1 Neutrino Phenomenology Boris Kayser Scottish Summer School August 11,

2 Are There Sterile Neutrinos? Rapid neutrino oscillation reported by LSND —  1eV 2 in contrast to >  m 2 sol = 8 x 10 –5 eV 2  m 2 atm = 2.7 x 10 –3 eV 2 At least 4 mass eigenstates, hence at least 4 flavors. Measured  (Z  ) only 3 different active neutrinos. At least 1 sterile 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 sin 2  13 < (at 2  ). The theoretical prediction of  13 is not sharp: Present bound Albright & Chen ( ) sin 2  13

The Central Role of  13 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. If sin 2  13 > ( – ), we can study both of these issues with intense but conventional and beams.

6 sin 2  13 =  U e3  2 is the small e piece of 3. 3 is at one end of  m 2 atm.  We need an experiment with L/E sensitive to  m 2 atm ( L/E ~ 500 km/GeV), and involving e.  m 2 atm    (Mass) 2  m 2 sol } sin 2  13 How  13 May Be Measured

7 Complementary Approaches Reactor e disappearance while traveling L ~ 1.5 km. This process depends on  13 alone: P( e Disappearance) = = sin 2 2  13 sin 2 [1.27  m 2 atm (eV 2 )L(km)/E(GeV)] Reactor Experiments

8 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 . Accelerator Experiments

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

10 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. The Mass Spectrum: or ?

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

12 Matter effects grow with energy E. At E ~ 1 GeV, matter effects  sin 2 2  M = sin 2 2  13 [ 1 + S ]. Sign[m 2 ( ) - m 2 ( )] At oscillation maximum, P(   e )>1 ; P(   e )<1 ; ~ (—)(—) E 6 GeV (—)(—) { Note fake CP violation. In addition, P Hi E (   e ) >1 ; P Lo 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, through Leptogenesis, the origin of the Matter - antimatter asymmetry of the universe?

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

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 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. Genuine CP and the matter effect both lead to a difference between and oscillation.

18 What Physics Is Behind Neutrino Mass?

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

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

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

22 Splitting due to m R Dirac neutrino N m N ~ m R – m ~ m D 2 / m R – The Majorana mass term splits a Dirac neutrino into two Majorana neutrinos. What Happens In the See-Saw? See-Saw Relation Note that m m N  m D 2  m q or l 2. See-Saw Relation

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

24 Predictions of the See-Saw  Each i = i (Majorana neutrinos)  The light neutrinos have heavy partners N How heavy?? m N ~––––– ~ –––––– ~ GeV Near the GUT scale. m 2 top 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  - + … and N  + + … 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 This measurement determines sin 2 2  23, but if  23  45°, there are two solutions for  23 :  23 and 90° –  23. Here  atm lies between the (very nearly equal)  31 and  32. A reactor experiment may be able to resolve this ambiguity.  What is the atmospheric mixing angle  23 ?

29  23 Assumes sin 2 2  23 =.95 .01 Sensitive to sin 2 2  13 = 0.01 (McConnel, Shaevitz)