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

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

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:

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 1957 T , P odd interactions In QFT: CPT Invariance

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

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 !!!

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

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

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

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

1. EDM 1.2 Experiments PDG ’06 95% CL EDM BELLE ‘02 WEDM ALEPH 1990-95 LEP runs (38506 events) en ALEPH ALEPH CP-even Belle CP-odd, 27X10^6 tau pairs(29.5 fb^-1)

1. EDM 1.2 Experiments For other fermions….

…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

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 10-19 e cm VER EWSTIMACION DE CZARNECKI

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

any other physics may also contribute… 2. Observables 2.1 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

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

x: Transverse y: Normal z: Longitudinal 2. Observables 2.1 High energies x: Transverse y: Normal z: Longitudinal

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

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

2. Observables 2.2 Low energies Diagrams:

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

2. Observables 2.2 Low energies

2. Observables 2.2 Low energies

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.

2. Observables 2.2 Low energies

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

2. Observables 2.2 Low energies +

2. Observables 2.2 Low energies

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

3. Conclusions  Polarized beams open the possibility for new observables Improving the number of t–pairs ( ...1011? ) allows to lower the EDM bound by many (...2?) orders of magnitude  These new bounds may be important for beyond the SM t-physics

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.