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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. Γ had Γ e.

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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



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



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 Im0 | 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




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





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

ntnm

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:

  • tm n n g

  • tm n n + random g

  • other background

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



t-  e- g

Search


t-  m- g

Search


Other Channels

DE = Ereco - s/2 Dm = mreco - mt



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 Muon pT > 14 GeV

Di-Muon pT > 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


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