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Heraeus School Flavour Physics and CP Violation

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Heraeus School

Flavour Physics and

CP Violation

29./30. August 2005

Contents

- Historical Intro: Discovery of the tau
- Basic Properties
- Branching Ratios
- Kinematics
- Mass
- Lifetime
- Hot Topics
- QCD / Isospin
- Lepton Flavour Violation

QCD in Tau Decays

Gluon

Γhad

Γe

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

0.1910 -0.023 0.0010

Tau Decays

υτ

τ

20% 20% 60%

e

µ

u

u

u

W

υe

υµ

d’

d’

d’

B (τ→υτhad)

B(τ→υτe υe)

=

1 - B (τ→υτeυe) -B (τ→υτµυµ)

B(τ→υτe υe)

=

1

B(τ→υτe υe)

- 1.9726

=

B(τ→υτe υe) = 0.1784 ± 0.0006

αs (mZ)= 0.121 ± 0.003

Determination of the strong coupling

Γ (τ→υτhad)

Γ(τ→υτe υe)

Rτ=

PDG

PDG 2004

- One of the most precise
measurements of as

- Many tests of QCD
predictions

Outline of Theoretical Calculation

1. Definition of Rt

mt

Rt = = ∫ ds

Ghad

Ge

1

Ge

dGhad

ds

0

2. Optical Theorem

GF

2

1

2 mt

LmnS 0 |Jm| had had |Jn†| 0 dfhad dFn

dGhad = (2p)4 d4(...)

GF

2

1

2 mt

dGhad =

Lmn 2 Im0 | Jm Jn† | 0 dFn

Outline of Theoretical Calculation

3. Lorentz decomposition

0 | Jm Jn† | 0 = (qmqn – gmn q2) P(1)(q2) + qmqnP(0)(q2)

4. Extension to the Complex Plain

ds

mt2

s

mt2

2 s

mt2

∫

Rt = 6 pi(1 – )2(1 + ) P(1)(q2)

Γhad

Γe

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

0.1910 -0.023 0.0010

Result

perturbative, strong correction calculated to 3rd order

theorists working on 4th order corrections

Spectral Functions

mτ2

12 πSew |Vud|2

mτ2

s

mτ2

2s

mτ2

ImΠ(s)

Rτ =

ds (1 - )2 (1 + )

0

v(s) = 2π Im Π(s)

a(s) = 2π Im Π(s)

s0

mτ2

mτ2

s0

s0

Running Coupling

12 πSew |Vud|2

mτ2

s

mτ2

2s

mτ2

ImΠ(s)

Rτ =

ds (1 - )2 (1 + )

0

αs()

Running Coupling

Okay down to ≈ 1 GeV

Running Coupling

PDG 2004

Vector and Axial Vector

consistent

Brookhaven: g-2

Deviations from standard model ?

e+e-→ had

Spectral Functions

optical

theoreme

Π(s) universal function

τ→ ντhad

(g-2)μ

gm - 2

2

am =

Contributions to g-2

exp

QED

hadr. contribution

weak contribution

new physics?

10-11

10-9

10-7

10-5

10-3

Comparison

(2003: 204 ± 7)

Conserved Vector Current

Isospin Violation ?

Isospin Violation

υτ

- quark charge
- QED radiation
- theor. estimate

τ

q

W

2. quark mass

phase space correction

negligible

q’

3. pion mass (po≠ p+)

phase space correction

taken into account

e

q

4. meson masses (ro≠ r+ ?)

phase space correction

should be small

but .......

g

q

e

but .......

but .......

PDG

Outlook

- Discrapency unresolved
- Better theoretical estimates of isospin violation
- More precise and more careful measurements

e+e-: radiative return

DaΦne, CLEO-c, b-factories, Nowosibirsk

e+e-: direct measurement

Nowosibirsk

τ: new measurements

τcf, CLEO-c, b-factories

Lepton

Flavour

Violation

t- m- nm nt

t+ m+ nm nt

t- p- p+ p- nt

D- t- nt

t- K- nt

Lepton Number Conservation

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

each generation separately

B0 D-t+ nt

e+e-t+ t-

t bt+ nt

no violation

observed

Neutrino

Oscillations

p -> m nm

violate lepton numbers

nm nt

t- m-

Lepton Number

Affects the Tau ?

nt

t-

nm

W-

m-

neutrino

oscillation

ntnm

t- m-

Lepton Number

Affects the Tau ?

nt

t-

nm

W-

m-

okay

But: energy/momentum conservation violated

t- m- g

Lepton Number

Affects the Tau ?

nt

t-

nm

g

W-

m-

branching ratio

standard model: 10-40

other Models: 10-40… 10-6

Lepton Number

Affects the Tau ?

nt

m+

t-

nm

m-

W-

m-

t- m- m+m-

branching ratio

standard model: 10-40… 10-14

other models: 10-40… 10-7

υ1

υ2

υ3

υe

υµ

υτ

mixing

matrix

=

GIM Mechanism

n

m

~ SUti Uim

t

W

W

m

Z

m

New Physics

breaks the GIM mechanism

Experimental Searches

t- m- g

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

Background:

- tm n n g
- tm n n + random g
- other background

tm m m is experimentally easier, but lower branching ratio (?)

Experimental Searches

t- e- g

Search

t- m- g

Search

Other Channels

DE = Ereco - s/2 Dm = mreco - mt

Current Status

t- m- m+m-

Search:

at the LHC

tau sources:

Advantage: more taus

Disadvantage: more background

1 year @ low luminosity

t- m- m+m- bei CMS

Simulation with underlying event

(low luminosity)

t- m- m+m- at CMS

W t nt

10.000 events

trigger

track reconstruction

Kinematics @ LHC

h = -ln tan q/2

Kinematics @ LHC

Level-1 Trigger:

Single MuonpT > 14 GeV

Di-MuonpT > 3 GeV

Outlook

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

LHC:only t m m m

> 1012 taus (low lumi)

efficiency 1% possible ???

limits of 10-10

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

work has just begun !

Summary

- Historical Intro: Discovery of the tau
- Basic Properties
- Branching Ratios
- Kinematics
- Mass
- Lifetime
- Hot Topics
- QCD / Isospin
- Lepton Flavour Violation