1. Several topics in Neutrino Physics Ali Ulvi Yılmazer Ali Ulvi Yılmazer Ankara University Ankara University Antalya - 2012 Antalya - 2012

2.  Recent progress on our understanding of the neutrinos is due mainly to experiments on neutrino oscillation.  There is now compelling evidence that atmospheric, solar, accelerator and reactor neutrinos change from one flavour to another.  This implies that neutrinos have masses and that leptons mix.  Neutrino physics now moved from dicovery stage to the precision measurement stage Neutrino oscillations Masses and Mixings

3. Neutrino Interactions in SM extended to take leptonic mixing into account

4. Leptonic mixing matrix : U PMNS Neutrino flavor state created in the decay is the state which is a superposition of the neutrino mass eigenstates. Inverse relation : Questions : Is the mixing matrix U PMNS unitary ? Is it unitary in N x N or 3 x 3 ?

5. Leptonic mixing matrix : U PMNS  LEP results on Z 0 decay indicates strongly that N = 3  However LSND result is not fully disfavored by MiniBooNE yet, so possibility of a light sterile neutrino(s) which does not have any weak couplings with SM particles !? Other physical motivations for such exotic sterile neutrinos come mainly from string cosmology, mirror sectors

6. Physically significant parameters of U PMNS  A complex N x N unitary mixing matrix U for N lepton generations may have :  a) Dirac case : N (N -1) / 2 mixing angles (N - 1)(N - 2) / 2 phase factors  b) Majorana case : N (N -1) / 2 mixing angles N (N - 1) / 2 phase factors Note : For N = 3 one gets one Dirac phase factor  and two Majorana phase factors    and  

7. Leptonic mixing matrix : U PMNS

8. Oscillation probability For the design and the analysis of the experiments the important factor is :

9. CP violation in neutrino oscillations Dirac phase factor  might cause CP violation. On the other hand the two Majorana phase factors  1 and  2 don’t enter the oscillation formula but they play important roles in 0  decays.

10. Present status  Matter effects are neatly taken into account (MSW effect for the solar case)  It is now understood that analysis assuming “Quasi – two neutrino oscillations” (namely one mass scale dominance) works very well (thanks to Nature !)  Assume CPT invariance, and 3 x 3 U PMNS matrix

11. Standard solar model for neutrino productions

12. Each experiment complement one another and a full picture of neutrino flavor change phenomenon is now better understood.

13. Present understanding Summary Table by B.Kayser (2008 - PDG)

14. Present understanding

15. Latest global fit Latest global fit for the solar, atmospheric, reactor and accelarator neutrino experiments ICHEP 2008 Summary Talk ( by Zhi-zong Xing ) (Also see: PDG 2010 Report : Neutrino mass, mixing and oscillations K.Nakamura and S.T.Petcov )

16. Masses and mixings Masses and mixings from B.Kayser 2006

17. LSND anomaly However a similar experiment KARMEN sees no indication for such an oscillation but does not exclude all the parameter space favored by LSND

18. LSND and KARMEN joint analysis This new large mass square difference is interpreted by several neutrino physicists via sterile neutrinos !!??

19. MiniBooNE result

20. Single and Double Beta Decays Absolute mass measurement; especially by famous tritium beta decay (Troitzk –Mainz) : Newly planned KATRIN Collaboration will start to take data soon and its aim is to probe neutrino masses down to 0.2 eV On the other hand there are 35 radioctive nuclei which can make 2  decays and for eight of them 2  have already been observed. But the  decay for them IS NOT OBSERVED YET.

21. Neutrinoless double beta decay Dominant mechanism for 0 , ; it does not exist unless

22. Role of Majorana phases Effective Majorana neutrino mass is defined as : and it does depend on the Majorana phases. Neutrinoless double beta decay is the single process which can definitely determine the Majorana character. Many projects exist : Heidelberg –Moscow, Cuoricino, and others

23. Constraints

24. Neutrino magnetic moment  A minimal extension of the standard model (with non- zero neutrino masses)yields a neutrino magnetic moment : Solar and reactor neutrino experiments; astrophysical and cosmological arguments bring bounds on its value :

25. Evolution equation (RSFP) The time evolution equation for the chiral components of the neutrinos in the case of two flavours :

26. Majorana case General magnetic moment matrix in the Dirac case : For the Majorana neutrinos the diagonal components are zero by the CPT theorem and

27. New resonances in addition to MSW In both cases there are several new resonances in addition to the MSW resonance. Hence the most interesting ones : MSW resonance : SFP Resonance :

28. RSFP allowed neutrino parameter space The allowed regions of neutrino parameter space at 95% CL. Columns show the results for the Cl, Ga, SK and SNO experiments respectively and each row corres- ponds to the  nu  B = 0,2,5,10 x10-7  Bohr) B values for Dirac (left) and Majorana (right) cases

29. Solar electron antineutrino flux If the neutrinos are Majorana type, first may change to inside the sun via SFP and then vacuum oscillation might yield Schematically the process is Hence the possible electron antineutrino flux on the Earth can be obtained by : ( first RSFP then vacuum osc. ) where the probability is given as

30. Absence of solar electron antineutrino flux from Absence of solar electron antineutrino flux from 8 B Expected electron antineutrino flux from 8 B for different  B values. The horizontal line shows the upper flux limit at SK Future observation of solar elecron antineutrinos at SK can be seen to be a signal of the Majorana character

31. Mass scale How far above the zero the whole pattern ?

32. Normal or Inverted Hierarchy How can we determine experimentally whether or not the mass spectrum is normal or not ? The answer : Design a LBL oscillation experiment and study the MSW effect of the earth crust.

33. Reasoning Difficulty : Amplitude depends again on sin  

34. Obtaining   from the solar and reactor data First assume CPT invariance Analysis of the solar and KamLAND data show that the allowed parameter space overlap but the best fit points are different. One idea to solve this behaviour is the nonzero value of the cross mixing angle.

35. KamLAND data and its   variation B.Balantekin + D.Yılmaz (2008)

36. Solar data and its   variation

37. Their best fit points changes

38. Conclusion : Best fit

39. Seesaw scenarios

40. Majorana neutrinos at the colliders

41. Cross section Inverse double beta decay process : Unpolarized cross section

42. Helicity amplitudes Helicity amplitudes ( Results in : Ş.Akaslan and A.U.Yılmazer Int.J.Mod.Phys.Lett.A, 2012 )

43. Conclusion There are still many open problems : More precise measurements of the mixing angles and other physical properties (e.g. OPERA experiment, TEXONO Collaboration and many others), CP violation, Majorana character, absolute mass scale, number of neutrino species, origin of tiny masses, leptogenesis in connection to baryon asymmetry, CPT and/or Lorentz invariance But experimental results certainly force us to go beyond the minimal Standard Model of particle physics.

44. THANKS

48. Motivations for the search of new bounds on the neutrino magnetic moment Checking of the new physics beyond the standard model ( SUSY, left-right symmetric models, extra dimensions, GUT’s, etc...) Astrophysical implications (direct probe to the interior of stars, supernovae, neutron stars, etc..) Implications on solar neutrino problem (RSFP)

49. Magnetic field in the solar interior  Standard Solar Model (SSM): Sun’s luminosity, temperature, mass, radius, nuclear chain reactions are perfectly understood.  SSM does not take into account the magnetic pressure or any impact of the magnetic field on the stellar dynamics.  So still little is known on the sun’s magnetic field.  But several models to inroduce magnetic field consistent with SSM and solar neutrino physics (MHD models, helioseismological studies, observations of solar oscilation frequency splitting)

50. Magnetic field profiles of the sun Magnetic field profiles : B 0 = B max = 300 k Gauss a) Wood-Saxon shape b) Gaussian shape

51. Resonant Spin Flavor Precession and Solar Neutrino Physics Global fit through the MSW enhanced neutrino oscillations of all solar neutrino experiments without RSFP is confirmed. Hence knowing that it is not dominant mechanism, one may explore what implications RSFP may still have. RSFP might be important in the pecision meaurements and analysis stage of the solar neutrino problem.

52. Dirac case For Dirac neutrinos : where V e and V  are the usual matter potantials for a neutral unpolarized medium given in terms of the electron and neutron densities in the Sun.

53. Numerical solution Time evolution equation is solved numerically and the allowed regions of neutrino oscillation parameter space are statistically analyzed at 95 % confidence level through the  - method based on the covariance matrix approach. Data and all other parameter values are taken from the Bahcall’s web page Typical Wood-Saxon and Gaussian profiles are used for the magnetic field of the Sun Dirac / Majorana cases are treated seperately.

54. Global analysis (Cl, Ga, SK, SNO, KamLAND) Allowed regions from the combined solar+new KamLAND spectral analysis at different  B values and at % 95 CL for the Dirac type neutrinos. Stars indicate best fit points

55. Some of RSFP implications  In the Dirac case the best fit point in the RSFP analysis of the neutrino parameter space shifted from LMA to SMA region as the    value is increased; this leads to an upper bound on   B < 1.0x10 -7  B x B Sun at 95 % CL  In the Majorana case, contrarily, the best fit point remained the same as  B is increased. However in this solution, the non-observability of electron antineutrino flux from the sun at SK, again brings an upper bound as   < 3.2x10-5  B x B Sun.

56. Further Results  In the analysis of the neutrino oscillations, at the first step, interaction between magnetic moment and sun’s magnetic field can safely be neglected.  However at the stage of precision measurements (all the lepton mixing angles and CP violation parameters in case of three generations) it might be inevitably taken into account which would make the analysis and measurements more difficult. But future experiments would not easily reach that precision to pinpoint the alternative solutions, other than the oscillation confirmed by KamLAND. (Balantekin-2006, Akhmedov et.al-2005…)

57. References on RSFP  [1] Okun et.al. Sov.J.Nucl.Phys. 44 (1989) 440  [2] Lim et.al. Phys. Rev. D 37 (1998) 1368  [3] Akhmedov, Phys.Lett. B 213 (1988) 64  [4] Wolfenstein. Phys. Rev. D 17 (1978) 2369 (1998)  [5] Mikheev+Smirnov, Nuvo Cim.C9 (1986) 17  [6] Bahcall, Neutrino Astrophysics (1989); web  [7] Balantekin et.al. Phys. Rev. D 41 (1990) 3583  [8] Kayser et.al., Physics of Massive Neutrinos (1989)  [9] Mohapatra et.al, Massive Neutrinos in Physics and Astrophysics (1998)  [10] Balantekin et.al. Phys. Rev. D 72 (2005) 033008  [11] Yilmazer et.al. J.Phys.G 31 (2005) 57; ibid 1123

58. Kinematics for polarized neutrino- electron scattering k k’ p’ x y z  s k : initial neutrino momentum k’: outgoing neutrino momentum p= 0 initial electron is rest p’ : recoiling electron’s momentum s : spin vector of rest electron s’: spin vector of recoil electron (specified via the initial directions as seen from the RF of recoil electron)  : azimuthal angle (nontrivially integrated out )

59. Michel-Wightman density matrix for the electron polarization In general : Spin four-vector is defined as a)For the initial electron which is rest in the laboratory :

60. b) For the recoiling electron RF : the frame in which the recoiling electron is rest ;

61. Polarization Density matrices  a) For the initial electron at rest in lab.  b) For the recoiling electron in the lab.

62. Differential cross sections in the lab. frame QED and Electroweak radiative corrections are ignored at the first step, which should be seriously taken always. Laboratory frame expressions :

63. Unpolarized cross sections

64. Fixed and free parameters in LAB frame calculations

65. Polarized crossed sections Notes : 1)A nontrivial integration over the azimuthal angle is necessary 2) Both weak and em terms depend on the initial and final electron polarizations

66. Polarization asymmetries Polarizations asymmetris can be defined with respect to initial or final electron polarizations s or s’ :

67. Parameters of asymmetries Note that initial and final electron spin polarizations are simply paremetrized as follows :

68. Preliminary results  Electroweak and electromagnetic terms separately depend on the spin polarizations of the initial and final recoil electrons. Not only numerical results but also analytic expressions can be obtained.  Suppression by polarization effects and also several asymmetries may help to differentiate the magnetic moment contribution.  Work is still going on ( almost finished )

69. THANKS

70. Global analysis Global fit for the solar, atmospheric, reactor and accelarator neutrino experiments