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Neutrino Phenomenology

Neutrino Phenomenology. Boris Kayser Scottish Summer School August 10, 2006 +. What We Have Learned.  3.  3. m 2 atm.  2.  2. m 2 sol. m 2 sol. }. }.  1.  1. ~. ~. m 2 sol = 8.0 x 10 –5 eV 2 , m 2 atm = 2.7 x 10 –3 eV 2. The (Mass) 2 Spectrum. or.

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Neutrino Phenomenology

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  1. Neutrino Phenomenology Boris Kayser Scottish Summer School August 10, 2006 +

  2. What We Have Learned

  3. 3 3 m2atm 2 2 m2sol m2sol } } 1 1 ~ ~ m2sol = 8.0 x 10–5 eV2, m2atm = 2.7 x 10–3 eV2 The (Mass)2 Spectrum or (Mass)2 m2atm Inverted Normal Are there more mass eigenstates, as LSND suggests?

  4. Leptonic Mixing • This has the consequence that — • |i> =  Ui |> . • Flavor- fraction of i = |Ui|2 . • When a i interacts and produces a charged lepton, the probability that this charged lepton will be of flavor  is |Ui|2 . 

  5. sin213 2 3 } m2sol 1 m2atm or (Mass)2 m2atm 2 } m2sol 3 1 sin213 [|Ui|2] [|Ui|2] e [|Uei|2] The spectrum, showing its approximate flavor content, is Inverted Normal

  6. Bounded by reactor exps. with L ~ 1 km From max. atm. mixing, { From (Up) oscillate but (Down) don’t { In LMA–MSW, Psol(e e) = e fraction of 2 From distortion of e(solar) and e(reactor) spectra { From max. atm. mixing, 1+ 2 includes (–)/√2 3 m2atm (Mass)2 2 } m2sol 1 [|Ui|2] [|Ui|2] e [|Uei|2]

  7. The 3 X 3 Unitary Mixing Matrix Caution: We are assuming the mixing matrix U to be 3 x 3 and unitary. Phases in U will lead to CP violation, unless they are removable by redefining the leptons.

  8. – Ui  l W+Hi  W+ Ui describes — – i l When i  eii , Ui  ei Ui When l   ei l ,Ui  e–i Ui – – Thus, one may multiply any column, or any row, of U by a complex phase factor without changing the physics. Some phases may be removed from U in this way.

  9. T i = ic = Ci Exception: If the neutrino mass eigenstates are their own antiparticles, then — Charge conjugate One is no longer free to phase-redefine iwithout consequences. U can contain additional CP-violating phases.

  10. How Many Mixing Angles and CP Phases Does U Contain? Real parameters before constraints: 18 Unitarity constraints — Each row is a vector of length unity: – 3 Each two rows are orthogonal vectors: – 6 Rephase the three l : – 3 Rephase two i ,if i  i: – 2 Total physically-significant parameters: 4 Additional (Majorana) CP phases ifi = i : 2

  11. How Many Of The Parameters Are Mixing Angles? The mixing angles are the parameters in U when it is real. U is then a three-dimensional rotation matrix. Everyone knows such a matrix is described in terms of 3 angles. Thus, U contains 3 mixing angles. Summary CP phases if i = i CP phases if i  i Mixing angles 3 1 3

  12. The Mixing Matrix Solar Atmospheric Cross-Mixing cij cos ijsij sin ij Majorana CP phases 12 ≈ sol ≈ 34°,23 ≈ atm ≈ 37-53°, 13 < 10°  would lead to P() ≠ P().CP But note the crucial role of s13 sin 13. ~

  13. The Majorana CP Phases The phase i is associated with neutrino mass eigenstate i: Ui = U0i exp(ii/2) for all flavors . Amp() =  Ui*exp(– imi2L/2E) Ui is insensitive to the Majorana phases i. Only the phase  can cause CP violation in neutrino oscillation. i

  14. The Open Questions

  15. What is the absolute scale of neutrino mass? • Are neutrinos their own antiparticles? • Are there “sterile” neutrinos? We must be alert tosurprises!

  16. What is the pattern of mixing among the different types of neutrinos? • What is 13? Is 23 maximal? • Is the spectrum like or ? • Do neutrinos violate the symmetry CP? Is P( )  P( ) ?

  17. What can neutrinos and the universe tell us about one another? • Is CP violation by neutrinos the key to understanding the matter – antimatter asymmetry of the universe? • What physics is behind neutrino mass?

  18. The Importance of the Questions, and How They May Be Answered

  19. } 3  Flavor Change m2atm (Mass)2 2 m2sol 1 } Tritium Decay, Double  DecayCosmology ?? 0 What Is the Absolute Scale of Neutrino Mass? How far above zero is the whole pattern?

  20. A Cosmic Connection Oscillation Data  m2atm < Mass[Heaviest i] • Cosmological Data + Cosmological Assumptions  •  mi < (0.17 – 1.0) eV. • Mass(i) • If there are only 3 neutrinos, • 0.04 eV < Mass[Heaviest i] < (0.07 – 0.4) eV • m2atm Cosmology ( ) Seljak, Slosar, McDonald Pastor ~

  21. Are Neutrinos Majorana Particles?

  22. How Can the Standard Model be Modified to Include Neutrino Masses?

  23. l+ l+ (—) (—) X Majorana Neutrinos or Dirac Neutrinos? • The S(tandard) M(odel) • and • couplings conserve the Lepton Number L defined by— • L() = L(l–) = – L() = – L (l+) = 1. • So do the Dirac charged-lepton mass terms • mllLlR l–  W Z   – – ml

  24. (—) (—)   mD X • Original SM: m = 0. • Why not add a Dirac mass term, • mDLR • Then everything conserves L, so for each mass eigenstate i, • i ≠ i (Dirac neutrinos) • [L(i) = – L(i)] • The SM contains no R field, only L. To add the Dirac mass term, we had to add Rto the SM. —

  25. —   X mR • Unlike L, R carries no Electroweak Isospin. • Thus, no SM principle prevents the occurrence of the Majorana mass term • mRRcR • But this does not conserve L, so now • i = i (Majorana neutrinos) • [No conserved L to distinguish i from i] • We note that i = i means — • i(h) = i(h) • helicity — — — —

  26. The objects R and Rcin mRRcR are not the mass eigenstates, but just the neutrinos in terms of which the model is constructed. mRRcR induces R Rc mixing. As a result of K0 K0 mixing, the neutral K mass eigenstates are — KS,L  (K0  K0)/2 . As a result of R Rc mixing, the neutrino mass eigenstate is — i =R +Rc = “  +  ” .

  27. Many Theorists Expect Majorana Masses The Standard Model (SM) is defined by the fields it contains, its symmetries (notably Electroweak Isospin Invariance), and its renormalizability. Leaving neutrino masses aside, anything allowed by the SM symmetries occurs in nature. If this is also true for neutrino masses, then neutrinos have Majorana masses.

  28. The presence of Majorana masses • i = i (Majorana neutrinos) • L not conserved — are all equivalent Any one implies the other two.

  29. Electromagnetic Properties of Majorana Neutrinos • Majorana neutrinos are very neutral. • No charge distribution: [ ] + – – CPT = ≠ + – + But for a Majorana neutrino, ] [ ] [ i i = CPT

  30. No magnetic or electric dipole moment: ] [ ] [   = – e– e+ But for a Majorana neutrino, i i = Therefore, [i] [i] = 0  = 

  31. e 2  e 1 Transition dipole moments are possible, leading to — One can look for the dipole moments this way. To be visible, they would have to vastly exceed Standard Model predictions.

  32. i Lab. Frame + + How Can We Demonstrate That i = i? • We assume neutrino interactions are correctly described by the SM. Then the interactions conserve L ( l– ;  l+). • An Idea that Does Not Work • [and illustrates why most ideas do not work] • Produce a i via— Spin Pion Rest Frame  i + + Give the neutrino aBoost: (Lab) > ( Rest Frame)

  33. The SM weak interaction causes— + —  i Target at rest Recoil i = i means that i(h) = i(h). helicity   — i , i  i will make + too.

  34. Minor Technical Difficulties • (Lab) > ( Rest Frame) E(Lab) E( Rest Frame) mm •  E(Lab) > 105TeV if m ~ 0.05 eV • Fraction of all  – decay i that get helicity flipped • ( )2 ~ 10-18 if m~ 0.05 eV Since L-violation comes only from Majorana neutrino masses, any attempt to observe it will be at the mercy of the neutrino masses. (BK & Stodolsky)  > i ~ i m E( Rest Frame) i i

  35. i e– e– i  i W– W– Nuclear Process Nucl’ Nucl The Idea That Can Work — Neutrinoless Double Beta Decay[0] By avoiding competition, this process can cope with the small neutrino masses. Observation would imply L and i = i .

  36. e– e– ()R L 0 u d d u W W ()R L : AMajorana mass term Whatever diagrams cause 0, its observation would imply the existence of aMajorana mass term: Schechter and Valle

  37. i In SM vertex e– e– i  Mixing matrix Uei Uei i W– W– Nuclear Process Nucl’ Nucl Mass (i) the i is emitted [RH + O{mi/E}LH]. Thus, Amp [i contribution]  mi Amp[0]   miUei2 m i

  38. The proportionality of 0 to mass is no surprise. 0 violates L. But the SM interactions conserve L. The L – violation in 0 comes from underlying Majorana mass terms.

  39. Backup Slides

  40. 2 sol < 3 1 atm atm 2 sol < 3 1 How Large is m? • How sensitive need an experiment be? • Suppose there are only 3 neutrino mass eigenstates. (More might help.) • Then the spectrum looks like — or

  41. m   miUei2 The e (top) row of U reads — 12 ≈  ≈ 34°, but s132 < 0.032

  42. { Majorana CP phases sol < atm m0 • If the spectrum looks like— • then– • m≅ m0[1 - sin22 sin2(–––––)]½ . • Solar mixing angle • m0 cos2 m  m0 • At 90% CL, • m0 > 46 meV (MINOS); cos2 > 0.28 (SNO), • so • m > 13 meV . 2–1 2

  43. atm sol < • If the spectrum looks like • then — • 0 < m < Present Bound [(0.3–1.0) eV] . • (Petcov et al.) • Analyses of m vs. Neutrino Parameters • Barger, Bilenky, Farzan, Giunti, Glashow, Grimus, BK, Kim, Klapdor-Kleingrothaus, Langacker, Marfatia, Monteno, Murayama, Pascoli, Päs, Peña-Garay, Peres, Petcov, Rodejohann, Smirnov, Vissani, Whisnant, Wolfenstein, • Review of  Decay: Elliott & Vogel Evidence for 0 with m = (0.05 – 0.84) eV? Klapdor-Kleingrothaus

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