t - LEPTON DIPOLE MOMENTS Gabriel González Sprinberg, Instituto de Física Facultad de Ciencias, Universidad de la República Montevideo, Uruguay gabrielg@fisica.edu.uy Nagoya University, January 2008

t - LEPTON DIPOLE MOMENTS Gabriel González Sprinberg, Instituto de Física Facultad de Ciencias, Universidad de la República Montevideo, Uruguay gabrielg@fisica.edu.uy Nagoya Uniiversity, January 2008

Outline 1. Tau lepton 2. Electric Dipole moments. 3. Magnetic dipole moments. 4. Conclusions.

Outline 0. Uruguay: a primer 1. Tau lepton 2. Electric Dipole moments. 3. Magnetic dipole moments. 4. Conclusions.

0. Yosoko Uruguay Soccer teams: Peñarol, Nacional Players Diego Forlan Most important historical fact from Uruguay history according to nationals: 1930 we won the 1st. Soccer World Cup, held at Montevideo, defeating Argentina 4-2 1950, again, but this time defeating Brasil at Rio de Janeiro, 2-1, a fact known as “Maracanazo” Soccer teams: Peñarol, Nacional Players Diego Forlan Alvaro Recoba Paolo Montero

0. Uruguay Antipodes: somewhere in between Japan and Korea

0. Uruguay More precise statement

0. Uruguay Flag Coat of arms Name “República Oriental del Uruguay “ (Orient Republic of Uruguay) Uruguay originates from “River of the uru”, coming from guarani, language from some natives, still official language from Paraguay Capital (and largest city) Montevideo language: Spanish Demonym: Uruguayan, Oriental (easterers) Government: Republic, presidential system President: Tabare Vazquez (both head of government and state) Independence: from Brazil/Portugal:  Oriental Revolution 1825

0. Uruguay Area - Total 176.215 km2 / 68,037sq mi Population - 2002 census 3,399,237 Highest point (513meters…)  Currency: uruguayan peso ( $) Litercy: 97% Birth rate: 17/1000 Spanish, italian, African descent(5%), Jewish, no natives. Density 19/km² - 50/sq mi (but only 1.4 /km2 outside cities) Climate: Tempered (hot summer, cold humid winters, never snows) Gini (2003) 4.49 (high) , HDI (2007) 0.852 (high) (46th)

0. Uruguay Poverty line 18%, indigence line 3% Life expect. 76.7 GDP per capita usd 12000 (61th) Unemployent 9.7% Religion: most secular country in Latin America (60% Roman catholic, 30% non professing, jewish 3%) Economy: Rice, citrus, cattle (grass-fed beef), sheep, milk, wool, software,wines Some writers: Juan Carlos Onetti, Horacio Quiroga, Mario Benedetti, Eduardo Galeano, Felisberto Hernandez, Juana de Ibarburu Music: Tango; most famous uruguayan: Carlos Gardel, tango singer Natives: Charruas, guaranies (around 5000 – 10000 at that time and exterminated in XIX century)

0. Uruguay Found by Juan Diaz de Solis, 1516, who was inmediately murdered, with all of his friends, by native indians (and beisde, they were cannibals…) Colonialism: Spain , Portugal, Brazil, Argentina, U.K (untill 1825). Montevideo: 1.350.000/1.814.000 people (42 % of population) Founded 1726 Nowadays city’s major: Ricardo Ehrlich (previous dean of the Faculty of Sciences) Latinoamerican city with the highest life quality (followed by Buenos Aires - Santiago de Chile) We are close to: Buenos Aires, Argentina 13.000.000 people, 300 km Sao Pablo, Brazil 20.000.000 people, 2000 km Monte vide ue (I see a hill) Monte VI EO (sixth hill from E to W)

0. Uruguay Universidad de la República, founded in 1870 70.000 students 5000 professors/assistents (only 10% full time !!) 130 M$/yr $ 2000 /yr/student Sciences: in  500 students/yr out  only 60/yr ! Physics: 35 people with PHD degree 8 HEP/Gravity 2007, 11 papers 2006, 17 papers total, 210 since 1990

0. Uruguay Faculty of Sciences (1995 !)

0. Uruguay Montevideo 100 km

0. Uruguay Montevideo

0. Uruguay Gauchos

0. Uruguay Mate, yerba mate, bombilla

0. Uruguay Asado (uruguayan barbecue, made with firewood)

0. Uruguay Pocitos beach, Buceo sailing port

0. Uruguay Pocitos beach

0. Uruguay Pocitos (long time ago it was a loundry place)

0. Uruguay Pocitos beach (some time ago)

0. Uruguay Pocitos beach (cloudy day in last December 24th, summer time!)

0. Uruguay Pocitos beach (cloudy day in last December 24th, summer time!)

0. Uruguay Pocitos beach, sunny day

0. Uruguay Estadio Centenario

0. Uruguay Carrasco

0. Uruguay Downtown

0. Uruguay Downtown

0. Uruguay Very typical view…

0. Uruguay Downtown

0. Uruguay Downtown, Palacio Legislativo (parliament)

1. Tau Physics Why are we (still) interested inTau physics? m = 1777 MeV ! Lifetime = 290 x 10-15 sec ! A lepton that decays into hadrons ! Lepton universality Sensitive to New physics m /L

1. Tau Physics Physical Review Letters 35 (1975) 1489 Evidence for Anomalous Lepton Production in e+ e− Annihilation

1. Tau Physics

1. Tau Physics

1. Tau Physics

1. Tau Physics Tau decay into hadrons: charged-current universality tests, (hadronic weak current in clean conditions) bounds on lepton-flavour violation, determination of αs from the inclusive t hadronic width, measurement of |Vus | through the Cabibbo- suppressed decays of the τ lepton. ms quark mass

1. Tau Physics

1. Tau Physics

1. Tau Physics

2. Electric dipole moments FIRST ORDER INTERACTION WITH ELECTROMAGNETIC FIELDS ELECTRIC DIPOLE MOMENT: Classical electromagnetism Ordinary quantum mechanics Relativistic quantum mechanics: Dirac equation Non-relativistic limit:

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

2. Electric dipole moments SYMMETRIES: Time reversal T-odd, Parity P-odd interaction of a fermion with gauge fields

2. Electric dipole moments EDM LANDAU 1957 T , P odd In local QFT: CPT Invariance

2. Electric dipole moments Besides: it is chirality flipping. Fermion of mass mf generated by physics at L- scale has EDM m/L2 T-odd t - EDM depends on the underlying physics of CP violation

2. Electric dipole moments SM : 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 !!!

2. Electric dipole moments g Z t t t t WEDM EDM More sensitivity HIGH ENERGY (Z-peak) LOW ENERGY

2. Electric dipole moments V = g, Z For q2 = 0 EDM GAUGE INVARIANT For OBSERVABLE QUANTITIES q2 = MZ2 WEDM Beyond SM EDM: Loop calculations

2. Electric dipole moments Light Fermions : Stables or with large lifetime  : spin precession in d : spin gap in Heavy Fermions: short lifetime Spin matrix and angular distribution of decay products depend on EDM/MDM

2. Electric dipole moments 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)

2. Electric dipole moments For other fermions….

…16 orders of magnitude below experiments... 2. Electric dipole moments SM for EDM is well below within present experimental limits: CKM 3-loops SM prediction CKM 4-loops Hopefully in the SM …16 orders of magnitude below experiments... VER EWSTIMACION DE CZARNECKI

EDM can scale as the cube of the mass! 2. Electric dipole moments Currents limits on electron EDM gives: However, in many models the EDM do not necessarily scale as the first power of the masses. Higgs models/Leptoquarks/Heavy majorana neutrino 1-loop contributions EDM can scale as the cube of the mass! BSM t-EDM can go up to 10-19 e cm VER EWSTIMACION DE CZARNECKI

2. Electric dipole moments 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. Electric dipole moments Indirect arguments: any other physics may also contribute… Look for , linear effects Genuine CPV observables in Tau–pair production: SPIN TERMS and/or SPIN CORRELATIONS (triple products)

2. Electric dipole moments Spin terms angular distribution of decay products • Asymmetries in the decay products • Expectation values of tensor observables

x: Transverse y: Normal z: Longitudinal 2. Electric dipole moments x: Transverse y: Normal z: Longitudinal

2. Electric dipole moments Tensor observables: Z-peak: W.Bernreuther,O.Nachtmann ‘89 Normal polarization: (and needs helicity-flip) Genuine CPV if

2. Electric dipole moments EDM (and ) is proportional to angular asymmetries, to extract sinqt cosqt sinfh (more details latter..) One can measure for and/or

2. Electric dipole moments Diagrams:

Longitudinally polarized beams can produce P-odd terms 2. Electric dipole moments What about the linear terms? Interference with the axial part of Z-exchange, suppressed by q2/MZ2 Longitudinally polarized beams can produce P-odd terms

2. Electric dipole moments

2. Electric dipole moments 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. Electric dipole moments

2. Electric dipole moments Bounds: Atto = 10^(-18)

2. EDM 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.

Classical physics/quantum mechanics 3. Magnetic dipole moment Classical physics/quantum mechanics Dirac’s equation anomalous MDM Interaction term for non-relativistic limit of Dirac’s equation gives HMDM Schwinger 1948 QED:

3. Magnetic dipole moment Hlo=0.000 003 40 hlomuon=7000 10^-11 Weak= 0.000 000 047 weakmuon=2 10^-11 Weak and hadronic contributions

3. Magnetic dipole moment Hlo=0.000 003 40 hlomuon=7000 10^-11 Weak= 0.000 000 047 weakmuon=2 10^-11

3. Magnetic dipole moment Hlo=0.000 003 40 hlomuon=7000 10^-11 Weak= 0.000 000 047 weakmuon=2 10^-11 HADRONIC 3-LOOPS WEAK 2-LOOPS

3. Magnetic dipole moment Effective Lagrangian CPV Operators Agregar los op que quedn al final, generando edm del foton z y nodiaginal

3. Magnetic dipole moment CPV Agregar los op que quedn al final, generando edm del foton z y nodiaginal

3. Magnetic dipole moment Hlo=0.000 003 40 hlomuon=7000 10^-11 Weak= 0.000 000 047 weakmuon=2 10^-11

3. Magnetic dipole moment Model independent /Effective lagragians

Both photons and t OFF-SHELL 3. Magnetic dipole moment Delphi, 2004 e+ e-  e+ e- t + t - Diagram e t Both photons and t OFF-SHELL

3. Magnetic dipole moment 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

3. Magnetic dipole moment Schwinger real and imaginary parts Flavor dependence

3. Magnetic dipole moment 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

3. Magnetic dipole moment Diagrams

3. Magnetic dipole moment 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

3. Magnetic dipole moment 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 3. Magnetic dipole moment 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

3. Magnetic dipole moment 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 ! 3. Magnetic dipole moment 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 !

3. Magnetic dipole moment 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. MDM. Conclusions 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…

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

Thank you for the opportunity of discussing my scientific work with you Japan is a very interesting/enjoyable country !!!!! Specially if you pay close attention to wise advices !!!