1. EDM and CPV in the t system
Gabriel González Sprinberg
Instituto de Física, Facultad de Ciencias
Montevideo Uruguay
DIF06 INFN
Laboratori Nazionali di Frascati

2. Outline 1. Electric Dipole Moment 1.1 Definition B = , Z, g, …
f = e, , , ..., b, t
1.2 Experiments
2. Observables
2.1 High energies
2.2 Low energies
3. Conclusions

3. 1. EDM 1.1Definition
P and T-odd interaction of a fermion with gauge fields:
Classical electromagnetism
Ordinary quantum mechanics
Relativistic quantum mechanics: Dirac equation
Non-relativistic limit:

4. 1. EDM 1.1Definition EDM LANDAU 1957 T , P odd interactions
SYMMETRIES: Time reversal T, Parity P
Besides, chirality flip (some insight into the mass origin)
EDM LANDAU T , P odd interactions
In QFT: CPT Invariance

5. 1. EDM 1.1Definition g t t SM : • vertex corrections
• at least 4-loops
Beyond SM: • one loop effect (SUSY,2HDM,...)
• dimension six effective operator

6. 1. EDM 1.1Definition SM : = 0 !!! V V* E.P.Shabalin ’78
We need 3-loops for a quark-EDM, and 4 loops for a lepton...
J.F.Donoghue ’78
I.B.Khriplovich,M.E.Pospelov ‘90
A.Czarnecki,B.Krause ‘97
= 0 !!!

7. 1. EDM 1.1Definition
Fermion of mass mf generated by physics at L- scale has
EDM mf/L2
T-odd t-EDM has particular interest and depends on the underlying physics of CP violation

8. 1. EDM 1.1Definition Effective Lagrangian: CPV: Operators:
Other operators:

9. 1. EDM 1.1Definition g Z t t t t More sensitivity
WEDM
EDM
More sensitivity
HIGH ENERGY (Z-peak) LOW ENERGY

10. 1. EDM 1.1Definition V = g, Z For q2=0 EDM GAUGE INVARIANT
OBSERVABLE QUANTITIES
q2=MZ2 WEDM
Beyond SM EDM: Loop calculations

11. 1. EDM 1.2 Experiments PDG ’06 95% CL EDM BELLE ‘02
WEDM ALEPH LEP runs
(38506 events) en ALEPH
ALEPH CP-even
Belle CP-odd, 27X10^6 tau pairs(29.5 fb^-1)

12. 1. EDM Experiments
For other fermions….

13. …15 orders of magnitude below experiments...
2. Observables
SM for EDM is well below within present experimental limits:
CKM 3-loops
SM prediction
CKM 4-loops
Hopefully
in the SM
…15 orders of magnitude below experiments...
VER EWSTIMACION DE CZARNECKI

14. EDM scale as the cube of the mass!
2. Observables
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 contributions
Vectrolike leptons
EDM scale as the cube of the mass!
BSM t-EDM can go up to e cm
VER EWSTIMACION DE CZARNECKI

15. 2. Observables
Non-vanishing signal in a t-EDM observable
NEW PHYSICS
One expects: special interest in heavy flavours
t-EDM: In order to be able to measure a genuine non-vanishing signal one has to deal with a -observable

16. any other physics may also contribute…
2. Observables High energies
Indirect arguments:
any other physics may also contribute…
Look for , linear effects
Genuine CPV observables in t–pair production:
SPIN TERMS and/or SPIN CORRELATIONS

17. 2. Observables 2.1 High energies
Spin terms angular distribution of decay products
• Asymmetries in the decay products
• Expectation values of tensor observables

18. x: Transverse y: Normal z: Longitudinal
2. Observables High energies
x: Transverse y: Normal z: Longitudinal

19. 2. Observables 2.1 High energies
Tensor observables:
Z-peak:
W.Bernreuther,O.Nachtmann ‘89
Normal polarization:
(and needs helicity-flip)
Genuine CPV if

20. 2. Observables 2.1 High energies
EDM (and ) is proportional to angular asymmetries,
to extract sinqt cosqt sinfh
(more details latter..)
One can measure for and/or

21. 2. Observables 2.2 Low energies
Diagrams:

22. 2. Observables 2.2 Low energies
What about the linear terms?
Interference with the axial part of Z-exchange, suppressed by q2/MZ2

23. 2. Observables 2.2 Low energies

24. 2. Observables 2.2 Low energies

25. 2. Observables 2.2 Low energies
These two spin correlations receive standard model contributions to their symmetric CP-even terms through absorptive parts generated in radiative corrections. At leading order it is the imaginary part of the Z propagator that produces a contribution to these correlations with the interference of the amplitudes of direct and Z-exchange. This termis suppressed at low energies by the factor ( q2/MZ2 gZ/mz) AND HAS BEEN COMPUTED AND CAN BE SUBS IF NECESSARY.

26. 2. Observables 2.2 Low energies

27. 2. Observables 2.2 Low energies
THIS SELECTS ONLY THE CP ODD PART OF nl CORR

28. 2. Observables 2.2 Low energies+

29. 2. Observables 2.2 Low energies

30. 2. Observables 2.2 Low energies
Bounds:
For 106/7 t and at low/U energies
upper bound

31. 3. Conclusions
 Polarized beams open the possibility for new observables
Improving the number of t–pairs ( ? ) allows to lower the EDM bound by many (...2?) orders of magnitude
 These new bounds may be important for beyond the SM t-physics

32. 3. 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.