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

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

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

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

5. 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

6. 0. Uruguay
Antipodes: somewhere in between Japan and Korea

7. 0. Uruguay
More precise statement

8. 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

9. 0. Uruguay Area - Total 176.215 km2 / 68,037sq mi
Population  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)  (high) (46th)

10. 0. Uruguay Poverty line 18%, indigence line 3% Life expect. 76.7
GDP per capita usd (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 – at that time and exterminated in XIX century)

11. 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: / 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 people, 300 km
Sao Pablo, Brazil people, 2000 km
Monte vide ue (I see a hill)
Monte VI EO (sixth hill from E to W)

12. 0. Uruguay Universidad de la República, founded in 1870
students
5000 professors/assistents (only 10% full time !!)
130 M$/yr $ 2000 /yr/student
Sciences:
in  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

13. 0. Uruguay
Faculty of Sciences (1995 !)

14. 0. Uruguay
Montevideo km

15. 0. Uruguay
Montevideo

16. 0. Uruguay
Gauchos

17. 0. Uruguay
Mate, yerba mate, bombilla

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

19. 0. Uruguay
Pocitos beach, Buceo sailing port

20. 0. Uruguay
Pocitos beach

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

22. 0. Uruguay
Pocitos beach (some time ago)

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

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

25. 0. Uruguay
Pocitos beach, sunny day

26. 0. Uruguay
Estadio Centenario

27. 0. Uruguay
Carrasco

28. 0. Uruguay
Downtown

29. 0. Uruguay
Downtown

30. 0. Uruguay
Very typical view…

31. 0. Uruguay
Downtown

32. 0. Uruguay
Downtown, Palacio Legislativo (parliament)

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

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

35. 1. Tau Physics

36. 1. Tau Physics

37. 1. Tau Physics

38. 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

39. 1. Tau Physics

40. 1. Tau Physics

41. 1. Tau Physics

42. 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:

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

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

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

46. 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

47. 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 !!!

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

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

50. 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

51. 2. Electric dipole moments
PDG ’ % 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)

52. 2. Electric dipole moments
For other fermions….

53. …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

54. 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 e cm
VER EWSTIMACION DE CZARNECKI

55. 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

56. 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)

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

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

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

60. 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

61. 2. Electric dipole moments
Diagrams:

62. 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

63. 2. Electric dipole moments

64. 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.

65. 2. Electric dipole moments

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

67. 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.

68. 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:

69. 3. Magnetic dipole moment
Hlo= hlomuon= ^-11
Weak= weakmuon=2 10^-11
Weak and hadronic contributions

70. 3. Magnetic dipole moment
Hlo= hlomuon= ^-11
Weak= weakmuon=2 10^-11

71. 3. Magnetic dipole moment
Hlo= hlomuon= ^-11
Weak= weakmuon=2 10^-11
HADRONIC 3-LOOPS
WEAK 2-LOOPS

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

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

74. 3. Magnetic dipole moment
Hlo= hlomuon= ^-11
Weak= weakmuon=2 10^-11

75. 3. Magnetic dipole moment
Model independent /Effective lagragians

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

77. 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

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

79. 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

80. 3. Magnetic dipole moment
Diagrams

81. 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

82. 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

83. 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

84. 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

85. 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 !

86. 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

87. 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…

88. 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

89. 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 !!!