summary

A. Bay Beijing October 2005 1

Summary

1. Some history2. Antiparticles3. Standard Model of Particles (SM) Discrete symmetries, CP violation, Connection with Cosmology Fermionic mass generation mechanism, Why do we think that the SM is not the final word ?


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 ×SU(2)L×U(1)YQCD ElecroweakTheory

123

do not forgetantiparticles... !

Spin 1/2 Spin 1


Discrete symmetries

Parity: left

Charge particle antiparticleconjugation

Temporal inversionright


symmetry violation

... suddenly we discover that we can observe a "non - observable".

A is discovered.

Some symmetries might have a deep reason to exist ... other not.

The Right-Left symmetry (Parity) was considered an

exact symmetry 1956


Discrete symmetries P and C

e.m. interactionsare P & C invariant

€

VCoulomb(r r ) ~ qQ

r 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.


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 −tT :

r p a −

r p

T :r J a −

r J

Ok with electrodynamics:


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


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.


100% P violation in DNA


Too much symmetry...

LL RRLR


Partial R-L symmetry in Rome

QuickTime™ et un décompresseurCinepak sont requis pour visualisercette image.

MUSEE ROMAIN DE NYON

? Bacchus, Arianna ?


Some asymmetry introduces more dynamics


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.


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.

* HEP conf. Rochester 1956 Tsung Dao Lee and Chen Ning Yangsuggest 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 violatedin weak interactions.


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)


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


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)


Parity P and neutrino helicity

right

left

P

P symmetry violated at (NLNR)/(NLNR) = 100%


Charge conjugation C

left

C

left

C symmetry violated at 100%

C transforms particles antiparticle


CPLast chance: combine C and P !

gauche ν droit_

P C

left right

Is our UniverseCP symmetric ?


(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


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


QuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

sensitivity (0.5 - 20 GeV):

He/He ~10

C/C ~10

AMS


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

rmatter =0.1rC =1 10-6 GeV/cm3 10-6 p/cm3

Nprotons

Nphotons 2511 51


Baryogenesis .3

N2 122 ( ) = 412 photons/cm 33kT

ch22

This suggests a Big Bang annihilation phasein which matter + antimatter was transformedinto photons...

Sky T observed by COBE~ 2.7K


Baryogenesis.4

N(q)N(q)

≈3×111

3×11

Toγehecorrecbaryo/hooraio,weeedaasyeryofheorder:

aihilaioγiveshoos

Hydroγelushoos

quarksaiquarkseee−

ie

Sceario:AaceraioiofhehisoryofheBiγBaγ,weeedhefollowiγcodiios:N(quarks)>N(aiquarks)adN(e)>N(e)


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


Baryogenesis .6

Prob(Xqq) = b Prob(Xqe-) = (1b)---Prob(Xqq) = a Prob(Xqe+) = (1a)-

Requirement: a>b

q q ouq e+

q q ouq e

X

X

1027°K

... forbidden by CP symmetry !

a=b

{

Xqq

--- XqqCP

CPmirror


CP violation

K0L

e

e MIRROR CP{

CP symmetry implies identical rates. Instead...K0

L 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


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


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 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.


CPTSchwinger-Lüders-Pauli show in the '50 that a theory with

locality,Lorentz invariancespins-statistics

is also CPT invariant.

Consequences:

* Consider particle y at rest. Its mass is related to:

€

yH0 ψ = ψ CPT( )+H0 CPT( ) ψ = anti − ψ H0 anti − ψ

particle and antiparticle have same mass (andalso same life time, charge and magnetic moment)

* If a system violates CP T must be violated,...


0

T from CPLear

€

AT (t) =K 0 → K0( ) − K0 → K 0( )

+(t)

(6.61.6)103

€

pp → K0K−π + K0 → e+π−ν

pp → K 0K+π− K 0 → e−π +ν

€

K0

−K 0 oscillations

s

d

K0 K0

s

dt

t

W W


Electric Dipole Moments

Energy shift for a particle with EDM d in a weak electric field Eis linear in E: DE = E d . d can be calculated from

d = ri qi

which is left unchanged by T: q a q 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 JUnder time reversal T: J a JThis implies k = 0 if T is a good symmetry: d = 0


E D M 2

expt [e cm] SM prediction

proton ( 4 6 ) 1023 1031 neutron < 0.63 1025 ( 95% CL) 1031electron ( 0.07 0.07 ) 1026 103muon ( 3.7 3.4 ) 1011035129-Xe <1027

199-Hg <1028

muon measurement in future "neutrino factories" 102

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 othersystems than K0, other particles decays, EDM...

No other signal until 2001. In 2001 Babar at SLAC and Belleat KEK observe a large CP vioaltion in the B0-B0bar system


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 realCP violation is associated to the existence of phases in thehamiltonian.


IIIII

I

CP violation and SM SM with 3 families canaccommodate CP violation

in the weak interactionsthrough the complex

Cabibbo-Kobayashi-Maskawa quark mixing matrix VCKM,

with 4 parameters.

uct

dsb

Up type quarkspinor field

Q = 2/3

Down type quarkspinor field

Q = 1/3 SM doesnot predict theseparameters...


In the '60 ...

Parameters Vij are used to calculate the transitions quark(i) quark(j)first introduced by N. Cabibbo for i,j=u, d, s

VCabibbo is real, while CPV implies that some of the Vij complex !

s

uW

Vus

€

Vud Vus

Vcd Vcs

⎛ ⎝ ⎜

⎞ ⎠ ⎟=

cosθ sinθ−sinθ cosθ ⎛ ⎝ ⎜

⎞ ⎠ ⎟≈

0.97 0.220.22 0.97 ⎛ ⎝ ⎜

⎞ ⎠ ⎟VCabibbo=

The quark c was introduced in 1970 (GIM), discovered in 1974.

qcabibbo ~ 12°

In the 1970 the "flavour mixing" matrix was


CKM matrix

CPV 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),V must 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 !


CKM matrix in the SM

L = L W,Z + L H + L Fermions + L interaction

L Fermions contains the (Yukawa) mass terms:

€

Hvev

u 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

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟


CKM matrix .2

€

uR

cR

tR

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟→ AR

−1

uR

cR

t R

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

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


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(l4)

l= sin(qCabibbo) =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)


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

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

s(Vij)/Vij ~

Today precision from direct measurements, no unitarity imposed:


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(l4)

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)


€

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

CKM Matrix and the Unitary Triangle(s)

SM Unitarity Vji*Vjk=dik VudVub + VcdVcb

+ VtdVtb = 0

V udV ub

Vtd V

tb *

VcdVcb*

*

b(f1)

a(f2)

γ(f3)

The UnitaryThe Unitary TriangleTriangle

Re

Im


b(f1)

a(f2)

γ(f3)

Re

Imh

1r

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(l4)

SM Unitarity Vji*Vjk=dik VudVub + VcdVcb

+ VtdVtb = 0

The UnitaryThe Unitary TriangleTriangle

afternormalization byVcdVcb*=Al3

€

arg(Vtd ) = −β

€

arg(Vub) = −γ


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

b

a

γ

~Vub ~Vtd

~Vcb

€

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

⎛

⎝

⎜ ⎜ ⎜

⎞

⎠

⎟ ⎟ ⎟

Use B mesonsphenomenology

t quark

oscillations

CP asymmetries

b quark

decays


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


CosmicsCosmics


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.


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) 66Lepton-quark mass relations first (?) discussed by

€

u c td s b ⎛ ⎝ ⎜

⎞ ⎠ ⎟e μ τν ν ν ⎛ ⎝ ⎜

⎞ ⎠ ⎟€

SU(3)C ⊗ SU(2)L ⊗U(1)Y ⊗ SU(x)H

V

H

(CKM)(NMS)

?


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


SUSY

particle superparticle

The Minimal Supersymmetric extension of the SM (MSSM) with gauge coupling unification at EGUT = 1016 GeV predictsthe EW mixing parameter:sin2qW= 0.2336 ± 0.0017to be compared withthe experiemental valuesin2qW= 0.23120±0.00015.

The model predictsthe existence ofnew particles.


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.


Introducing the B mesons family & processes


€

B 0 = bd B− = bu B s

0 = bs Bc− = bc + antiparticles

M (B) ≈ M (B0) ≈ ≈ 5279 MeV/c2

lifetime ≈ 1.5 1012 s

mixing/oscillation

b s,d

qq

u,c,t

WQuickTime™ and aTIFF (Uncompressed) decompressorare needed to see this picture.

qq

B0 B0

d

b

u,c,tW W

b

d


€

l

W

b u,c

direct decay

loop decay

B factories

u,c,t


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

dNew

FCNC

VtsVtb*

B0bd

s

s

d K0

fs

W

t

??????b

d

s

sd K0

fs

c

squark+?

+?

( The MSSM has 43 additional CP violating phases ! )

summary

Documents

bay beijing

photon of parity

parity violationlemmon

parity doublets

parity conserving

rightleft symmetry parity

symmetry violation

p conservation