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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

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Heraeus school flavour physics and cp violation

Heraeus School

Flavour Physics and

CP Violation

29./30. August 2005


Heraeus school flavour physics and cp violation

Contents

  • Historical Intro: Discovery of the tau

  • Basic Properties

  • Branching Ratios

  • Kinematics

  • Mass

  • Lifetime

  • Hot Topics

  • QCD / Isospin

  • Lepton Flavour Violation


Heraeus school flavour physics and cp violation

QCD in Tau Decays


Heraeus school flavour physics and cp 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’


Heraeus school flavour physics and cp violation

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=


Heraeus school flavour physics and cp violation

PDG

PDG 2004


Heraeus school flavour physics and cp violation

  • One of the most precise

    measurements of as

  • Many tests of QCD

    predictions


Heraeus school flavour physics and cp violation

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


Heraeus school flavour physics and cp violation

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)


Heraeus school flavour physics and cp violation

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


Heraeus school flavour physics and cp violation

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)


Heraeus school flavour physics and cp violation

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()


Heraeus school flavour physics and cp violation

Running Coupling

Okay down to ≈ 1 GeV


Heraeus school flavour physics and cp violation

Running Coupling

PDG 2004


Heraeus school flavour physics and cp violation

Vector and Axial Vector

consistent


Heraeus school flavour physics and cp violation

Brookhaven: g-2

Deviations from standard model ?


Heraeus school flavour physics and cp violation

e+e-→ had

Spectral Functions

optical

theoreme

Π(s) universal function

τ→ ντhad

(g-2)μ


Heraeus school flavour physics and cp violation

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


Heraeus school flavour physics and cp violation

Comparison

(2003: 204 ± 7)


Heraeus school flavour physics and cp violation

Conserved Vector Current

Isospin Violation ?


Heraeus school flavour physics and cp 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


Heraeus school flavour physics and cp violation

but .......


Heraeus school flavour physics and cp violation

but .......


Heraeus school flavour physics and cp violation

PDG


Heraeus school flavour physics and cp violation

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


Heraeus school flavour physics and cp violation

Lepton

Flavour

Violation


Heraeus school flavour physics and cp 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


Heraeus school flavour physics and cp violation

Neutrino

Oscillations

p -> m nm

violate lepton numbers

nm nt


Heraeus school flavour physics and cp violation

t-  m-

Lepton Number

Affects the Tau ?

nt

t-

nm

W-

m-


Heraeus school flavour physics and cp violation

neutrino

oscillation

ntnm

t-  m-

Lepton Number

Affects the Tau ?

nt

t-

nm

W-

m-

okay

But: energy/momentum conservation violated


Heraeus school flavour physics and cp violation

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


Heraeus school flavour physics and cp violation

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


Heraeus school flavour physics and cp violation

υ1

υ2

υ3

υe

υµ

υτ

mixing

matrix

=

GIM Mechanism

n

m

~ SUti Uim

t

W

W

m

Z

m


Heraeus school flavour physics and cp violation

New Physics

breaks the GIM mechanism


Heraeus school flavour physics and cp violation

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 (?)


Heraeus school flavour physics and cp violation

Experimental Searches


Heraeus school flavour physics and cp violation

t-  e- g

Search


Heraeus school flavour physics and cp violation

t-  m- g

Search


Heraeus school flavour physics and cp violation

Other Channels

DE = Ereco - s/2 Dm = mreco - mt


Heraeus school flavour physics and cp violation

Current Status


Heraeus school flavour physics and cp violation

t-  m- m+m-

Search:

at the LHC

tau sources:

Advantage: more taus

Disadvantage: more background

1 year @ low luminosity


Heraeus school flavour physics and cp violation

t-  m- m+m- bei CMS

Simulation with underlying event

(low luminosity)


Heraeus school flavour physics and cp violation

t-  m- m+m- at CMS

W  t nt

10.000 events

trigger

track reconstruction


Heraeus school flavour physics and cp violation

Kinematics @ LHC

h = -ln tan q/2


Heraeus school flavour physics and cp violation

Kinematics @ LHC

Level-1 Trigger:

Single MuonpT > 14 GeV

Di-MuonpT > 3 GeV


Heraeus school flavour physics and cp violation

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 !


Heraeus school flavour physics and cp violation

Summary

  • Historical Intro: Discovery of the tau

  • Basic Properties

  • Branching Ratios

  • Kinematics

  • Mass

  • Lifetime

  • Hot Topics

  • QCD / Isospin

  • Lepton Flavour Violation


  • Login