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Neutrinos Theory

Neutrinos Theory. ~. Carlos Pena Garay IAS, Princeton. Plan. I. Neutrinos as Dirac Particles Neutrinos from earth and heavens Neutrinos as Majorana Particles. Plan. I. Neutrinos as Dirac Particles Making Neutrinos Neutrinos as Majorana Particles.

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Neutrinos Theory

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  1. Neutrinos Theory ~ Carlos Pena Garay IAS, Princeton Benasque

  2. Plan • I. Neutrinos as Dirac Particles • Neutrinos from earth and heavens • Neutrinos as Majorana Particles

  3. Plan • I. Neutrinos as Dirac Particles • Making Neutrinos • Neutrinos as Majorana Particles

  4. Nuclear b-decay

  5. Neutrinos are left-handed

  6. Neutrinos must be massless Helicity = Chirality (massless) All neutrinos left handed => massless If neutrinos are massive neutrino right-handed => Contradiction!

  7. Standard Model Exact Lepton number symmetry : terms never arise in perturbation theory Renormalizability : All gauge currents satisfy anomaly cancellation What about global symmetries : L is broken non perturbatively through the anomaly, but B-L is conserved to all orders : terms never arise in the Standard Model

  8. Anti-neutrinos are right-handed - CPT : nL => nR

  9. 3 neutrino families (flavors)

  10. Standard Model

  11. Global symmetries The results of charged-current experiments (until recently) were consistent with the existence of three different neutrino species with the separate conservation of Le, Lm and Lt.

  12. Massive Neutrinos : Dirac n(p,h) n(p,-h) CPT Boost, if m ≠ 0 Boost, if m ≠ 0 n(p,-h) n(p,h) CPT

  13. Standard Model + right handed

  14. Standard Model + right handed

  15. Standard Model + right handed Masses : Several distinctive features I am going to concentrate today is neutrino oscillations

  16. Parameters : Dirac Exercise

  17. Neutrino Oscillations X W nj lk li Uij* Ujk

  18. Neutrino Oscillations in Vacuum Due to different masses, different phase velocities Osc. Length : distance to come back to the initial state

  19. Production, propagation and detection as a unique process, where neutrinos are virtual particles propagating between production and detection : Neutrinos are described by propagators S (xP-xD) Consider finite production and detection regions and finite energy and momentum resolution

  20. If neutrinos can be considered real (on shell) and production, propagation, and detection can be treated separately Match initial and final conditions Wave packet formalism

  21. Correct calculation of the phase Phases calculated in the same space-time point Second summand is small by either one and/or the other term => standard result Oscillation effects disappear if neutrino masses are all equal

  22. Exercise : Write Pee, Pem Exercise : Minimal number of Pab to know all the others

  23. One example :

  24. Some real cases :

  25. Neutrino Oscillations in matter After a plane wave pass through a slab, the phase is shifted : p (x+(n-1)R) Net effect :

  26. Only the difference of potential is relevant Net effect :

  27. Two Neutrino Oscillations in matter Dm2 2E Dm2 4E ne nm - cos 2q + Vesin 2q sin 2q 0 ne nm d dt i = Dm2 4E sin22q sin22qm = ( cos2q - 2 2GFNeE/Dm2)2 + sin 22q Difference of the eigenvalues Dm2 2E ( cos2q - 2 2GFneE/Dm2)2 + sin 22q H2 - H1 =

  28. Resonance sin2 2qm n n In resonance: sin2 2qm = 1 sin2 2q= 0.08 sin2 2q= 0.825 Flavor mixing is maximal Level split is minimal ln = l0 cos 2q ~ Vacuum oscillation length ~ Refraction length ln / l0 ~ n E Resonance width: DnR = 2nR tan2q Resonance layer: n = nR + DnR

  29. Level crossing sin2 2q = 0.08 sin2 2q = 0.825 ne ne n2m n2m nm nm ln / l0 n1m n1m ln / l0 Small mixing Large mixing -if(t) n (t) = cosqan1m + sinqa n2m e

  30. Graphical interpretation n = (Re ne+nm, Im ne+nm, ne+ne - 1/2) elements of density matrix 2p lm B = (sin 2qm, 0, cos2qm) oscillation length lm = 2p/ D H Evolution equation dn dt = ( B x n) Coincides with equation for the electron spin precession in the magnetic field f= 2pt/ lm - phase of oscillations P = ne+ne = nZ+ 1/2 = cos2qZ/2

  31. A real case: solar neutrinos

  32. The Neutrino Matrix :SM + n mass 3 s ranges: ALL oscillation neutrino data BUT LSND

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