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