heraeus school flavour physics and cp violation 29./30. august 2005
TRANSCRIPT
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