EDM and CPV in the ττττ - fisica.edu.uygabrielg/gonzalez.pdfEDM and CPV in the ττττsystem...

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

Gabriel González SprinbergInstituto de Física, Facultad de Ciencias

Montevideo Uruguay

gabrielg@fisica.edu.uy

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

−→

1. EDM 1. EDM 1.1Definition1.1Definition

CP ≈ T

SM : • vertex corrections

• at least 4-loops

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

• dimension six effective operator

EDM

γγγγ

ττττττττ

1. EDM 1. EDM 1.1Definition1.1Definition

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

1. EDM 1. EDM 1.1Definition1.1Definition

= 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

≈

1. EDM 1. EDM 1.1Definition1.1Definition

Effective Lagrangian:

CPV:

Operators:

Other operators:

1. EDM 1. EDM 1.1Definition1.1Definition

More sensitivity

HIGH ENERGY (Z-peak) LOW ENERGY

ττττ ττττττττ ττττ

WEDM EDM

ΖΖΖΖ γγγγ

1. EDM 1. EDM 1.1Definition1.1Definition

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 = +

1. EDM 1. EDM 1.1Definition1.1Definition

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

2. Observables2. Observables

242 4 10

−< ×d . ecmττττ

γγγγ

2. Observables2. Observables

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

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

Spin terms angular distribution of decay products

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

CP :

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

x: Transverse y: Normal z: Longitudinal

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

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

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

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

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

What about the linear terms?

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

2

J.Bernabeu,GGS,J.Vidal ‘04

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

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

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

T , P

CPV

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

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

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

+

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

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( )

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

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.