1. t- LEPTON DIPOLE MOMENTS @ SUPER B FACTORIES
Gabriel González Sprinberg
Facultad de Ciencias, Uruguay
BNM2008 – Atami, Japan

2. t- LEPTON DIPOLE MOMENTS @ SUPER B FACTORIES
t - dipole moments can be measured from high statistic B/Super B factories data. For unpolarized/polarized beams we study new observables and we find that limits of the order of e-cm can be obtained for the EDM, while the magnetic form factor can be measured with a sensitivity of
OUTLINE
1. t - ELECTRIC DIPOLE MOMENT (EDM)
1.1 Definition, measurements
1.2 Observables
2. t - MAGNETIC DIPOLE MOMENT (MDM)
2.1 Definition, measurements
2.2 Observables
3. CONCLUSIONS

3. 1. EDM 1.1 Definition, measurements
P and T- odd first order interaction of a fermion with gauge fields (Landau 1957)
Besides, chirality flipping (some insight into the mass origin)
Classical electromagnetism
Ordinary quantum mechanics
Dirac’s equation
Interaction term for non-relativistic limit of Dirac’s equation gives HEDM
CPT: CP and T are equivalent

4. 1. EDM 1.1 Definition, measurementsg t t
EDM
SM : • vertex correction coming from CKM
• at least 4-loops for leptons
Beyond SM: • one loop effect (SUSY, 2HDM,...)
• dimension six effective operator

5. 1. EDM 1.1 Definition, measurements
SM :
VCKM V *CKM E.P.Shabalin ’78
We need 3-loops for a quark-EDM, and 4 loops for a lepton...
= 0 !!!
J=2.6x10-5 BotellaNuclear Physics B also pospelov-ritz give the same J .Volume 725, Issues 1-2, 3 October 2005, Pages

6. 1. EDM 1.1 Definition, measurements
SM - EDM:
CKM 3-loops
CKM 4-loops
Well below present experimental limits!
Hopefully in the SM
…16 orders of magnitude below experiments...
VER EWSTIMACION DE CZARNECKI

7. Beyond SM physics predictions for the t-EDM can go up to 10-19 e cm
1. EDM Definition, measurements
Non-vanishing signal in a t-EDM  NEW PHYSICS
Beyond SM physics predictions for the t-EDM can go up to e cm
VER EWSTIMACION DE CZARNECKI

8. 1. EDM 1.1 Definition, measurements
If the EDM goes as mf, then, current limits on the electron EDM would give a limit:
(still many orders of magnitude above SM prediction)
However, in many models the EDM do not necessarily scale as mf .
Higgs models / Leptoquarks / Majorana neutrino
EDM scales different
Non-universal couplings may generate e-EDM << t-EDM
VER EWSTIMACION DE CZARNECKI

9. 1. EDM 1.1 Definition, measurements
de : dm : dt = mu2 me : mc2 mm : mt2 mt
(mt / me)2 = , (mt / me)3 =1011
Then, stronger than present t - EDM bounds can be much more competitive than e - EDM bounds !!
This will probably be the case for Super B Factories
VER EWSTIMACION DE CZARNECKI, split susy, papers del italiano de eps

10. 1. EDM 1.1 Definition, measurements
Light Fermions :
Stables or with enough large lifetime
EDM : spin dynamics in electric fields
Heavy Fermions:
Short living particles
Spin matrix and angular distribution of decay products
in t -pair production may depend on the EDM
(38506 events) en ALEPH
ALEPH CP-even
Belle CP-odd, 27X10^6 tau pairs(29.5 fb^-1)

11. 1. EDM 1.1 Definition, measurements
BOUNDS:
PDG ’ % CL
EDM BELLE ’02
Errata: PDG pone 0.08
(38506 events) en ALEPH
ALEPH CP-even
Belle CP-odd, 27X10^6 tau pairs(29.5 fb^-1)

12. Sensitive to many contributions
1. EDM Definition, measurements
HOW DO WE MEASURE  ELECTRIC DIPOLE MOMENT?
Total cross sections e+e  +-
e+e e+e- +-
Partial widths Z +- 
Sensitive to many contributions
Triple products
Spin correlations
Linear polarizations
Triple products, correlations and asymmetries observables select EDM by symmetry properties
(38506 events) en ALEPH
ALEPH CP-even
Belle CP-odd, 27X10^6 tau pairs(29.5 fb^-1)

13. 1. EDM 1.2 Observables Tau pair production EDM: T-odd P-odd Vs.
NORMAL - TRANSVERSE / LONGITUDINAL CORRELATIONS:
T - odd P - odd
(no need of additional P-odd source: unpolarized beam)
And
NORMAL POLARIZATION:
T - odd but P - even
(needs additional P-odd source: beam polarization)
Extended models predictions and mass cosiderations in eps talk

14. 1. EDM Observables
Diagrams

15. 1. EDM 1.2 Observables Tau pair production
NORMAL - TRANSVERSE / CORRELATIONS:
J. Bernabéu, GGS and J.Vidal.
Nucl. Phys. B701 (2004)
x: Transverse y: Normal z: Longitudinal

16. NORMAL - TRANSVERSE / CORRELATIONS:
1. EDM Observables
Tau pair production
NORMAL - TRANSVERSE / CORRELATIONS:
( NORMAL- LONGITUDINAL CORRELATION: SIMILAR ANALYSIS )

17. 1. EDM 1.2 Observables Tau pair production Normal polarization:
and needs helicity-flip so for the Tau it is mass enhanced
Genuine if
NORMAL POLARIZATION: T-odd P-even
Vs.
EDM: T-odd P-odd
Polarized beams provide another P-odd source
J. Bernabèu, GGS and J.Vidal.
Nuclear Physics B763 (2007)

18. EDM and polarized beams produce a P - even observable
1. EDM Observables
Tau pair production
Normal polarization:
EDM and polarized beams produce a P - even observable

19. 1. EDM 1.2 Observables One can also measure for and/or
For polarized beams
Angular asymmetries ( ) are proportional to EDM
One can also measure for and/or
P_n+ -> -P_N- by CP so P_N+ + P_N- is CP odd: P_N+ + P_N- -> - ( P_N+ + P_N- ) by CP.
IN A_N^CP we are testing if the normal pol. Terms have origin in CP-odd interactions, such as the EDM

20. 1. EDM 1.2 Observables Bounds:
(Some other observables can also be defined in order to measure the EDM imaginary part)
Valores de modelos exxtendidos, bern,over? Citado por Inami

21. Classical physics/quantum mechanics
2. MDM Definition, measurements
Classical physics/quantum mechanics
Dirac’s equation anomalous MDM
Interaction term for non-relativistic limit of Dirac’s equation gives HMDM
Schwinger 1948 QED:

22. 2. MDM 2.1 Definition, measurements
Hlo= hlomuon= ^-11
Weak= weakmuon=2 10^-11

23. 2. MDM 2.1 Definition, measurements
Model independent /Effective lagragians

24. Both photons and t OFF-SHELL
2. MDM Definition, measurements
Delphi, e+ e-  e+ e- t + t -
Diagram e t
Both photons and t OFF-SHELL

25. 2. MDM 2.1 Definition, measurements
The anomaluos magnetic moment is defined by
a = F2 ( q2 = 0 ).
This quantity is gauge independent
AND
for QED, F2 ( q2 ≠ 0 ) is also gauge independent
Besides, weak interactions gauge dependence goes to 0 for q2 0
At one loop QED:
Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

26. 2. MDM 2.1 Definition, measurements
Schwinger real and imaginary parts
Flavor dependence

27. 2. MDM 2.1 Definition, measurements
At B-factories:
Real and imaginary parts are same order of magnitude
THIS FORM FACTOR CAN BE MEASURED
AT SUPER B FACTORIES
Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

28. 2. MDM Observables
Diagrams

29. 2. MDM 2.2 Observables Diagrams Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

30. 2. MDM 2.2 Observables UNPOLARIZED BEAM
Normal polarization asymmetries: Imaginary part
Angular distribution:
Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

31. L / T pol. are P-odd  beam polarization needed
2. MDM Observables
POLARIZED BEAM
Longitudinal and Transverse polarization asymmetries:
Real part
L / T pol. are P-odd  beam polarization needed
Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

32. 2. MDM 2.2 Observables Combining both observables POLARIZED BEAM
Angular distribution L/T polarization asymmetries:
Combining both observables
Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

33. Z interference is eliminated in this last observable !
2. MDM Observables
Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma
Z interference is eliminated in this last observable !

34. 2. MDM 2.2 Observables Vacumm pol is gauge indep
Box calcenls between them, te direct and the crossones
Then, the vertex gauge dep can only cancel with fermion self enrgy, but this is prop to gamma

35. 3. Conclusions
Linear polarization and correlation CP-odd observables at super B factories can lower the Tau-EDM bound by 2-3 orders of magnitude.
Tau-EDM bounds become competitive with other EDM bounds at this level.
Polarized beams observables are independent from other low and high energy observables already investigated.
The Tau-MDM form factor can be measured for the first time in asymmetries at Super B factories.
Both unpolarized and polarized beam observables allow to do so.
Correlation observables for MDM: coming soon…

36. 3. Conclusions Discussions with J.Bernabèu, J.Vidal and A.Santamaria
are gratefully acknowledged
J.Bernabèu1, GGS,2 J.Vidal1
1. Valencia Univ., Spain
2. Republic Univ., Uruguay
Nuclear Physics B 702 (2004)
EDM in correlations, unpolarized beams
Nuclear Physics B 763 (2007)
EDM in polarizations, polarized beams
Nuclear Physics B 790 (2008)
MDM, polarized and unpolarized beams

37. 3. Conclusions Discussions with J.Bernabèu, J.Vidal and A.Santamaria
are gratefully acknowledged
J.Bernabèu1, GGS,2 J.Vidal1
1. Valencia Univ., Spain
2. Republic Univ., Uruguay
Nuclear Physics B 702 (2004)
EDM in correlations, unpolarized beams
Nuclear Physics B 763 (2007)
EDM in polarizations, polarized beams
Nuclear Physics B 790 (2008)
MDM, polarized and unpolarized beams