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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 ~ Carlos Pena Garay IAS, Princeton Benasque
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
Neutrinos must be massless Helicity = Chirality (massless) All neutrinos left handed => massless If neutrinos are massive neutrino right-handed => Contradiction!
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
Anti-neutrinos are right-handed - CPT : nL => nR
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.
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
Standard Model + right handed Masses : Several distinctive features I am going to concentrate today is neutrino oscillations
Parameters : Dirac Exercise
Neutrino Oscillations X W nj lk li Uij* Ujk
Neutrino Oscillations in Vacuum Due to different masses, different phase velocities Osc. Length : distance to come back to the initial state
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
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
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
Exercise : Write Pee, Pem Exercise : Minimal number of Pab to know all the others
Neutrino Oscillations in matter After a plane wave pass through a slab, the phase is shifted : p (x+(n-1)R) Net effect :
Only the difference of potential is relevant Net effect :
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 =
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
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
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
The Neutrino Matrix :SM + n mass 3 s ranges: ALL oscillation neutrino data BUT LSND