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NEUTRINO MASSES AND MIXING ANGLES theory confronts experiments

NEUTRINO MASSES AND MIXING ANGLES theory confronts experiments. Ferruccio Feruglio Padova. IFT Mini Workshop on Neutrino Physics Madrid May 18-20 2005. PREMISE. it does not exist! Neither for neutrinos nor for charged fermions. We lack a unifying principle.

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NEUTRINO MASSES AND MIXING ANGLES theory confronts experiments

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  1. NEUTRINO MASSES AND MIXING ANGLES theory confronts experiments Ferruccio Feruglio Padova IFT Mini Workshop on Neutrino Physics Madrid May 18-20 2005

  2. PREMISE it does not exist! Neither for neutrinos nor for charged fermions. We lack a unifying principle. theory of neutrino masses like weak interactions before the electroweak theory all fermion-gauge boson interactions in terms of 2 parameters: g and g’ gauge invariance ? Yukawa interactions between fermions and spin 0 particles: many free parameters (up to 22 in the SM!) Only ideas and prejudices about neutrino masses and mixing angles No well-defined program a priori

  3. Assume a timescale of ten years from now • -- What do we need from experiments? • - What are the priorities? • - What are the desirable experimental precisions? SUMMARY • Check or disprove LSND • Push sensitivity to in 0 to the limit • [+ help from cosmology if negative result] • Sensitivity/precision on and of significant • impact on theory’s development:

  4. 1. Check LSND How many light neutrinos? 1st pillar of any model

  5. 3 active neutrinos (invisible Z width) • all experiments but LSND explained by 3 LSND 3 + [at least] 1 • inclusion of worsens the fits • solar: • atm: favoured over - zenith angle dependence of high-energy [SK,MACRO] 3 (no matter effects for ) - no NC interactions for [SK] - -like CC events [SK] 2 • 2+2 and 3+1 fits have a poor quality [Bahcall&Pena-Garay 2003] [Cirelli,Marandella,Strumia,Vissani 2004] • WMAP + LSS [Hannestad&Raffelt 2004 Crotty, Lesgourgues, Pastor 2004] • from now on: 3 light assumed • LSND soon checked by MiniBooNE (1st event September 2002) no room for LSND with 3 (CPT violation disfavoured by now) [Pakvasa&Valle 0301061, Barenboim, Borissov, Lykken 0212116]

  6. 2. Sensitivity to in 0 L violated or not? 2nd pillar of any model

  7. L Most plausible explanation of m << mf : leading L-violating operator smallness of due to [Buchmuller, Di Bari, Plumacher 0406014 Akhmedov, Frigerio, Smirnov 0305322 Broncano, Gavela, Jenkins 0307058 Hambye 0412053, Joaquim 0501221] [GUT scale, see-saw, leptogenesis…] L violation expected at some level - global symmetries are broken by quantum gravity - B/L violated in all attempts to unify fundamental interactions - B/L broken by anomalies already in the SM but p-decay still unobserved! • oscillations are insensitive to L violation • L violation can be tested in 0 decay [90%CL] uncertainty from nuclear matrix elements [Bilenky, Petcov 0405237 Bilenky 0504075]

  8. expected range of can be predicted from mee (eV) Future expected sensitivity on : CUORE 130Te (30-50) meV Majorana 76Ge (20-70) meV GERDA 76 Ge (90-290) meV (phase II) 10 meV (phase III ?) Lightest neutrino mass (eV) [F, Strumia, Vissani 2003 Petcov&Pascoli 0310003 Bilenky 0403245 Bahcall, Murayama, Pena-Garay 0403167 Joaquim 0304267] positive signal: -- L violation -- degenerate spectrum or inverted hierarchy negative signal: -- worst case -- help from cosmology needed to constrain at least the type of spectrum -- not satisfactory: any attempt to further improve the sensitivity welcome -- L conserved still an option next CMB satellite + weak grav. lensing + improved galaxy survey

  9. How to explain if L is conserved ? [smallest ratio is 1/100 for charged fermions in same gen.] Interesting attempts in models with extra dimensions [Dienes, Dudas, Gherghetta, Arkani-Hamed,Dimopoulos, Dvali, March-Russell, Barbieri, Creminelli, Strumia] large ED: standard Yukawa couplings to a singlet fermion who lives in the bulk [Lukas, Ramond, Romanino, Ross 2001 Cacciapaglia, Cirelli, Romanino 0302246] no experimental hints from oscillations effects subdominant, if present dimension 5, L-violating operators not sufficiently suppressed by alternative models: warped compactifications, L gauged in the bulk,… not fully realistic in their minimal realization [Grossman&Neubert’99 Gherghetta 0312392]

  10. Model building in two pages hierarchies in fermion spectrum quarks leptons perhaps less pronounced in neutrino sector in modern model building we have two ways of understanding

  11. are small breaking terms of an approximate flavour symmetry [Froggatt, Nielsen 1978] example in QED when the theory becomes invariant under a flavour symmetry F very appealing approach, unfortunately freedom is huge breaking terms from SSB, from radiative corrections, ad-hoc explicit breaking symmetries global or local continuous or discrete no compelling model from data at the moment general questions -- can we establish some general result, independent on details of model building? -- how can data help in uncovering the right picture? [more on this later on…]

  12. are small due to geometry [unknown at present] a four-dimensional description of particle interactions might break down • Large Extra Dimensions flat zero mode for • localized fermion zero modes extra dimension could be tiny • Yukawa coupling in string theory matter as twisted states in orbifold compactification of heterotic string matter from intersecting D branes in type IIA strings Ibanez; Hamidi, Vafa; Dixon, Friedan, Martinec, Shenker; Casas, Munoz; Cremades, Ibanez, Marchesano; Abel, Owen -- it could provide an explanation to Ng =3 -- relation to flavour symmetries possible but not straightforward -- connection with data unclear, worth to explore

  13. too many models. Here: try to classify models by their predictions Present and (near) future sensitivities [Strumia, Vissani 0503246, Gonzales-Garcia 0410030, Maltoni, Schwetz, Tortola, Valle 0405172] LBL conventional beams superbeams escattering rate of pp neutrinos to 1% down by about a factor 2: challenging LBL, ChoozII superbeams down by about a factor 2 superbeams > 10 yr > 10 yr

  14. significant level of precision for model building most of existing models predict ``normal’’ models only in ``special’’ models either of these conditions is violated define: ``tiny’’ ``maximal’’

  15. normal models: some examples -- degenerate spectrum [Hall, Murayama, Weiner 2000 De Gouvea, Murayama 0301050 Nir, Shadmi 2004] can be produced in part by the see-saw • anarchy accidental fortuitous • flavour democracy [Fritzsch, Xing] [estimates by allowing 3 exp. and ( factors ½ and 2) th. uncertainties]

  16. inverted hierarchy • the best we have, at present corrections << |a|, |b| - leading order determined by either with or without see-saw • leading order it’s off by 6 good! large 23 expected, maximal only by a fine-tuning • turning SB terms on off by a factor > 10

  17. substantial contribution to from charged leptons needed standard parametrization by expanding to 1st order in [Frampton, Petcov, Rodejohann 0401206 Altarelli, F, Masina 0402155 Romanino 0402508] if, by analogy with the quark sector: 1.4 0.25 0.1 excluded by tan212<0.3 excluded by tan212>0.64 [right amount] [Raidal 0404046 Minakata, Smirnov 0405088 Antush, King, Mohapatra 0504007] 0.05 0 1 3 > 0.1 expected 0 1

  18. Normal Hierarchy • Several viable mechanisms for large • and small but • see-saw dominance of light equally coupled to and large 23 expected, maximal only by a fine-tuning [King] • lopsided structure of or/and : [Albright, Barr Altarelli, F] [1st order in ] -dominated e-dominated if we make a similar estimate in the quark sector 1 3 not tiny, barring cancellations

  19. Ue3 in models with U(1) flavour symmetry [SS] [SS] [SS] [NoSS]  optimised case by case to fit [Isabella Masina] inverse hierarchy=IH anarchy=A semianarchy=SA normal hierarchy=H matrix elements up to unknown O(1) coeff.

  20. Why and are difficult to achieve? [RGE do not work. Casas, Espinosa, Navarro 0306243] in some symmetry limit? of great help in our search for a unifying principle… If the symmetry is realistic can never arise in the limit of exact symmetry charged lepton mass matrix symmetry breaking effects: vanishing when flavour symmetry F is exact symmetric limit similarly for neutrinos

  21. realistic ml0 has rank ≤1 undetermined [omitting phases] undetermined determined entirely by breaking effects (different, in general, for  and e sectors) vacuum alignment problem should have specific magnitudes and relative directions in flavour space. if symmetry breaking is spontaneous

  22. requirements for ``special’’ models based on a SB flavour symmetry • alignment should be natural no ad-hoc relations desired VEVs from most general V in a finite region of parameter space • alignment not spoiled by sub-leading terms from higher-dimensional operators compatible with gauge and flavour symmetries often then needed for special models leading order • alignment compatible with mass hierarchies should vanish in the limit of exact symmetry

  23. example [only lepton sector] [Altarelli, F. 0504165] group of even permutations of four objects flavour symmetry [Ma, Rajasekaran 2001; Babu, Ma, Valle 2003; Hirsch, Romao, Skandage, Valle, Villanova de Moral 2003; Ma 0409075] controls charged lepton mass hierarchies higher orders in

  24. results [Harrison, Perkins, Scott 2002] expected  spectrum is between normal and degenerate [units ] to reproduce prediction:

  25. SUMMARY • Lack of a unifying principle. Programs and/or strategies difficult to plan • urgent: -- check or disprove LSND -- push sensitivity to |mee| down to 0.01 eV or better • aimed for sensitivities might provide a significant progress in theory most of existing models predict ``special models’’ e.g. SB flavour symmetry -- natural vacuum alignment -- special suppression of subleading contributions

  26. Most of plausible range for Ue3 explored in 10 yr from now double CHOOZ JPARK-SK NuMI -factory MINOS OPERA ICARUS Present bound >> 10 yr 10 yr anarchy, inverted hierachy |Ue3|<0.05 would select a very narrow (not empty) subset of existing models ``normal models’’ similar conclusion by: Barbieri, Hambye, Romanino 0302118 Ibarra, Ross 0307051 Chen, Mahanthappa 0305088 Lebed, Martin 0312219 Joshipura @ NOON 2004

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