Implicazioni Teoriche delle Masse dei Neutrini

1. Roma Tre, 22 Novembre 01 Implicazioni Teoriche delle Masse dei Neutrini G. Altarelli CERN

4. How to guarantee a massless neutrino? 1) nR does not exist No Dirac mass nLnR + nRnL and 2) Lepton Number is conserved No Majorana mass nCn->nTRCnR or nTLCnL C=ig0g2

5. Consider an electron state fixed p, helicity h: |e-, h= +1/2> "Lorentz": Boost to rest + p-rotation + + boost back "Lorentz" |e-, h= +1/2> |e-, h= -1/2> TCP TCP "Lorentz" |e+, h= -1/2> |e+, h= +1/2> A massive charged fermion needs all four! 4 d.o.f. yLyR + yRyL Dirac mass:

6. Neutrinos: Dirac mass: nLnR + nRnL (needs nR) n's have no electric charge. Their only charge is lepton number L IFL is not conserved (not a good quantum number) n and n are not really different TCP, "Lorentz" | n, h= -1/2> | n, h= +1/2> Majorana mass: nTR nR or nTL nL (we omit the charge conj. matrix C) Violates L, B-L by |DL| = 2

7. Reminder: We only observe nR nL p p spin spin left-handed neutrino right-handed antineutrino The field ynL = (1-g5)/2yn (short-hand yn =n) • annihilates a L-H n (nL) • creates a R-H n ( nR) In the Minimal Standard Model there may be no nR field (and no nR and nL particles)

8. Weak isospin I nL => I = 1/2, I3 = 1/2 nR => I = 0, I3 = 0 Dirac Mass: nLnR + nRnL |DI|=1/2 Can be obtained from Higgs doublets:nLnRH Majorana Mass: •nTLnL |DI|=1 Non ren., dim. 5 operator: nTLnLHH Directly compatible with SU(2)xU(1)! •nTRnR |DI|=0

9. See-Saw Mechanism Yanagida; Gell-Mann, Ramond, Slansky MnTRnR allowed by SU(2)xU(1) Large Majorana mass M (as large as the cut-off) mDnLnR Dirac mass m from Higgs doublet(s) nL nR nL nR 0 mD mD M M>>mD Eigenvalues -mD2 nlight = , nheavy = M M sign conventional for fermions

10. In general n mass terms are: Majorana Dirac mD=hv v=<0|H|0> More general see-saw mechanism: nL nR nL nR lv2/ML mD mD MR mD2 lv2 mlight ~ and/or MR ML mheavy ~ MR meff = nTLmlightnL

11. Both the dim-5 operator and the see-saw mechanism are present: see-saw O5 The two terms have the same form, the same transf. properties under n'L=UnL, but different origin (e.g. in GUT's mD is related to quark and lepton Dirac masses) They can be of comparable or very different size (e.g. 1/MGUT vs 1/MPlanck)

12. Neutrino oscillations measureDm2 Dm2atm ~ 2.5 10-3 eV2; Dm2sun< Dm2atm •Direct limits (PDG '00) m"ne" < 3 eV m"nm" < 190 KeV m"nt" < 18 MeV •Cosmology Simi ≤ ~6 eV [Wn ≤ ~0.2] Any n mass ≤ ~2 eV Why are n's so much lighter than quarks and leptons?

13. A very natural and appealing explanation: n' are nearly massless because they are Majorana particles and get masses through L non conserving interactions suppressed by a large scale M ~ MGUT m2 m ≤ mt~ v ~ 200 GeV M: scale of L non cons. mn ~ M Note: mn ~ (Dm2atm)1/2~ 0.05 eV m ~ v ~ 200 GeV M ~ 1015 GeV Neutrino masses are a probe of physics at MGUT !

14. GUT's Effective couplings depend on scale M a3(M) The log running is computable from spectrum a2(M) a1(M) MPl mW MGUT logM The large scale structure of particle physics: • (SUSY) SU(3) SU(2) U(1) unify at MGUT • at MPl: quantum gravity Superstring theory: a 10-dim non local, unified th of all int's x x The really fundamental level

15. Energy scale The large scale structure of particle physics Quantum Gravity GUT Assume: • A TOE at L~MGUT~MPl • A low en. th. at o(TeV) • A "desert" in between MPl MGUT The low en. th. must be renormalisable as a necessary condition for insensitivity to physics at L. Low energy effective th. mW [the cutoff can be seen as a parametrisation of our ignorance of physics at L] But, as L is so large, in addition the dep. of ren. masses and couplings on L must be reasonable: e.g. a mass of order mW cannot be linear in L The "hierarchy problem": why mW << MGUT??

16. With new physics at L the low en. th. is only an effective theory. After integration of the heavy d.o.f.: Li: operator of dim i L = o(L2)L2 + o(L)L3 + o(1)L4 + { Renorm.ble part + o(1/L)L5 + o(1/L2)L6 +... { Non renorm.ble part In absence of special symmetries or selection rules, by dimensionsciLi ~o(L4-i)Li L2: Boson masses f2. In the SM the mass in the Higgs potential is unprotected: c2~ o(L2) L3: Fermion masses yy. Protected by chiral symmetry and SU(2)xU(1): L -> mlogL L4: Renorm.ble interactions, e.g. ygmyAm Li>4: Non renorm.ble: suppressed by 1/Li-4 e.g. 1/L2ygmyygmy

17. The hierarchy problem demands new physics near the Fermi scale L: scale of new physics beyond the SM • L>>mZ: the SM is so good at LEP • L~ few times GF-1/2 ~ o(1TeV) for a natural explanation of mW Examples: SUSY • Supersymmetry: boson-fermion symm. exact (unrealistic): cancellation of dm2 approximate (possible): L ~ mSUSY-mord The most widely accepted • The Higgs is a yy condensate. No fund. scalars. But needs new very strong binding force: Lnew ~ 103LQCD (technicolor). Strongly disfavoured by LEP • Large extra spacetime dimensions that bring MPl down to o(1TeV) Somewhat drastic. Under intense study

18. SUSY is important for GUT's Coupling unification:Precise matching of gauge couplings at MGUT fails in SM and is well compatible in SUSY From aQED(mZ), sin2qW measured at LEP predict as(mZ) for unification (assuming desert) Non SUSY GUT's as(mZ)=0.073±0.002 SUSY GUT's as(mZ)=0.130±0.010 Langacker, Polonski EXP: as(mZ)=0.119±0.003 Present world average Dominant error: thresholds near MGUT Proton decay:Far too fast without SUSY • MGUT ~ 1015GeV non SUSY ->1016GeV SUSY • Dominant decay: Higgsino exchange While GUT's and SUSY very well match, (best phenomenological hint for SUSY!) in technicolor or large extra dimensions there is no gound for unification

19. B and L conservation in SM: "Accidental" symmetries: in SM there is no dim.≤4 gauge invariant operator that violates B and/or L (if no nR, otherwise M nTR nR is dim-3 |DL|=2) The same is true in SUSY with R-parity cons. For the DB=DL= -1 transition u + u -> e+ + d all good quantum numbers are conserved: e.g. colour u~3, d~3 and 3x3 = 6+3 but l dcGu ecGu dim-6 M2 SU(5): p-> e+p0 Once nR is introduced (Dirac mass) a large Majorana mass is naturally induced see-saw

20. Summarizing Dirac masses for n's? If so, why so much smaller than quark and lepton masses? Need nR. But then M nTR nR should be present with M at ~MGUT see-saw m2 mn ~ Smallness explained! M With L not conserved n masses can also arise without nR via Majorana n masses are small because they are inversely proportional to the scale M~MGUT of L non conservation

21. Recent impressive experimental results on cosmological parameters • Hubble constant: H0~ 0.7 100Km/Mpc s Hubble telescope (Inflation) • WTOT = Wm+ WL~1 1st acoustic peak: Boomerang/MAXIMA/DASI • Wm = Wbaryon + Wdark ~ 0.35 Mass distrib.s at large scales, gravit. lensing... • Wbaryon ~ 0.04 Wdark ~ 0.3 Nucleosynthesis, now confirmed by 2nd acoustic peak •Cosmological constant: WL~ 0.65 WTOT- Wm, Age of universe, Supernovae

22. Dark Matter Non relativistic at freeze out SUSY: Cold Neutralino: an excellent candidate Good clustering at small distances (galaxies, …) Hot Relativistic at freeze out Could be n's if 3- n's with mn~0(1eV) Relevant for large scale mass distrib'ns Until recently the best DM model was 80%CDM+20%HDM With WL~0.65, HDM no more required

23. n: power-law index of density perturb.s n = 0.99±0.07 (inflation n = 0.7-1.2) nCDM has an island of viability around H0~0.6, n~0.95 but LCDM is nearby

24. Baryogenesis nB/ng~10-10, nB <<nB Conditions for baryogenesis:(Sacharov '67) • B non conservation (obvious) • C, CP non conserv'n (B-B odd under C, CP) • No thermal equilib'm (n=exp[m-E/kT] mB=mB, mB=mB by CPT If several phases of BG exist at different scales the asymm. created by one out-of-equilib'm phase could be erased in later equilib'm phases:BG at lowest scale best Possible epochs and mechanisms for BG: • At the weak scale in the SM Excluded • At the weak scale in the MSSM Disfavoured • Near the GUT scale via Leptogenesis Very attractive

26. By now this domain of parameters is disfavoured by LEP

28. The current experimental situation is still unclear •LSND: true or false? •which solar oscillation solution is true? ••• Different classes of models are possible: •≥4n's: if LSND true sterile n(s)?? m2~1-2eV2 atm LSND sol If LSND false 3 light n's are OK • Degenerate Dm2≤m2 m2≤o(1)eV2 m2~10-3 eV2 sol • Inverse hierarchy atm m2~10-3 eV2 •Normal hierarchy atm sol

29. nR is a heavy "sterile" neutrino: sterile = no gauge interact's nR quantum numbers colour=TW=Q=0 nR is a light "active" neutrino LEP: Nnactive = 3 Are there light sterile neutrinos? If LSND is true 3 different oscill. frequencies Dm2 LSND + solar + atm. at least 4 light n's But LSND not confirmed by KARMEN Will be double checked by MiniBoone Perhaps will fade away

30. m2~1-2eV2 atm 4-n Models LSND (Bilenky et al; Barger et al; Gonzales-Garcia et al...) Compatible with hot Dark Matter sol Note:pure nactive<-->nsterile oscillations disfavoured both for sol. and atm. oscill's. Viable alternatives: • 6->4 mixing angles: ne <-->nsterile+nm,t for solar • A K-K tower of nsterile (extra-dim models) Gonzales-Garcia et al Fogli,Lisi Since nsterile mixings better be small (limits from weak processes, supernovae, nucleosynthesis) the preferred solar solution is MSW-SA Increasingly disfavoured by the data (SNO)

31. 3-n Models ne n1 n2 n3 ne nm nt e- = U W- U = UMNS mass flavour Maki, Nakagawa, Sakata In basis where e-, m-, t- are diagonal: c12 s12 0 -s12 c12 0 001 1 0 0 0 c23 s23 0-s23 c23 c13 0 s13e-id 0 1 0 -s13eid 0c13 U = ~ solar: possibly large CHOOZ: |s13|<~0.2 c13 c12 c13 s12 s13e-id ... ... c13 s23 ... ... c13 c23 atm.: ~ max ~ (some signs are conventional)

32. eif1m1 0 0 0 eif2m2 0 0 0 m3 UT mn ~ U LTmnL In general 9 parameters: 3 masses, 3 angles, 3 phases Relation between masses and frequencies: P(ne<->nm)= P(ne<->nt)=1/2 sin22q.sin2Dsun P(nm<->nt)=sin2Datm- 1/4 sin22q.sin2Dsun m1c2+m2s2 (m1-m2)cs/V2 (m1-m2)cs/V2 ... (m1s2+m2c2+m3)/2 (m1s2+m2c2-m3)/2 ... ... (m1s2+m2c2+m3)/2 mn~ Note: •mn is symmetric •phases included in mi

33. Degenerate n's • Could be compatible with hot dark matter (m~2 eV) • Limits om mee from 0nbb imply double maximal mixing for both solar and atmospheric oscillations: (Vissani, Georgi,Glashow) mee≤0.3-0.5 eV mee= c213 (m1c212+ m2s212)+s213m3~ ~ m1c212+ m2s212 If |m1|~ |m2|~ |m2|~2 eV m1= -m2 and c212~s212 [Note: sin22q>0.99 ->cos2q-sin2q<0.1] 0nbb near the bound would be a signal!! For naturalness Dm/m cannot be too small (e.g. vacuum sol Dm/m~10-11).MSW-LA would be preferred, but is q12 large enough?

34. In summary, a degenerate model with m~2 eV (hot dark matter) is unlikely: (0nbb, naturalness, m too large for leptogenesis). But, if MSW-LA is established, a degenerate model with m≤0(0.1) eV could be a candidate. For degenerate n's, see-saw dominance is unlikely: See-saw: mn=mTDM-1mD We expect mD to be hierarchical as for q&l. More likely: Degenerate n's from dim-5 operators: O5=1/M LTlLHH unrelated to mD and to q&l masses

35. A model which is suggestive but difficult to realize from symmetry alone: Fritzsch,Xhing Assume that in first approximation: U 0 0 0 0 0 0 0 0 3 1 1 1 1 1 1 1 1 1 mq,l ~ diag SLxSR perm. symmetry LR Dirac "Democratic" For n's, in the same basis: Both allowed by SL 1 1 1 1 1 1 1 1 1 1 0 0 0 1 0 0 0 1 mn~ a + b LTL Majorana assume negligible (?) In basis of l- diagonal, imposing CHOOZ 1/ -1/ 0 1/ 1/ -2/ 1/ 1/ 1/ V2 V2 U~ sin22qatm=8/9 V6 V6 V6 V3 V3 V3

36. 2 m2~ 10-3 eV2 Inverted Hierarchy sol 1 Zee, Joshipura et al, Mohapatra et al, Jarlskog et al, Frampton&Glashow, Barbieri et al atm 3 1/ -1/ 0 1/2 1/2 -1/ 1/2 1/2 1/ An interesting model for double maximal mixing: V2 V2 U~ V2 V2 m 0 0 0 -m 0 0 0 0 0 m m m 0 0 m 0 0 mndiag = ; UmndiagUT =1/ V2 • From see-saw or dim-5 LTLHH • e.g. by approximate Le-Lm-Lt symmetry • 1-2 degeneracy stable under rad. corr.'s • Prefers LOW or VO for solar. • For MSW-LA problems because prefers qsol closer to maximal than qatm and qsol-p/4 small for (Dm2sol/Dm2atm)LA

37. m2~10-3 eV2 Normal Hierarchy 3 atm 2 • Assume 3 widely split light neutrinos. • For u, d and l- Dirac matrices the 3rd generation eigenvalue is dominant. • It is natural to assume this is also true for mnD: diag mnD~(0,0,mD3). • Assume see-saw is dominant: see-saw mn~mTDM-1mD • See-saw quadratic in mD: tends to enhance hierarchy • Maximally constraining: GUT's relate q, l-, n masses! sol 1

38. • A possible difficulty: in the 2-3 sector we need both large m3-m2 splitting and large mixing. m3 ~ (Dm2atm)1/2 ~ 5 10-2 eV m2 ~ (Dm2sol)1/2 ~ 10-2 - 10-5 eV MSW-LA - VO • The "theorem" that large Dm32 implies small mixing (pert. th.: qij ~ 1/|Ei-Ej|) is not true in general; all we need is (sub)det[23]~0 x2 x x 1 • Example: m23~ For x~1 large splitting and large mixing! Det = 0; Eigenvl's: 0, 1 +x2 Mixing: sin22q = 4x2/(1+x2)2 So all we need are natural mechanisms for det[23]=0

39. Examples of mechanisms for Det[23]~0 see-saw mn~mTDM-1mD 1) A nR is lightest and coupled to m and t King; Allanach; Barbieri et al...... 1/e 0 0 1 e 0 0 1 1/e 0 0 0 ~ M-1~ M ~ ~ a b c d a c b d a2 ac ac c2 1/e 0 0 0 mn~ ~ 1/e ~ 00 x 1 2) M generic but mD "lopsided" Albright, Barr; GA, Feruglio, ..... mD~ 00 x 1 0 x 0 1 a b b c x2 x x 1 ~ mn~ ~ f

40. • Hierarchical n's and see-saw dominance mn~mTDM-1mD allow to relate q, l, n masses and mixings in GUT models. • The correct pattern of masses and mixings, also including n's, is obtained in simple models based on SU(5)xU(1)horizontal Froggatt,Nielse; Ramond et al; GA, Feruglio; Buchmuller et al; King et al; Yanagida et al, Berezhiani et al; Lola et al....... • models are often more predictive, but are based on specific textures from a set of special operators. SO(10) Albright, Barr; Babu et al; Buccella et al; Barbieri et al

41. An important property of SU(5) Left-handed quarks have small mixings (VCKM), but right-handed quarks can have large mixings (unknown). In SU(5): LH for d quarks RH for l- leptons 10 5 md~dRdL 5 : (d,d,d, n,e-) L 10 5 R me~eReL md = meT cannot be exact, but approx. Most "lopsided" models are based on this. Large atm. mixing arises from the charged lepton sector.

42. Conclusion •n masses point to very large energy scales where L is not conserved (GUT's) • Many crucial questions for experiments: LSND true or false? Which solar oscill.s solution? How maximal is maximal mixing? ••• • These questions pending, many inventive models and elegant speculative solutions have been proposed. • Experiments now running or in preparat'n can make n oscill.'n experiment precise and eliminate most models. n physics will remain a central issue in particle physics in the next decade(s)