1. 1. Curriculum Académico y de Gestión 2. Curriculum Investigador 3. Proyecto Docente SuperB: Flavour Physics Workshop Tau Dipole Moments J. Vidal IFIC-Universitat de València-CSIC Spain Benasque, Spain, 18-21 January 2011

2. Benasque, Spain, January 2011J. Vidal2 Introduction Electric and magnetic dipole moments. Magnetic Dipole form factor Tau polarization as analyzer in e + e - collisions. Observables. Bounds Conclusions Outlin e Tau Dipole Moments

3. Benasque, Spain, January 2011J. Vidal3 In the Hamiltonian describing the interaction of a fermion with the electromagnetic field, the electric dipole moment is defined by the interaction term In the non-relativistic limit, it gives the classical interaction term Similarly, the magnetic dipole moment is given by the expression Which, in the non-relativistic limit, gives the classical interaction term - 1 2 e 2m2m Chirality flipping couplings

4. Benasque, Spain, January 2011J. Vidal4 The most general Lorentz invariant structure describing the interaction amplitude of a vector boson V and two fermions f + f -, on the mass shell, is given in terms a 6 independent form factors: With all the particles on-shell, the form factors F i only can be function of the fermion mass, m f, and the momentum q 2. If, in addition, the current J μ is conserved For the photon and q 2 =0, one gets: Charg e Magnetic Dip. Moment Electric Dip. Moment Anapole Moment

5. Benasque, Spain, January 2011J. Vidal5 Electric Dipole Moment (EDM) γ f f Symmetries CP odd (-) P oddr (-) T odd (-) In the SM only can be different of zero through vertex corrections with CKM matrix elements = 0 One has then to consider 3 loops for quarks and 4 loops for leptons. = 0 E.P.Shabalin ’78

6. Benasque, Spain, January 2011J. Vidal6 W. Bernreuther, M. Suzuki '91 PDG 2010 For quarks, at 3 loops Estimates in the SM: For leptons (electron), at 4 loops: For a fermion of mass m, the EDM generated at Λ- scale is assumed to scale as

7. Benasque, Spain, January 2011J. Vidal7 Still 16 orders of magnitude below the experimental limit If some signal is found in EDM observables New Physics ! PDG 2010

8. Benasque, Spain, January 2011J. Vidal8 The behaviour of Nature can be different. There are models where the rule is not satisfied Models with scalar leptoquarks W. Bernreuther, A. Brandenburg, P. Overmannn Phys. Lett. 1997 Conclusion: There is interest in searching for the electric dipole moments for each lepton independently Models where the EDM scales as cannot be ruled out See Oscar's Talk

9. Benasque, Spain, January 2011J. Vidal9 Magnetic Dipole Moment (MDM) The electron MDM is the magnitude best measured in physics Schwinger 1948 A lot of quantum corrections have been incorporated to the previous one The first calculation, at 1 loop, QED Precision: (3 / 10 10 ) 12 figures PDG 2010

10. Benasque, Spain, January 2011J. Vidal10 Similarly for the Muon Precision: (3 / 10 7 ) 9 figures is used to determine ! PDG 2010

11. Benasque, Spain, January 2011J. Vidal11 What is the present situation for the Tau? One order of magnitude below the first order QED contribution After the incorporation of higer order corrections, the theoretical value of the Tau MDM is known with high accuracy Eidelman, Passera 2008 3 loops 2 loops PDG 2010

12. Benasque, Spain, January 2011J. Vidal12 The experimental conditions for the determination of the Tau MDM are completely different than those for the same measurement for electrons and muons. The experimental bound on the Tau MDM reported by DELPHI, was done looking at the cross section of the process The Tau is a short living particle and this makes impossible any direct measurement of its interaction with an external electromagnetic field. The determination of the MDM must always be done looking at the effects of the electromagnetic interaction in e + e - taus (+ X) observables. These can be : 1.- Total production cross sections 2.- Angular distributions of Tau decay products at LEP, for energies 183- 208 GeV and assuming that any deviation of the SM value is due to the MDM contribution.

13. Benasque, Spain, January 2011J. Vidal13 The photon involved in the interaction is off-shell One of the taus is also off-shell DELPHI imposes cuts to the momentum transfer Which process was used for OPAL and L3 for their bounds ? PDG 2010

14. Benasque, Spain, January 2011J. Vidal14 OPAL and L3 use the process In that case the photon is on-shell but one of the Taus involved in the vertex is off-shell Some cuts are also imposed over the photon energy to limit the Tau off-shell effects. In all cases it is assumed that any deviation of the measured magnitude from the SM prediction it is due to the added MDM term. to get their bounds to the Tau MDM

15. Benasque, Spain, January 2011J. Vidal15 The MDM was defined with ALL particles on- shell The last results must be seen as bounds to New Physics contributions to the MDM The Dipole Form Factor generated by New Physics at Λ- scale (that we can assume of the order of TeV) will run as On these bases, a global (for weak-magnetic and γ -magnetic Dipole Moment) analysis with all available data gives the bound : One order of magnitude better than previous ones PDG 2010

16. Benasque, Spain, January 2011J. Vidal16 Let us change our point of view. In what follows we will focus our attention not in the determination of an “effective” coupling generated at a high scale but in the measurement of the Magnetic Dipole Form Factor of the Tau F 2 (q 2 ). With all massive particles on-shell, this is a well defined magnitude so that any deviation of the SM value can be unambiguously interpreted as a signal of New Physics. Furthermore, we will define dedicated observables which will be sensitive to the Magnetic Form Factor, with no contribution from other sectors of the theory. Is it possible to define a Magnetic Form Factor at q 2 ≠ 0 ?

17. Benasque, Spain, January 2011J. Vidal17 The electroweak contribution to the MFF, at one loop, with off-shell photons is a gauge dependent magnitude. It is not an observable ! Only in the q 2 0 limit the gauge independence is restored. The QED one loop contributions to the MFF F 2 (q 2 ) are gauge independent for any q 2 Contrary to non-abelian theories, not only S-matrix but QED Green functions, like the vertex from factors, are gauge-independent:

18. Benasque, Spain, January 2011J. Vidal18 Vacuum polarization Gauge independent Boxe s X Verte x Fermion self- energy + Gauge independent

19. Benasque, Spain, January 2011J. Vidal19 Only at q 2 =0 the MFF, F 2 (q 2 ), coincides with the magnetic anomaly, a τ. Then, we must know the behavior of F 2 (q 2 ) because this is the factor which enters in the amplitude. A direct one loop QED calculation of the Magnetic Form Factor gives the following result: Imaginary Part

20. Benasque, Spain, January 2011J. Vidal20 We have now the opportunity to see the behaviour of the form factor with the momentum q 2, for a pure abelian theory as QED, together with its strong dependence on the flavour (mass) of the fermion - For the τ, in our range of energy, the MFF value is about ¼ of the on-shell MDM. - The Schwinger term (order 0) is independent of the lepton mass while the MFF depends strongly with the mass of the interacting fermion. - For the electron this dependence is unobservable and goes quickly to 0 - For s>4m τ 2 an Imaginary part, of he same order, shows up that can be also measured

21. Benasque, Spain, January 2011J. Vidal21 For a SuperB factory with 10GeV, CM, one gets PDG 2010 Two orders of magnitude below present bounds

22. Benasque, Spain, January 2011J. Vidal22 X X The MFF is associated with the pure vertex contribution We do not want the ad-hoc removal of the QED box contribution to our observables. We have to look for a procedure to get rid of the box contributions We have to work on a resonance

23. Benasque, Spain, January 2011J. Vidal23 Tau Dipole moment measurements at a SuperB Factory on the top of the resonance = =X X

24. Benasque, Spain, January 2011J. Vidal24 We must see first the sensitivity of the different Tau polarization terms to Dipole Moments Then, we must study how to measure this polarization looking at the Tau decay products Deca y We only consider tau decays to charged hadrons because this channel allows the reconstruction of the tau direction (only one !) which is crucial to define our observables Production

25. Benasque, Spain, January 2011J. Vidal25 Longitudinal (L) Transverse (T) Normal (N)

26. Benasque, Spain, January 2011J. Vidal26 PTPT Im(d) PLPL PNPN Im(a)

27. Benasque, Spain, January 2011J. Vidal27 How to be sensitive to the real part of Dipole Moments detecting only one Tau? + a, axial coupling + Absorptive + a, axial coupling Two choices: Look at spin correlations in the measurement of both Taus Longitudinal polarized electron beam and single Tau observables In QED there are no axial couplings (unlike in the Z case) a

28. Benasque, Spain, January 2011J. Vidal28 Longitudinally polarized electrons. Cross sections X + and F 2 : flipping chirality terms F 1 : non-flipping chirality term Let us now see how these polarizations can be measured by looking at the angular distribution of Tau decay products + Terms not depending on λ

29. Benasque, Spain, January 2011J. Vidal29 Considering only Tau semileptonic decay channel and making the convolution of the production cross section with tau decay width, we get: For polarized electrons one has to subtract cross section for different electron polarization Spin analyze r

30. Benasque, Spain, January 2011J. Vidal30 Re (F 3 ) measurement The total integration over the angular variables of the Tau erases all the Longitudinal Polarization information Z + To increase the sensitivity for the Normal Polarization, one has to integrate as much as variables as possible, without erasing the signal. Then, integrating

31. Benasque, Spain, January 2011J. Vidal31 This asymmetry is not a genuine CP violating observable because it may contain signals from T odd terms. In order to define a true CP violating Observable one has to do the measurement for Taus and anti-Taus and sum them up:

32. Benasque, Spain, January 2011J. Vidal32 Where can we get a T odd signal from? Absorptive parts and axial coupling : Z exchange A detailed calculation of the contribution gives: For s=10 Gev., Two orders of magnitude below the expected sensitivity for the EDM

33. Benasque, Spain, January 2011J. Vidal33 Tau EDM bounds from SuperB Considering only the channels Three orders of magnitude better than present bounds from triple products PDG 2010

34. Benasque, Spain, January 2011J. Vidal34 Re (F 2 (q 2 )) determination For longitudinally polarized electrons, the Tau Longitudinal and Transverse Polarization is sensitive to the MDM 0 Asymmetric integration that erases sin Φ and keeps cos Φ

35. Benasque, Spain, January 2011J. Vidal35 Transverse Azimuthal Asymmetry Use F 1 =1, tree level, and assume that any other contribution will be of the same order than F 2 but chirality suppressed Look for other observable with a different combination of form factors F 1 and F 2 Better

36. Benasque, Spain, January 2011J. Vidal36 Longitudinal Polarization Z + Symmetric integration of the Tau polar angle erases all the information on the MDM. One must perform an asymmetric integration (Forward-Backward) of the Tau polar angle with respect to the direction of the incoming electron Integrating now the azimuthal angles Φ ± and keeping polar angles θ * ± one gets In that way the Transverse and Normal polarization terms, X +, Y +, are wiped out and only remains the Longitudinal polarized term

37. Benasque, Spain, January 2011J. Vidal37 Longitudinal Asymmetry: + -

38. Benasque, Spain, January 2011J. Vidal38 Weak contributions (Z exchange) For s=10 Gev., Contrary to what happens with the resonant contribution of this -mediated γ -Z contribution to the EDM (which is two orders of magnitude smaller), for the MDM it must be taken into account when extracting F 2 from longitudinal and transverse asymmetries for polarized electrons. Nevertheless, as the interference proceeds through the vector neutral current coupling to leptons, the structure of this amplitude is like the one for the contribution of the charge form factor F 1. We have thus shown that, with the proposed combination of asymmetries, Re{F 2 } can be separated out from other contributions without any ambiguities. The same combination of the two asymmetries able to cancel the contribution of F 1 automatically cancels the contribution of the Z interference too As a consequence,

39. Benasque, Spain, January 2011J. Vidal39 Non-polarized electron beams In absence of electron polarization, only the imaginary part of the Dipole Moments can be measured: Chirality suppressed Using similar techniques we can define the following Normal and Transverse Asymmetries sensitive to Electric and Magnetic Dipole Moments, respectively:

40. Benasque, Spain, January 2011J. Vidal40 CPCP CPCP No contribution from the Z- γ interference

41. Benasque, Spain, January 2011J. Vidal41 Result s Longitudinally polarized electrons are needed !

42. Benasque, Spain, January 2011J. Vidal42 Tau Dipole Moments can be measured without ambiguities (real and imaginary parts) in the SuperB Factory, with longitudinally polarized electron beams, with a precision which is better, by few orders of magnitude, than present bounds.

43. Benasque, Spain, January 2011J. Vidal43 What can we do if Longitudinally Polarized electrons are not available? Tau spin correlations

44. Benasque, Spain, January 2011J. Vidal44 LN, TN LL, TT, NN, TL Spin correlation terms Zero correlation terms for EDM and MDM with no P(-) source. No information neither on Im(d) nor on Im(F 2 ) from tau spin correlations

45. Benasque, Spain, January 2011J. Vidal45 CP(+), P(-) CP(-), P(+)

46. Benasque, Spain, January 2011J. Vidal46 Considering now the angular distribution of the decay products of both Taus, we can use similar techniques as used in the single tau polarization case. Then we are able to define dedicated Observables sensitive to Tau MDM and Tau EDM without any ambiguity. Contribution from the γ -Z interference are under control: - either they are very small and they are below the expected sensitivity ( LN and TN correlations) - or they cancel in the appropriate combination of asymmetries used to extract F 2, in a similar way as they did in the single tau polarization case.

47. Benasque, Spain, January 2011J. Vidal47 Non polarized electron beams

48. Benasque, Spain, January 2011J. Vidal48 Conclusions Tau Dipole Moments can be measured without ambiguities at SuperB factories with a precision which is better, by 2 orders of magnitude, than present bounds. Polarized electron beams are needed to be sensitive to the real part of the Dipole Moments in single tau decay observables Tau spin correlations can also do the job but probably with a more difficult experimental work (uncertainties). Observables with polarized electron beams have the best sensitivity and are independent of other high energy observables. The Tau MDM form factor can be measured for the first time in the SuperB factory. At least two SM/QED figures can be obtained.

49. Benasque, Spain, January 2011J. Vidal49 Thank you ! Tau Dipole Moments can be measured without ambiguities at SuperB factories with a precision which is better, by 2 orders of magnitude, than present bounds. Polarized electron beams are needed to be sensitive to the real part of the Dipole Moments in single tau decay observables Tau spin correlations can also do the job but probably with a more difficult experimental work (uncertainties). Observables with polarized electron beams have the best sensitivity and are independent of other high energy observables. The Tau MDM form factor can be measured for the first time in the SuperB factory. At least two SM/QED figures can be obtained.