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

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 10-19 e-cm can be obtained for the EDM, while the magnetic form factor can be measured with a sensitivity of 10 - 6. 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

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

1. EDM 1.1 Definition, measurements g 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

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 155-172

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

Beyond SM physics predictions for the t-EDM can go up to 10-19 e cm 1. EDM 1.1 Definition, measurements Non-vanishing signal in a t-EDM  NEW PHYSICS Beyond SM physics predictions for the t-EDM can go up to 10-19 e cm VER EWSTIMACION DE CZARNECKI

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

1. EDM 1.1 Definition, measurements de : dm : dt = mu2 me : mc2 mm : mt2 mt (mt / me)2 =107 , (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

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)

1. EDM 1.1 Definition, measurements BOUNDS: PDG ’06 95% 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)

Sensitive to many contributions 1. EDM 1.1 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)

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

1. EDM 1.2 Observables Diagrams

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

NORMAL - TRANSVERSE / CORRELATIONS: 1. EDM 1.2 Observables Tau pair production NORMAL - TRANSVERSE / CORRELATIONS: ( NORMAL- LONGITUDINAL CORRELATION: SIMILAR ANALYSIS )

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)

EDM and polarized beams produce a P - even observable 1. EDM 1.2 Observables Tau pair production Normal polarization: EDM and polarized beams produce a P - even observable

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

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

Classical physics/quantum mechanics 2. MDM 2.1 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:

2. MDM 2.1 Definition, measurements Hlo=0.000 003 40 hlomuon=7000 10^-11 Weak= 0.000 000 047 weakmuon=2 10^-11

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

Both photons and t OFF-SHELL 2. MDM 2.1 Definition, measurements Delphi, 2004 e+ e-  e+ e- t + t - Diagram e t Both photons and t OFF-SHELL

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

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

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

2. MDM 2.2 Observables Diagrams

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

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

L / T pol. are P-odd  beam polarization needed 2. MDM 2.2 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

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

Z interference is eliminated in this last observable ! 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 Z interference is eliminated in this last observable !

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

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…

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) 87-102 EDM in correlations, unpolarized beams Nuclear Physics B 763 (2007) 283-292 EDM in polarizations, polarized beams Nuclear Physics B 790 (2008) 160-174 MDM, polarized and unpolarized beams

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) 87-102 EDM in correlations, unpolarized beams Nuclear Physics B 763 (2007) 283-292 EDM in polarizations, polarized beams Nuclear Physics B 790 (2008) 160-174 MDM, polarized and unpolarized beams