd
~Vcb
€
Vud Vus Vub
Vcd Vcs Vcb
Vtd Vts Vtb
⎛
⎝
⎜ ⎜ ⎜
⎞
⎠
⎟ ⎟ ⎟
Use B mesonsphenomenology
t quark
oscillations
CP asymmetries
b quark
decays
A. Bay Beijng October 2005 43
Why do we expect some NEW PHYSICS ?* SM has 18 free parameters (more with massive neutrini),in particular masses and CKM parameters are free.* Some of the neutrinos have masses>0.* Why the electric charge is quantized ?* The choice of SU(2)U(1) is arbitrary.* Gravitation is absent.
* Problems in Cosmology: What is the nature of dark matter and dark energy ? Baryogenesis does not work in the SM:
The SM amount of CP violation is too lowThe requirement of non-equilibrium cannot be obtainedwith heavy Higgs => new light scalar must exist
A. Bay Beijng October 2005 44
Cosmics
A. Bay Beijng October 2005 45
masses & mixings
In the SM, CPV is related to the mass generation mechanismfor the fermions. The fermionic system is far from being understood.
Is there any "periodicity" in the mass spectrum?
Similar question for the mixing matrices.
A. Bay Beijng October 2005 46
Any horizontal symmetry ?
CPV, mix., baryogenesis: hep-ph/0108216v2 * Neutrino mix and CPV in B: hep-ph/0205111v2Bs-Bs mixing in SO(10) SUSY GUT linked to mix. hep-ph/0312145
A. Buras, J. Ellis, M.K. Gaillard and D.V. Nanopoulos, Nucl. Phys. B135 (1978) 66
Lepton-quark mass relations first (?) discussed by
€
u c t
d s b
⎛
⎝ ⎜
⎞
⎠ ⎟e μ τ
ν ν ν
⎛
⎝ ⎜
⎞
⎠ ⎟
€
SU(3)C ⊗ SU(2)L ⊗U(1)Y ⊗ SU(x)H
V
H
(CKM)(NMS)
?
A. Bay Beijng October 2005 47
Models beyond the SMSM is believed to be a low-energy effective theory of a more fundamental theory at a higher energy scale (compare situation of classical mechanics and relativistic). Grand Unified Theory (GUT) theories have beensuggested to cope with (some of) the SM problems. Theypredicts that the coupling constants meet at EGUT~1015-16 GeV
EW SSB: SU(2)LU(1)YU(1)em
gGUT
you arehere
A. Bay Beijng October 2005 48
SUSY
particle superparticle
The Minimal Supersymmetric extension of the SM (MSSM) with gauge coupling unification at EGUT = 1016 GeV predictsthe EW mixing parameter:sin2W= 0.2336 ± 0.0017to be compared withthe experiemental valuesin2W= 0.23120±0.00015.
The model predictsthe existence ofnew particles.
A. Bay Beijng October 2005 49
How to detect New Physics ?
Direct searches:search for new particles, for instance the supersymmetricpartners of particles.
New phenomenologies, indirect effects:ex.1: proton decay
ex.2: EDM measurement ex.3: Hadronic flavour physics very powerful (think to KM prediction of 3 quark families). It can in principle probe veryhigh energies (think to the Z was "seen" in low energy experiments, as an interference effect).Problem: very often complex underlying theory, with large errors.
A. Bay Beijng October 2005 50
Introducing the B mesons family & processes
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
€
B 0 = bd B− = bu
B s0 = bs Bc
− = bc + antiparticles
M (B) ≈ M (B0) ≈ ≈ 5279 MeV/c2
lifetime ≈ 1.5 1012 s
mixing/oscillation
b s,d
u,c,t
WQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
B0 B0
d
b
u,c,t
W W
b
d
QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.
€
l
W
b u,c
direct decay
loop decay
B factories
u,c,t
A. Bay Beijng October 2005 51
Where New Physics can show up ?
...may modify rates and inject new phases in the processes.For instance:
d
b
W W
b
d
d
b
b
d
NewFCNC
VtsV
tb*
B0b
d
s
s
d K0
s
W
t
??????
b
d
s
s
d K0
s
squark+?
+?
( The MSSM has 43 additional CP violating phases ! )