Neutrino Phenomenology

1. Neutrino Phenomenology Boris Kayser Scottish Summer School August 11, 2006 +

2. At least 4 mass eigenstates, hence at least 4 flavors. Are There Sterile Neutrinos? Rapid neutrino oscillation reported by LSND —  1eV2 in contrast to m2atm = 2.7 x 10–3 eV2 > m2sol = 8 x 10–5 eV2 Measured (Z) only 3 different active neutrinos. At least 1sterile neutrino.

3. Is the so-far unconfirmed oscillation reported by LSND genuine? MiniBooNE aims to definitively answer this question.

4. What Is the Pattern of Mixing? • How large is the small mixing angle 13? We know only that sin213 < 0.032 (at 2). The theoretical prediction of 13is not sharp: Present bound ( ) Albright & Chen sin213

5. The Central Role of 13 If sin213 > (0.0025 – 0.0050), we can study both of these issues with intense but conventional  and  beams. Both CP violation and our ability to tell whether the spectrum is normal or inverted depend on 13. Determining 13 is an important stepping-stone.

6. How 13 MayBe Measured sin213 3 m2atm (Mass)2 2 } m2sol 1 sin213 = Ue32 is the small e piece of 3. 3 is at one end of m2atm. We need an experiment with L/E sensitive to m2atm (L/E ~ 500 km/GeV), and involving e.

7. Complementary Approaches Reactor Experiments Reactore disappearance while traveling L ~ 1.5 km. This process depends on 13 alone: P(e Disappearance) = = sin2213 sin2[1.27m2atm(eV2)L(km)/E(GeV)]

8. Accelerator Experiments Accelerator  e while traveling L > Several hundred km. This process depends on 13, 23, on whether the spectrum is normal or inverted,and on whether CP is violated through the phase.

9. Neglecting matter effects (to keep the formula from getting too complicated): (—) The accelerator long-baseline e appearance experiment measures — The plus (minus) sign is for neutrinos (antineutrinos).

10. The Mass Spectrum: or ? Generically, grand unified models (GUTS) favor — GUTS relate the Leptons to the Quarks. is un-quark-like, and would probably involve a lepton symmetry with no quark analogue.

11. Exploit the fact that, in matter, ( ) e e W ( ) e e raises the effective mass of e, and lowers that of e. How To Determine If The Spectrum Is Normal Or Inverted This changes both the spectrum and the mixing angles.

12. E6 GeV Matter effects grow with energy E. At E ~ 1 GeV, matter effects  sin2 2M = sin2 213 [ 1 + S ] . Sign[m2( ) - m2( )] At oscillation maximum, P(e) >1 ; P(e)<1 ; ~ (—) (—) { Note fake CP violation. In addition, { ( ) PHi E(e) >1 ; PLo E(e) <1 ; Mena, Minakata, Nunokawa, Parke

13. CP Violation and the Matter-Antimatter Asymmetry of the Universe

14. Leptonic CP Violation • Is there leptonic CP, or is CP special to quarks? • Is leptonic CP, throughLeptogenesis, the origin of theMatter-antimatterasymmetry of the universe?

15. Look forP( )  P( ) How To Search for Leptonic CP “   ”is a different process from   even when i= i e  - e-  Source Detector “ e  ” + e+  Source Detector

16. CPT: P() = P()  P() = P() No CP violation in a disappearance experiment. But if is present, P(e)  P(e): Note that all mixing angles must be nonzero for CP.

17. Separating CP From the Matter Effect Genuine CP and the matter effect both lead to a difference between  and  oscillation. But genuine CP and the matter effect depend quite differently from each other on L and E. To disentangle them, one may make oscillation measurements at different L and/or E.

18. What Physics Is Behind Neutrino Mass?

19. The See-Saw Mechanism — A Summary — This assumes that a neutrino has botha Majorana mass term mRRcRand a Dirac mass term mDLR. No SM principle prevents mRfrom being extremely large. But we expect mD to be of the same order as the masses of the quarks and charged leptons. Thus, we assume that mR >> mD.

20.     When We have 4 mass-degenerate states: This collection of 4 states is a Diracneutrino plus its antineutrino.

21.   When= We have only 2 mass-degenerate states: This collection of 2 states is a Majorananeutrino.

22. N mN ~ mR – Splitting due to mR Dirac neutrino  m ~ mD2 / mR – What Happens In the See-Saw? • The Majorana mass term splits a Dirac neutrino into two Majorana neutrinos. Note that mmN  mD2  mq or l2. See-Saw Relation

23. { Familiar light neutrino  } Very heavy neutrino N The See-Saw Relation

24. Predictions of the See-Saw • Each i =i (Majorana neutrinos) • The light neutrinos have heavy partners N • How heavy?? • mN ~ ––––– ~ –––––– ~ 1015 GeV • Near the GUT scale. – m2top m2top m0.05 eV Coincidence??

25. A Possible Consequence of the See-Saw — Leptogenesis The heavy see-saw partners N would have been made in the hot Big Bang. Then, being very heavy, they would have decayed. The see-saw model predicts — Nl- + … and Nl+ + … If there was CP in these leptonic processes, then unequal numbers of leptons and antileptons would have been produced. Perhaps this was the origin of today’s matter-antimatter asymmetry.

26. Enjoy The Rest Of The School!

27. Backup Slides

28. Here atm lies between the (very nearly equal) 31 and 32. This measurement determines sin2223, but if 23  45°, there aretwo solutions for 23: 23 and 90° – 23. A reactor experiment may be able to resolve this ambiguity. • What is the atmospheric mixing angle 23?

29. Assumes sin2223 = .95  .01 23 Sensitive to sin2213 = 0.01 (McConnel, Shaevitz)