1. Neutrino mass and mixing parameters - a short review - Eligio Lisi INFN, Bari, Italy Rencontres de MoriondMarch 2005 Special thanks to: G.L. Fogli, A. Marrone, A. Melchiorri, A. Mirizzi, D. Montanino, A.M. Rotunno, A. Palazzo 1

2. Outline: Overview of 3 mass-mixing parameters Constraints from oscillation searches Constraints from non-oscillation searches Combining oscill. & non-oscill. observables Beyond the standard 3 scenario (LSND) Conclusions 2 Organizers’ request: “Talk should be a short introduction aimed at PhD students in experimental (non-neutrino) particle physics”  I shall skip all refs. or details for experts/theorists, with apologies to colleagues (for more info, see Proceedings or ask me)

3. 3 mixing Neutrinos mix (as quarks do): The standard rotation ordering of the CKM matrix for quarks happens to be useful also for neutrinos: … but with very different angles: Only if s 2 13  0 one can hope to probe the CP-violating phase  (“holy grail” of future oscillation experiments  see Kayser’s talk) 3

4. mass 2 spectrum e   3 mass 2 spectrum and flavor content ( e   ) +m2+m2 m2m2 22 2 1 3 3 -m2-m2 Abs. scale Normal hierarchy Inverted hierarchy mass 2 splittings Absolute mass scale  unknown [but < O(eV)] Hierarchy [sign(∆m 2 )] unknown e content of 3 unknown [but < few%] (“solar” splitting) (“atmospheric” splitting) 4

5. 3 oscillations Flavor is not conserved as neutrinos propagate Oscill. phase: Two macroscopic oscillation lengths governed by  m 2 and  m 2, with amplitudes governed by  ij. Leading expt. sensitivities: (  m 2,  23,  13 ) (  m 2,  12,  13 ) (  m 2,  13 ) Atmospheric, K2K long baseline accelerator (a) Solar, KamLAND long baseline reactor (b) CHOOZ short-baseline reactor (a,b) (a) ( 1, 2 ) difference weakly probed (b) ( ,  ) difference not probed 5

6. Constraints on (  m 2,  23,  13 ) from SK + K2K + CHOOZ See talks by Sulak (SK) and Mariani (K2K) 6

7. Super-Kamiokande atmospheric For  13 ~0 and  m 2 ~0, a very simple formula fits all SK data (+ MACRO & Soudan2) 1st oscillation dip still visible despite large L & E smearing Strong constraints on the parameters (  m 2,  23 ) 7

8. Atmospheric oscillation evidence robust & confirmed with lab- in K2K Many interesting details depend on theoretical input & subleading effects Contours at 1, 2, 3  (1 dof). Note linear scale for  m 2 and sin 2  23, with 2nd octant of  23 unfolded 8

9. At the  m 2 scale of SK+K2K, nonobservation of e  e in the CHOOZ reactor experiment sets strong upper bounds on  13  SK+K2K+CHOOZ Growing literature & interest in subleading effects due to  13,  m 2, sign(  m 2 ),  But need very significant error reduction to probe them A challenge for future high-statistics experiments 9

10. Constraints on (  m 2,  12,  13 ) from solar + KamLAND See talks by Sulak (SK), Berger (kamLAND), Miknaitis (new SNO data) 10

11. Solar e  e, ,  vs atmospheric    : matter (MSW) effect Atmospheric  and  feel background fermions in the same way (through NC); no relative phase change (~ vacuum-like) But e, in addition to NC, have CC interac. with background electrons (density N e ). Energy difference: V =  2 G F N e Solar analysis must account for MSW effects in the Sun and in the Earth (Earth matter effects negligible for KamLAND reactor neutrinos) Solar+KamLAND combination provide evidence for V sun (not yet for V earth ) 11 ,  fermion Z W e e e e

12. Dramatic reduction of the (  m 2,  12 ) param. space in 2001-2003 (note change of scales) Cl+Ga+SK (2001) +SNO-I (2001-2002) +KamLAND-I (2002) +SNO-II (2003) Direct proof of solar e  ,  in SNO through comparison of 12 (+ confirmation of solar model)

13. … in 2004 (KamLAND-II with revised background): unique Large Mixing Angle solution, and another change of scale… + evidence for oscillatory effects in KamLAND reactor L/E spectrum What about MSW effects? 13

14. Exercise: (1) Change MSW potential “by hand,” V  a MSW V (2) Reanalyze all data with (  m 2,  12,a MSW ) free (3) Project (  m 2,  12 ) away and check if a MSW ~1 (… a way of “measuring” G F through solar neutrino oscillations …) Results: with 2004 data, a MSW ~1 confirmed within factor of ~2 and a MSW ~0 excluded  Evidence for MSW effects in the Sun But: expected subleading effect in the Earth (day-night difference) still below experimental uncertainties. 14

15. 2005 (last week): new data + detailed analysis from SNO   2004 2005 Solar Solar+KL Previous results basically confirmed Slightly higher ratio CC/NC ~ P( e  e ) Slight shift (<1  upwards) of allowed range for  12 15

16. 3 analysis of 2004 solar+KamLAND data (  13 free) Solar and KamLAND data also prefer  13 ~0 (nontrivial consistency with SK+CHOOZ) Bounds on (  m 2,  12 ) not significantly altered for unconstrained  13 16

17. “Grand Total” from global analysis of oscillation data 17

18. Marginalized  2 curves for each parameter (2004) 18

19. Numerical ±2  ranges (95% CL for 1dof), 2004 data: 19 Note: Precise values for  12 and  23 relevant for model building (see talk by Tanimoto)

20. Probing absolute masses through non-oscillation searches 20

21. Three main tools (m , m ,  ): 1)  decay: m 2 i  0 can affect spectrum endpoint. Sensitive to the “effective electron neutrino mass”: (most direct method) 2) 0 2  decay: Can occur if m 2 i  0 and =. Sensitive to the “effective Majorana mass” (and phases): (several talks this afternoon) 3) Cosmology: m 2 i  0 can affect large scale structures in (standard) cosmology constrained by CMB+other data. Probes: (see talk by Pastor) 21

22. Even without non-oscillation data, the (m , m ,  ) parameter space is constrained by previous oscillation results: Significant covariances Partial overlap between the two hierarchies Large m  spread due to unknown Majorana phases 22

23. But we do have information from non-oscillation experiments: 1)  decay: no signal so far. Mainz & Troitsk expts: m  < O(eV) 2)0 2  decay, no signal in all experiment, except in the most sensitive one (Heidelberg-Moscow). Rather debated claim. Claim accepted: m  in sub-eV range (with large uncertainties) Claim rejected: m  < O(eV). 3)Cosmology. Upper bounds:  < eV/sub-eV range, depending on several inputs and priors. E.g., 23

24. 0 2  claim rejected 0 2  claim accepted Cosmological bound dominates, but does not probe hierarchy yet Tension with cosmological bound (no combination possible at face value) But: too early to draw definite conclusions 24

25. E.g., if 0 2  claim accepted & cosmological bounds relaxed: Combination of all data (osc+nonosc.) possible Complete overlap of the two hierarchies (degenerate spectrum with “large” masses) High discovery potential in future (m , m ,  ) searches 25

26. Beyond three-neutrino mixing: LSND Many theoretical reasons to go beyond the standard 3 scenario A purely experimental reason: the puzzling LSND oscillation claim  M 2 ~O(eV 2 ) with very small mixing? Solutions invented so far (new sterile states, new interactions or properties) seem rather “ad hoc” and/or in poor agreement with world neutrino data If MiniBoone (talk by McGregor) confirms LSND this year, many ideas will be revised, and the neutrino session of Moriond 2006 will be fun! 26

27. 27 Conclusions Neutrino mass & mixing: established fact Determination of (  m 2,  12 ) and (  m 2,  23 ) Upper bounds on  13 Oscillation-induced spectral distortions Direct evidence for solar flavor change Evidence for matter effects in the Sun Upper bounds on masses in (sub)eV range ………… Determination of  13 Leptonic CP violation Absolute m from  -decay and cosmology Test of 0 2  claim and of Dirac/Majorana Matter effects in the Earth Normal vs inverted hierarchy Beyond the standard 3 scenario Deeper theoretical understanding ………… Great progress in recent years … … and great challenges for the future!