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

τ

υe υµ

υτ

We µ u

d’

uu

d’ d’

Rτ = = NC Sew ( 1 + δpert(αs) + δnon-pert + δew )Γhad

Γe0.1910 -0.023 0.0010

Gluon

20% 20% 60%

Γ (τ → υτ had)

Γ (τ → υτ e υe)Rτ =

B (τ → υτ had)

B (τ → υτ e υe)=

= 1 - B (τ → υτ e υe) - B (τ → υτ µ υµ)

B (τ → υτ e υe)

1

B (τ → υτ e υe)= - 1.9726

B (τ → υτ e υe) = 0.1784 ± 0.0006

αs (mZ) = 0.121 ± 0.003

PDG 2004

One of the most precise

measurements of s

Many tests of QCD predictions

1. Definition of R

R = = ∫ ds had

e

e

dhad

ds0

m

2. Optical Theorem

dhad = (2)4 4(...) 1

2 m

GF

2L 0 |J| had had |J

†| 0 dhad d

dhad = 1

2 m

GF

2L 2 Im0 | J J

† | 0 d

s

m2

3. Lorentz decomposition

4. Extension to the Complex Plain

0 | J J† | 0 = (qq – g q2) (1)(q2) + qq

(0)(q2)

R = 6 i (1 – )2 (1 + ) (1)(q2) ds

m2∫ 2 s

m2

Rτ = = NC Sew ( 1 + δpert(αs) + δnon-pert + δew )Γhad

Γe0.1910 -0.023 0.0010

perturbative, strong correction calculated to 3rd order

theorists working on 4th order corrections

Rτ = 12 π Sew |Vud|2

mτ2

ds (1 - )2 (1 + ) smτ

22smτ

2Im Π(s)

0

mτ2

v(s) = 2π Im Π(s) a(s) = 2π Im Π(s)

Rτ = 12 π Sew |Vud|2

mτ2

ds (1 - )2 (1 + ) smτ

22smτ

2Im Π(s)

0

αs( )

s0

s0

mτ2

mτ2

s0

Okay down to ≈ 1 GeV

PDG 2004

consistent

Deviations from standard model ?

optical

theoreme

Π(s) universal function

e+e- → had τ → ντ had (g-2)μ

10-11 10-9 10-7 10-5 10-3

QED

hadr. contribution

weak contribution

new physics?

exp

a = g - 2

2

(2003: 204 ± 7)

Isospin Violation ?

τ

υτ

Wq

q’

e

q

q

e

2. quark mass phase space correction negligible

1. quark charge QED radiation theor. estimate

3. pion mass (o ≠ +) phase space correction taken into account

4. meson masses (o ≠ + ?) phase space correction should be small but .......

Discrapency unresolved

Better theoretical estimates of isospin violation

More precise and more careful measurements

e+e-: radiative return

Nowosibirsk

τ: new measurements

τcf, CLEO-c, b-factories

e+e-: direct measurement

DaΦne, CLEO-c, b-factories, Nowosibirsk

(leptons – anti-leptons)initial = (leptons – anti-leptons)final

each generation separately

- -

- -+-

+ +

- K-

B0 D- +

t b +

e+ e- + -

D- -

no violationobserved

->

violate lepton numbers

Affects the Tau ?

-

-

W-

- -

Affects the Tau ?

-

-

W-

- -

neutrinooscillation

okay

But: energy/momentum conservation violated

Affects the Tau ?

-

-

W-

- -

branching ratiostandard model: 10-40

other Models: 10-40… 10-6

Affects the Tau ?

-

-

W-

- - + - branching ratiostandard model: 10-40… 10-14

other models: 10-40… 10-7

-

+

W W

Z

=

υe

υµ

υτ

mixingmatrix

υ1

υ2

υ3

~ Ui Ui

breaks the GIM mechanism

- - inv. mass (,) = tau mass energy (,) = tau energy

Background:

randomother background

is experimentally easier, but lower branching ratio (?)

- e-

- -

E = Ereco - s/2 m = mreco - m

- - + -

at the LHC

Advantage: more tausDisadvantage: more background

tau sources:

W 1.7 108

/Z 8.0 108

Ds X 1.5 1012

B0 X 4.0 1011

B± X 3.8 1011

Bs X 7.9 1010

1 year @ low luminosity

- - + - bei CMS

Simulation with underlying event

(low luminosity)

- - + - at CMS

W

10.000 eventstriggertrack reconstruction

= -ln tan /2

Level-1 Trigger: Single Muon pT > 14 GeV Di-Muon pT > 3 GeV

b-factories: can approach 10-8 in most channels

LHC: only 1012 taus (low lumi)

efficiency 1% possible ???limits of 10-10

LHC: can we use high-lumi running ???

work has just begun !

Historical Intro: Discovery of the tau

Basic Properties- Branching Ratios

- Kinematics

- Mass

- Lifetime

Hot Topics- QCD / Isospin

- Lepton Flavour Violation