Heraeus SchoolFlavour Physics and

CP Violation

29./30. August 2005

Historical Intro: Discovery of the tau

Basic Properties- Branching Ratios

- Kinematics

- Mass

- Lifetime

Hot Topics- QCD / Isospin

- Lepton Flavour Violation

1937: Consistent Picture

µ

e

Discovery 1937

Cloud chamber

Who orderedthat ?

Isidor Rabi

The missing c-Quark:

W u dW u sZ d s

Z d dZ u uZ s s

predicted from symmetry

predicted from GIM mechanism

GIM mechanism needs the c-Quark

for ex.: K0L µ+µ-

K0L

µ-

µ+

s

d

Burt RichterSLAC

Sam TingBNL

November 1974Autumn 1974

mass

/ e

nerg

y

charmonium:cc-atom

D0D0 / D+D- productionopen charm threshold

Burt RichterSLAC

Sam TingBNL

Ψ

J

ΨJ

StanfordPositronElectronAcceleratorRing

e+ e-

3 … 7 GeVcenter-of-mass energy

November 1974

StanfordPositronElectronAcceleratorRing

e+ e-

3 … 7 GeVcenter-of-mass energy

November 1974

Martin Perl

lepton number

+ +

- e- e

Z0 + -

Z0 e+ - LEP

e+ e- e+ -

missing energy

Hypothesis:

e+ e- + -

- -

+ e+ e

But !

Who orderedthat ?

greek

the third

kinematically forbidden

2-body-decaymono-energetic µ

3-body-decaycontinious spectrum

Discovery or the tau-neutrino ?

+ e+ e e

+ + µ e

para-lepton

+ e+ e e

+ + µ e

ortho-lepton

+ e+ e

+ + µ

sequential lepton

Ve 2

Vµ 1=

17,84 %

17,36 %

+ e+ e+ e-

okay

+ ≡ e+

+ ≡ e-

its owngeneration

DONUTJuly 2000

υτ - Strahl

τ

υτ

W

f

f’τ → υτ e υe

τ → υτ µ υµ

τ → υτ ud us ub

x 3 colours

20 %

20 %

60 %

approx. 100 known decays

hadronic tau decay

1. phase space suppression

dΓ~ (1 - Q2/mτ2)2 (1 + 2 Q2/mτ

2)J

2. Cabibbo suppression

ud ~ |Vud|2 ≈ 0.9483

us ~ |Vus|2 ≈ 0.0484

5. helicity suppression

~ (mu + md) / mτ

4. isospin suppression

separate JP = 0- and 0+

0- ~ (mu + md) / mτ

0+ ~ (mu - md) / mτ

5. exotic states

Not all JPG can be created from qq

JPG helicity isospin 2nd cl. exotic

0++ x x x

0+- x x x a0 ---

0-+ x x x

0-- x π 11.08 %

1++ x b1 ---

1+- a1 18.38 %

1-+ ρ 25.02 %

1-- x x

τ

υe υµ

υτ

We µ

Corrections: + e+ e

+ + µ

daughter mass 0.00 % -2.74 %

QED rad. -0.43 % -0.43 %

W-propogator +0.03 % +0.03 %

bre = 17.824 ± 0.052 %

brµ = 17.331 ± 0.048 %

0.9999 ± 0.0020

τ decay - µ decay

0.9982 ± 0.0021

e+e- storage rings

e

e

τ

τ

hadron decays: i.e. Ds → τ υτ

boson decays: W → τ υτ

Exotics: z.B. H → τ τ, τ� → χ0 τ

back-back kinematics

+ had+

2-body-decay

had

boost

Ehad* = (mτ2 + mhad

2) / 2 mτEhad, mhad

m and m

decay angle or tau direction

tau energy

beam spot

had

2 mτ

σ = 4 πα2/ 3E2 β ( (3-β2)/2 )

Corrections: final state radiation vacuum polarization initial state radiation Coulomb correction beam energy spread

1776.96+0.31 MeV-0.27

ee

Spin determines thershold behavious

DELCO

ARGUS: ee at 10.58 GeV

τ- → - + - υτ

Ehad, mhad measured

m and m m = 0, m ?

decay angle or tau direction not measured

tau energy known from Ebeam

m = 1776.3 ± 2.8 MeV

CPT symmetry: Static properties of particle and anti-particle must be identical m(+) = m(-)

measure + and - separately:

( m(+) - m(-) ) / m() = 0.0 ± 1.8 10-3

a typical eventat OPAL / LEP

e+ e- Z0 + -

+ +

- - - +

decay lengthl = c sin

SLC / SLD

Ecm = 91 GeV

e+e- → τ+τ-

τ- → - + - υτ

to scale at

SLC / LEP / CESR

3-prong

Eτ = Ecm / 2

βγ cτ = 2.3 mm

τ = 290.6 fsec

289.40 ± 0.91 ± 0.90 fsec

CPT:

secondaryvertex

primaryvertex

d0

xy

track

l = c sin sin xy

for 1 – prong decays

secondaryvertexprimary

vertexd0

xy

track +

secondaryvertex

d0

xy

track -

Impact Parameter Sum: d0+ + d0

-

independent of the primary vertex

secondaryvertexprimary

vertexd0

xy

track +

secondaryvertex

d0

xy

track -

Impact Parameter Sum: d0+ + d0

-

independent of the primary vertex

τ = 290.6 ± 1.0 10-15 sec

cτ = 87.11 µm

l = 2.2 mm @ LEP

l = 240 m @ sym. b-factory

pointlike particle

spin ½

mass 1777 MeV

lifetime: 290.6 fsec

charge e

g-2 ≈ 10-3

el. dipole moment: 0

approx. 100 known decays