EDM and CPV in the ττττ - fisica.edu.uygabrielg/gonzalez.pdfEDM and CPV in the ττττsystem Gabriel González Sprinberg Instituto de Física, Facultad de Ciencias Montevideo

EDM and CPV in the EDM and CPV in the ττττττττ systemsystem

Gabriel González SprinbergInstituto de Física, Facultad de Ciencias

Montevideo Uruguay

[email protected]

DIF06 INFN Laboratori Nazionali di Frascati

OutlineOutline

1. Electric Dipole Moment

1.1 Definition

B = γγγγ, Z, g, …f = e, µµµµ, ττττ, ..., b, t

1.2 Experiments

2. Observables

2.1 High energies2.2 Low energies

3. Conclusions

B

fd

1. EDM 1. EDM 1.1Definition1.1Definition

P and T-odd interaction of a fermionwith gauge fields:Classical electromagnetismOrdinary quantum mechanics

Relativistic quantum mechanics: Dirac equation

Non-relativistic limit:

sdρρ

=d,Edρρ

⋅−=EDMH

( ) 5( )

2

iH i eA m d Fµυ

µυγ σ/= Ψ ∂/ + − Ψ + Ψ Ψ

Edρρ

⋅−=→ EDMHH

EDM LANDAU 1957 T , P odd interactions

In QFT: CPT Invariance

EDMEDM HH −→

SYMMETRIES: Time reversal T, Parity PBesides, chirality flip (some insight into the mass origin)

tt −→ ,EE:ρρ

→ ssρρ

−→


CP ≈ T

SM : • vertex corrections

• at least 4-loops

Beyond SM: • one loop effect (SUSY,2HDM,...)

• dimension six effective operator

EDM

γγγγ

ττττττττ


SM :

V V*

E.P.Shabalin ’78

We need 3-loops for a quark-EDM, and 4 loops for a lepton...

J.F.Donoghue ’78I.B.Khriplovich,M.E.Pospelov ‘90A.Czarnecki,B.Krause ‘97


= 0 !!!

Fermion of mass mf generated by physics atΛΛΛΛ−−−− scale has

EDM mf/ΛΛΛΛ2222

T-odd ττττ−−−−EDM has particular interest anddepends on the underlying physics of CP violation

≈


Effective Lagrangian:

CPV:

Operators:

Other operators:


More sensitivity

HIGH ENERGY (Z-peak) LOW ENERGY

ττττ ττττττττ ττττ

WEDM EDM

ΖΖΖΖ γγγγ


V = γ, Ζγ, Ζγ, Ζγ, Ζ

For q2=0 EDM GAUGE INVARIANT

OBSERVABLE QUANTITIES

q2=MZ2 WEDM

Beyond SM EDM: Loop calculations

5 2 5 2

5( , ) ( ) ( )

V Vp p ie a q q d q

µ µ µννγ γ σ γ− +

Γ = +


dττττγγγγ

Zd ττττ

PDG ’06 95% CL

EDM BELLE ‘02

WEDM ALEPH 1990-95 LEP runs

1. EDM 1. EDM 1.2 Experiments1.2 Experiments

170 50 10

−≤ ×ZRe(d ) . ecmττττ

171 1 10

−≤ ×ZIm(d ) . ecmττττ

162 2 0 45 10

−− ×Re(d ) : ( . to . ) e cmττττ

γγγγ

160 25 0 008 10

−− ×Im(d ) : ( . to . ) ecmττττ

γγγγ

For other fermions….

1. EDM 1. EDM 1.2 Experiments1.2 Experiments

260 069 0 074 10

−= ± ×ed ( . . ) e cmγγγγ

193 7 3 4 10

−= ± ×d ( . . ) e cmµµµµ

γγγγ

250 63 10 90

−< ×nd . e cm, % CLγγγγ

SM for EDM is well below within present experimental limits:

CKM 3-loopsSM prediction

CKM 4-loops

Hopefullyin the SM

…15 orders of magnitude below experiments...

2. Observables2. Observables

32 3410 10

− −≈ −qd ecmγγγγ

3810

−≈ed ecmγγγγ

33 3410 10

− −≈ ≈ −e

e

md d ecm

mττττ ττττγ γγ γγ γγ γ

Currents limits on electron EDM gives:

However, in many models the EDM do not necessarily scale as the first power of the masses.

Multihiggs models 1-loop contributionsVectorlike leptons

EDM scale as the cube of the mass!

BSM ττττ-EDM can go up to 10-19 e cm


242 4 10

−< ×d . ecmττττ

γγγγ


2≈

md eττττ ττττ

γγγγΛΛΛΛ

Non-vanishing signal in a ττττ−−−−EDM observable

NEW PHYSICS

One expects: special interest in heavy flavours

ττττ−−−−EDM: In order to be able to measure a genuine non-vanishing signal one has to deal with a -observable CP

2. Observables 2. Observables 2.1 High energies2.1 High energies

Indirect arguments:

any other physics may also contribute…

Look for , linear effects

Genuine CPV observables in ττττ–pair production:

SPIN TERMS and/or SPIN CORRELATIONS

+ − + −

+ −

→

→

(e e )

(Z )

∆σ τ τ∆σ τ τ∆σ τ τ∆σ τ τ

∆Γ τ τ∆Γ τ τ∆Γ τ τ∆Γ τ τ

2

≈ Zdττττ

CPP


Spin terms angular distribution of decay products

• Asymmetries in the decay products• Expectation values of tensor observables

CP :


x: Transverse y: Normal z: Longitudinal


Tensor observables:

Z-peak:

W.Bernreuther,O.Nachtmann ‘89

Normal polarization:

(and needs helicity-flip)

Genuine CPV if

J.Bernabeu,GGS,J.Vidal ‘93

+ − + −= − × + ↔ij i jT (q q ) (q q ) (i j)

±ττττ±

±(q )ππππ

νννν

≈ Zij ij Z

mT c

edsππππππππ

ππππππππ

ττττ

↔ − −NP T odd, P evenττττ

+ −

↔N NP Pτ ττ ττ ττ τ


EDM (and ) is proportional to angular asymmetries,to extract sinθθθθττττ cosθθθθτ τ τ τ sinφφφφh

(more details latter..)

One can measure for and/or

1

2

+ −≡ +CPVA (A A )

NP ττττ

A +ττττ−ττττ

CP :

+ −

+ −

−=

+A

σ σσ σσ σσ σ

σ σσ σσ σσ σ

2 2 22 + + ∝N

ZP sin v (v a ) ma cose

dτττττ τ ττ τ ττ τ ττ τ τ

ττττ

γβ θ β θγβ θ β θγβ θ β θγβ θ β θ

2. Observables 2. Observables 2.2 Low energies2.2 Low energies

Diagrams:

+ − + −+ −→ →e e , (s ) (s )γ ϒ τ τγ ϒ τ τγ ϒ τ τγ ϒ τ τ

d ττττ

γγγγ

d ττττ

γγγγ


What about the linear terms?

Interference with the axial part of Z-exchange, suppressed by q2/MZ

2

J.Bernabeu,GGS,J.Vidal ‘04




T , P

CPV




+


T

2

w 0

A

dd d

d d

w 2

>>>>

−−−−

−−−−<<<<

−−−−

± ±± ±± ±± ±±±±± + −+ −+ −+ −

± ±± ±± ±± ±

+ −+ −+ −+ −

±±±±

±±±±ττττ±±±±ττττ

±±±±

±±±±ττττ

σ − σσ − σσ − σσ − σ====

σ + σσ + σσ + σσ + σ

σσσσσ = θ φσ = θ φσ = θ φσ = θ φ

θ φθ φθ φθ φ

= θ φ= θ φ= θ φ= θ φ

∫∫∫∫ coscos

sin cos (((( ))))

T 2

CPV

T T

2mA d

2 3 e

1A A A

2

± γ± γ± γ± γττττ± τ± τ± τ± τ

+ −+ −+ −+ −

βγβγβγβγ = − α= − α= − α= − α − β− β− β− β

= += += += +

Im( )


Bounds:

For 106/7 ττττ and at low/ΥΥΥΥ energies

upper bound

16 1710

− −< /Re(d ) ecmττττ

γγγγ

3. Conclusions3. Conclusions

�� Polarized beams open the possibility for new

observables

� Improving the number of ττττ–pairs ( ...1011? ) allows to lower the EDM bound by many (...2?) orders of magnitude

�� These new bounds may be important for

beyond the SM ττττ−−−−physics

3. Summary3. Summary

Discussions with J.Bernabeu, J.Vidal and A.Santamaría are gratefully acknowledged

SOME REFERENCES

� J. Bernabeu, G.S., Jordi Vidal

Nuclear Physics B 701 (2004) 87–102

� Daniel Gomez-Dumm, G.S.

Eur. Phys. J. C 11, 293{300 (1999)

� W. Bernreuther, A. Brandenburg, and P. Overmann

Phys. Lett. B 391 (1997) 413; ibid., B 412 (1997) 425.

Documents

EDM and CPV in the ττττ - fisica.edu.uygabrielg/gonzalez.pdfEDM and CPV in the ττττsystem Gabriel González Sprinberg Instituto de Física, Facultad de Ciencias Montevideo