The Physics of Neutrinos. Renata Zukanovich Funchal IPhT/Saclay, France Universidade de São Paulo, Brazil

The Physics of Neutrinos Renata Zukanovich Funchal IPhT/Saclay, France Universidade de São Paulo, Brazil

ectures : 1. Panorama of Experiments 2. Neutrino Oscillations 3. Models for Neutrino Masses 4. Neutrinos in Cosmology

ecture III Models for Neutrino Masses

False facts are highly injurious to the progress of science, for they often endure long; but false views, if supported by some evidence, do little harm, for every one takes a salutary pleasure in proving their falseness. Charles Darwin

Majorana x Dirac

Majorana x Dirac Dirac spinor Ψ=P Ψ+P R Ψ=Ψ +Ψ R 4 independent components Dirac equation iγ µ µ Ψ = mψ R iγ µ µ Ψ R = mψ

Majorana x Dirac Dirac spinor Ψ=P Ψ+P R Ψ=Ψ +Ψ R 4 independent components Dirac equation Weyl (1929) iγ µ µ Ψ = mψ R iγ µ µ Ψ R = mψ if m = 0 2-component spinor is enough ( or R ) Pauli (1933) rejected this idea because leads to Parity Violation andau, ee-yang, Salam (1957) propose to describe the massless neutrino by a Weyl spinor introduced in the SM in the 60 s

Majorana x Dirac Can we also describe a massive fermion using a 2-component spinor? (E. Majorana, 1937)

Majorana x Dirac Can we also describe a massive fermion using a 2-component spinor? (E. Majorana, 1937) _ c = C T charge conjugate field ( ) C = ( C ) R ( R ) C = ( C ) charge conjugation change chirality iγ µ µ (Ψ ) c = m(ψ R ) c iγ µ µ (Ψ R ) c = m(ψ ) c _,R ( R, ) C = C T R, e -i phase factor

Majorana x Dirac Can we also describe a massive fermion using a 2-component spinor? Yes! (E. Majorana, 1937) is unphysical - can be eliminated by rephasing Majorana Condition: ( ) C particle antiparticle Majorana Field: = + R = + ( ) C Majorana Equation: iγ µ µ Ψ = mcψ T e.m. current vanishes Q 0 neutral particle Ψγ µ Ψ = Ψ c γ µ Ψ c = Ψ T C γ µ CΨ T = ΨC T γ µt C Ψ = Ψγ µ Ψ

Some Properties 0 = 0 C T = C = C -1 = -C C -1 = - T C -1 _ c = (C 0 * ) 0 = T 0 C 0 = T C C T T C * = (-C ) T (-C -1 ) = C T C -1 C T T C * = - C C -1 = -

Majorana x Dirac Dirac: Pˆ _ ˆT Ĉ _ (p, h) (-p, -h) (-p, -h) (p, -h) H neutrino (h =-1) RH antineutrino (h=+1) Majorana: Pˆ Ĉ ˆT (p, h) (-p, -h) (-p, -h) (p, -h) H neutrino (h=-1) interactions involve on H fields _ destroys H neutrino creates RH antineutrino destroys RH antineutrino creates H neutrino RH neutrino (h=+1) Dirac

Majorana x Dirac Dirac: Pˆ _ ˆT Ĉ _ (p, h) (-p, -h) (-p, -h) (p, -h) H neutrino (h =-1) RH antineutrino (h=+1) Majorana: Pˆ Ĉ ˆT (p, h) (-p, -h) (-p, -h) (p, -h) H neutrino (h=-1) interactions involve on H fields _ destroys H neutrino creates RH neutrino destroys RH neutrino creates H neutrino RH neutrino (h=+1) Majorana

Mass Problem Standard Model Atmo So Neutrino Oscillations Physics Beyond m 0 the Standard Model

Mass Problem Standard Model Elementary Particle Masses Span 11 orders of magnitude!

Mass Term M X R

Poor man s extension of the SM If ν = ν c = C ν T Dirac Particle symmetrize the model, offers no explanation to the smallness of m α (2,-1/2) E α (1,-1) N α (1,-0) Y = y d αβ Q α ΦD β + y u αβ Q α ΦU β + y αβ α ΦE β +h.c. + y ν αβ α ΦN β +h.c. EWSB Dirac Mass Term Higgs acquires a vev m D ν ν R +h.c.

Poor man s extension of the SM Y = v + h y R + N yν N R 2 +h.c.,r e µ τ,r,r = V,R,R y = V y V R unitary matrices real positive numbers y αβ = y α δ αβ N,R ν e ν µ ν τ,r N,R = V ν,r N,R y ν = V ν yν V ν R real positive numbers y ν αβ = y ν α δ αβ unitary matrices

Poor man s extension of the SM m eα m νi D mass = v 2 y α e α e αr + v 2 y ν i ν i ν ir +h.c. charged fermions neutrino masses e,r µ τ,r e e e µ e τ,r new fields masses N,R ν 1 ν 2 ν 3,R Yukawas have to be fine-tuned to explain smallness of neutrino masses Ok. But what happens to the CC and NC?

Poor man s extension of the SM charged current for leptons j µ W, = 2 ν αγ µ P e α = 2 ν α γ µ e α = 2 N γ µ chiral flavor diagonal interaction = 2 N V ν V γ µ = 2 ν i U αi γ µ e α Mixing Matrix (Pontecorvo, Maki, Sakata, Nakagawa) define H flavor neutrinos as ν α = U αi ν i Mixing family epton Number ( e,, ) violated but Total epton Number () conserved

Poor man s extension of the SM neutral current for neutrinos j µ Z,ν = ν α γ µ ν α chiral flavor diagonal interaction = ν i γ µ ν i No Mixing here! NC is the same (GIM Mechanism) [S..Glashow, J. Iliopolos,. Maiani, Phys. Rev. D 2, 1285 (1970)] R is sterile!

Violating Processes Dirac mass term allows for e,, processes such as: ± e ± or ± e ± e + e - eg. ± e ± Γ = G Fm 5 µ 192π 3 3α em 32π j U µju ej = 0 jtext U µju ej m νi M W GIM Mechanism 2 SM : BR 10-25 BR exp 2.4 x 10-12 suppression W W W * U j e e j j j U ej e

Phases of U j µ W, = 2 ν i U αi γ µ e α Can re-phase e α e iφ α e α ν i e iφ i ν i j µ W, = 2 ν i e i(φ 1 φ e ) e i(φ i φ 1 ) e i(φ α φ e ) U αi γ µ e α 1 N - 1 N - 1 1 + 2(N-1) = 2N-1 phases can be arbitrarily chosen N=3 5 phases can be eliminated from U only 1 physical phase

Basic Points : we need to introduce singlet R neutrino fields ( R ) we make use of the SM Higgs Mechanism D mass = m νν= m( ν R ν + ν ν R ) mass hierarchy problem remains e,, are violated is conserved (exact global symmetry at the classical level, just like B) m ν j = yν j v 2 generates a mixing matrix analogous to V CKM

+Clever extensions of the SM If ν = ν c = C ν T Majorana Particle if we introduce R we can have Majorana Mass Term 1 2 m R ν c R ν R +h.c. is violated by 2 units P ν c R = ν c R this is invariant under SU(2) U(1) Y

+Clever extensions of the SM If ν = ν c = C ν T Majorana Particle if we don t introduce R we can have Majorana Mass Term 1 2 m ν c ν +h.c. is violated by 2 units P R ν c = ν c but not invariant need to extend the SM... under SU(2) U(1) Y

Majorana Mass Term we can write a Majorana mass term with only P R ν c = ν c (or R ) ν c = ν = ν = ν + ν c = M mass = 1 2 m ν c ν +h.c. the 1/2 factor avoids double counting since and c are not independent M = 1 2 [ν ı ν + ν c ı ν c m (ν c ν + ν ν c )] M mass = m 2 ν T C ν + ν C ν

Basic Points: no need to introduce singlet R fields ( R ) use ν R ν c = C ν T and ν = ν c ν = ν + ν R = ν + C ν T M mass = m 2 (νc ν +h.c.) need a Higgs triplet (Y=1) to form a SU(2) U(1) Y invariant term ( ) e,, are violated is also violated by 2 units

The most general mass term is a Dirac-Majorana Mass Term D+M mass = D mass + M mass + MR mass D mass = m D ν R ν +h.c. Dirac Mass Term M mass = 1 2 m ν T C ν +h.c. Majorana Mass Term MR mass = 1 2 m R ν T R C ν R +h.c. Majorana Mass Term

Mixing in General N ν ν c R ν ν e ν µ ν τ ν c R D+M mass 1 2 N T C M D+M N +h.c. M D+M = ν c 1R ν c Ns R M M D (M D ) T M R Diagonalization of the Dirac-Majorana Mass Term Massive Majorana Neutrinos R R eptogenesis next week...

Dirac-Majorana 0 (M D ) T M D+M = M D M R complex symmetric matrix M D is a 3xm complex matrix M R is a mxm symmetric matrix (a) mass eigenvalues of M R >> v framework of seesaw mechanism sterile neutrinos integrated out & get a low energy effective theory with 3 light active Majorana neutrinos (b) some mass eigenvalues of M R v more than 3 light Majorana neutrinos (c) M R = 0 equivalent to impose conservation, m=3 and we can identify the 3 sterile neutrinos c/ RH components of the H fields (Dirac Neutrinos)

Neutrino Mass & The Standard Seesaw Mechanisms

Effective agrangian Perspective SM is an Effective ower Energy Theory eff = SM + δ d=5 + δ d=6 +... non-renormalizable higher-dimension operators invariant under SU(2) X U(1) Y made of SM fields active @ low energies with coefficients (model dependent) weighted by inverse powers of (new physics scale) δ d=5 = g Λ (T σ 2 Φ) C (Φ T σ 2 )+h.c. [S. Weinberg, Phys. Rev. ett. 43, 1566 (1979)] only possible d=5 operator δ d=5 = δ M mass = 1 2 EWSB gv 2 Λ νt C ν +h.c. Majorana Mass

Tree-level Realizations [E. Ma, Phys. Rev. ett. 81, 1171 (1998)]

Tree-level Realizations Φ Φ [E. Ma, Phys. Rev. ett. 81, 1171 (1998)] y N N R y N seesaw type I fermion singlets

Tree-level Realizations Φ Φ [E. Ma, Phys. Rev. ett. 81, 1171 (1998)] y N N R y N seesaw type I Φ µ Φ fermion singlets scalar triplet seesaw type II y

Tree-level Realizations Φ Φ [E. Ma, Phys. Rev. ett. 81, 1171 (1998)] y N N R y N seesaw type I Φ µ Φ fermion singlets Φ Φ y Σ Σ R y Σ seesaw type III fermion triplet y scalar triplet seesaw type II

Effective agrangian Perspective integrate out the heavy fields e is eff = exp i d 4 x eff (x) DN DNe is = e is SM DN DNe is N effective agrangian obtained by functional integration over heavy fields S N [N 0 ] : N 0 is the solution of the classical equations of motion for the N-field 1 D M = 1 M + 1 M D 1 M +... fermions

Φ y N N R y N Seesaw Type I Φ [P. Minkowski, Phys. ett. B 67, 421 (1977); M. Gell-Mann, P. Ramond and R. Slansky, Supergravity (1979); T. Yanagida, Proc. Workshop on the Unif. Theo. and the Baryon Numb. in the Univ. (1979); R.N. Mohapatra and G. Senjanovic, Phys. Rev. ett. 44, 912 (1980) ] minimal seesaw agrangian: only add R neutrinos to SM KE = ı D+ ı RDR+ ı N R N R SM lepton doublets SM lepton singlets R neutrino singlets New Physics Scale Y = Φy R Φy N N R 1 2 N R M R N c R +h.c.

Φ y N N R y N Seesaw Type I Φ [P. Minkowski, Phys. ett. B 67, 421 (1977); M. Gell-Mann, P. Ramond and R. Slansky, Supergravity (1979); T. Yanagida, Proc. Workshop on the Unif. Theo. and the Baryon Numb. in the Univ. (1979); R.N. Mohapatra and G. Senjanovic, Phys. Rev. ett. 44, 912 (1980) ] minimal seesaw agrangian: only add R neutrinos to SM KE = ı D+ ı RDR+ ı N R N R EWSB SM lepton doublets SM lepton singlets m ν g Λ v2 = 1 2 yt N R neutrino singlets 1 y N v 2 M R New Physics Scale Y = Φy R Φy N N R 1 2 N R M R N c R +h.c. Majorana Mass Matrix for light neutrinos Needs 3 N R to give mass to 3 ν M R should of the order 10 11 TeV (10 5 TeV ) for y N 1 (y N 10-3 )

Φ y N N R y N Seesaw Type I Φ [A. Broncano, M.B. Gavela and E.E. Jenkins, Phys. ett. B 552, 177 (2003); Nucl. Phys. B 672, 163 (2003) ] only one d=6 tree level operator δ d=6 = g d=6 ( Φ) ı ( Φ ) EWSB corrections to d=4 KE terms of leptons where g d=6 = y N quadratically suppressed 1 M R 1 M R y N non-unitary low-energy leptonic mixing matrix

Φ µ Φ Seesaw Type II y [M. Magg and C. Wetterich, Phys. ett. B 94, 61 (1980); J. Schechter and J.W.F. Valle, Phys. Rev. D 22, 2227 (1980); R.N. Mohapatra and G. Senjanovic, Phys. Rev. D 23, 165 (1981)] add SU(2) triplet scalar field (Y=1) minimal agrangian gauge invariant allows for,(,φ) = y (σ ) + µ Φ (σ ) Φ+h.c. coupling to SM lepton doublets coupling to SM Higgs doublet = ( 1, 2, 3 ) where = ıσ2 () c physical fields 0 = u/ 2 = µ v 2 /( 2M 2 ) ++ 1 2 ( 1 ı 2 ) + 3 0 1 2 ( 1 + ı 2 ) if M Δ >> v EWSB m ν g Λ v2 = 2y u = 2y New Physics Scale µ M 2 v 2 Majorana Mass Matrix for light neutrinos

Φ µ Φ Seesaw Type II y [M. Magg and C. Wetterich, Phys. ett. B 94, 61 (1980); J. Schechter and J.W.F. Valle, Phys. Rev. D 22, 2227 (1980); R.N. Mohapatra and G. Senjanovic, Phys. Rev. D 23, 165 (1981)] add SU(2) triplet scalar field (Y=1) minimal agrangian gauge invariant allows for,(,φ) = y (σ ) + µ Φ (σ ) Φ+h.c. coupling to SM lepton doublets coupling to SM Higgs doublet = ( 1, 2, 3 ) physical fields if M Δ >> v EWSB where 0 = u/ 2 = µ v 2 /( 2M 2 ) m ν g Λ v2 = 2y u = 2y New Physics Scale = ıσ2 () c ++ 1 2 ( 1 ı 2 ) + 3 0 1 2 ( 1 + ı 2 ) µ One Δ can give mass to 3 ν M 2 v 2 Majorana Mass Matrix for light neutrinos

Φ µ y Φ Seesaw Type II [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] three d=6 tree level operators δ 4 = 1 M 2 y σ σy quartic Φ couplings δ 6Φ = 2(λ 3 + λ 5 ) µ 2 δ ΦD = µ 2 M 4 Φ σ Φ M 4 Φ Φ 3 D µ D µ Φ σ Φ many deviations from SM predictions but no non-unitary mixing matrix! [G F gets a correction, v gets shifted, M Z gets a correction etc.]

Φ Φ y Σ Σ R y Σ Seesaw Type III [R. Foot, H. ew, X.G.He and G.C. Joshi, Z. Phys. C 44, 441 (1989); E. Ma, Phys. Rev. ett. 81, 1171 (1998) ] add SU(2) fermion triplet Σ (Y=0)

Φ y Σ Σ R y Σ Φ Seesaw Type III [R. Foot, H. ew, X.G.He and G.C. Joshi, Z. Phys. C 44, 441 (1989); E. Ma, Phys. Rev. ett. 81, 1171 (1998) ] Σ = ı Σ R D Σ R add SU(2) fermion triplet 1 (Y=0) 2 Σ R M Σ Σ c R + Σ R y Σ ( Φ σ )+h.c. Majorana Mass Term Σ =(Σ 1, Σ 2, Σ 3 ) Σ ± 1 2 (Σ 1 ı Σ 2 ) Σ 0 Σ 3 Σ coupling with and Φ

Φ y Σ Σ R y Σ Φ Seesaw Type III [R. Foot, H. ew, X.G.He and G.C. Joshi, Z. Phys. C 44, 441 (1989); E. Ma, Phys. Rev. ett. 81, 1171 (1998) ] Σ = ı Σ R D Σ R if M Σ >> v EWSB add SU(2) fermion triplet 1 m ν g Λ v2 = y T Σ 1 y Σ v 2 2M Σ New Physics Scale (Y=0) 2 Σ R M Σ Σ c R + Σ R y Σ ( Φ σ )+h.c. Majorana Mass Term coupling with and Φ Σ =(Σ 1, Σ 2, Σ 3 ) Σ ± 1 2 (Σ 1 ı Σ 2 ) Σ 0 Σ 3 Majorana Mass Matrix for light neutrinos One Σ can give mass to 3 ν Σ

Φ y Σ Σ R y Σ Φ Seesaw Type III [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] only one d=6 tree level operator δ d=6 = g d=6 ( σ Φ) ıd ( Φ σ ) EWSB corrections to d=4 KE terms of light leptons and their coupling to W where g d=6 = y Σ quadratically suppressed 1 M Σ 1 M Σ y Σ non-unitary low-energy leptonic mixing matrix

Φ y Σ Σ R y Σ Φ Seesaw Type III [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] only one d=6 tree level operator δ d=6 = g d=6 ( σ Φ) ıd ( Φ σ ) EWSB corrections to d=4 KE terms of light leptons and their coupling to W where U N = g d=6 = y Σ quadratically suppressed 1 + Σ 2 1 M Σ 1 M Σ y Σ non-unitary low-energy leptonic mixing matrix U NN =(1 + Σ ) N N = U (1 + Σ )U with Σ v2 2 gd=6 j µ 3 (ν) 1 2 νγµ (N N) 1 ν j µ 3 () 1 2 γµ (NN ) 2

About the Seesaw = regulator cutoff Scale δm 2 H = y N y N 16π 2 one-loop contribution to the Higgs mass 2Λ 2 + 2M 2 N log M2 N Λ 2 [J.A. Casa, J. R. Espinosa and I. Hidalgo, JHEP 11, 057 (2004)] δm 2 H = 1 16π 2 3 λ 3 Λ 2 M 2 log Λ2 M 2 12 µ 2 log Λ2 M 2 [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] δm 2 H = 3 y Σ y Σ 16π 2 2Λ 2 + 2M 2 Σ log M2 Σ Λ 2

About the Seesaw = regulator cutoff Scale δm 2 H = y N y N 16π 2 one-loop contribution to the Higgs mass 2Λ 2 + 2M 2 N log M2 N Λ 2 [J.A. Casa, J. R. Espinosa and I. Hidalgo, JHEP 11, 057 (2004)] seesaw type I δm 2 H = 1 16π 2 3 λ 3 Λ 2 M 2 log Λ2 M 2 12 µ 2 log Λ2 M 2 [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] δm 2 H = 3 y Σ y Σ 16π 2 2Λ 2 + 2M 2 Σ log M2 Σ Λ 2

About the Seesaw = regulator cutoff Scale δm 2 H = y N y N 16π 2 one-loop contribution to the Higgs mass 2Λ 2 + 2M 2 N log M2 N Λ 2 [J.A. Casa, J. R. Espinosa and I. Hidalgo, JHEP 11, 057 (2004)] seesaw type I δm 2 H = 1 16π 2 3 λ 3 Λ 2 M 2 log Λ2 M 2 12 µ 2 log Λ2 M 2 [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] δm 2 H = 3 y Σ y Σ 16π 2 2Λ 2 + 2M 2 Σ log M2 Σ Λ 2 seesaw type III

About the Seesaw = regulator cutoff Scale δm 2 H = y N y N 16π 2 one-loop contribution to the Higgs mass 2Λ 2 + 2M 2 N log M2 N Λ 2 [J.A. Casa, J. R. Espinosa and I. Hidalgo, JHEP 11, 057 (2004)] seesaw type I δm 2 H = 1 16π 2 3 λ 3 Λ 2 M 2 log Λ2 M 2 seesaw type II 12 µ 2 log Λ2 M 2 [A. Abada, C. Biggio, F. Bonnet, M. B. Gavela and T. Hambye, JHEP 12, 061 (2007)] δm 2 H = 3 y Σ y Σ 16π 2 2Λ 2 + 2M 2 Σ log M2 Σ Λ 2 seesaw type III

RADIATIVE MODES [K. S. Babu, E. Ma, Phys. Rev. ett. 61, 674 (1988)] add only one N R so only 1 gets mass @ tree-level h - k ++ h - ν l c l R ν c Two-loop origin of neutrino mass Doubly suppressed by GIM masses too small!

RADIATIVE MODES [A. Zee, Phys. ett. 93B, 389 (1980)] 1, 2 = scalar doublets = charged scalar singlet h - k ++ h - ν l c l R ν c 2 does not couple to leptons One-loop origin of neutrino mass Ruled-out by data...

RADIATIVE MODES [A. Zee, Phys. ett. B93, 389 (1980); K. S. Babu, Phys. ett. B203, 132 (1988); J. T. Peltoniemi and J. W. F. Valle, Phys. ett. B304, 147 (1993)] trilinear coupling which breaks B- double suppressed by lepton mass ν f h - k ++ y l v h μ y l v h - l c l R c l R l f ν c k ++ = doubly-charged scalar h - = singly-charged scalar Two-loop origin of neutrino mass M M µ fy l hy l f T v 2 I Not yet ruled-out by data...

RADIATIVE MODES [E. Ma Phys. Rev. D73, 077301 (2006)] add 3 N R s + a new scalar doublet scotogenic neutrino h - k ++ h - assume new conserved Z 2 symmetry : N and odd under Z 2 ν l c l R c l R l SM ν c particles even under Z 2 One-loop origin of neutrino mass (νφ 0 lφ + )N (νη 0 lη + )N Not yet ruled-out by data...

SUSY & R-parity Violation [see Y. Grossman and S. Rakshit, Phys. Rev. D 69, 093002 (2004) and Ref. therein] EWSB H d, H u and sneutrinos acquire vev

SUSY & R-parity Violation

SUSY & R-parity Violation only one massive neutrino @ tree-level inclusion of radiative corrections give rise to masses to all 3 neutrinos

B- SPONTANEOUSY BROKEN [Y. Chikashige, R.N. Mohapatra, R.D> Peccei, Phys. ett. B98, 265 (1981); PR 45, 1926 (1980)] introduce a gauge singlet scalar S =2 y = l,l a ll N c lr N l R S + h.c. <S> acquires a vev global U B- M ll = a ll S Majorana Mass J Majoron (Goldstone Boson)

Extra Flat Dimensions [K.R. Dienes et al., Nucl. Phys. B557, 25 (1999); N. Arkani-Hamed et al., Phys. Rev D65, 024032 (2002); G.R. Dvali and A.Yu. Smirnov, Nucl. Phys. B563, 63 (1999); R. N. Mohapatra et al., Phys. ett. B 466, 115 (1999); R.N. Mohapatra and A. Perez-orenzana, Nucl. Phys. B576, 466 (2000)] δ = 1 S = Γ J J =0,..., 4 SM particles propagate in the 3-D brane 3 families of SM singlets propagate in the 4-D bulk d 4 xdyiψ α Γ J J Ψ α + SM flavor neutrinos d 4 x (i ν γ α µ µ ν α + λ αβ H ν Ψ α β (x, 0) + h.c.) R Yukawa couplings to SM H λαβ = h αβ / M : the 5D Dirac ϒ matrices SM singlet bulk fermion fields One can decompose Ψ α (x,y) in KK-modes a = radius of the largest compact extra dimension M 2 Pl =(M ) δ+2 V δ Ψ α (x, y) = 1 2πa N= Ψ α(n) (x) e iny/a

Extra Flat Dimensions [K.R. Dienes et al., Nucl. Phys. B557, 25 (1999); N. Arkani-Hamed et al., Phys. Rev D65, 024032 (2002); G.R. Dvali and A.Yu. Smirnov, Nucl. Phys. B563, 63 (1999); R. N. Mohapatra et al., Phys. ett. B 466, 115 (1999); R.N. Mohapatra and A. Perez-orenzana, Nucl. Phys. B576, 466 (2000)] ν (0) αr Ψ(0) αr ν (0) α ν α ν (N) αr, 1 Ψ (N) αr, ± Ψ( N) αr, 2 N =1,..., α,β m D αβ = h αβ vm /M Pl m D αβ + g 2 ν (0) α ν(0) βr + 2 α N=1 l α γ µ (1 γ 5 ) ν (0) α Naturally Small Dirac Mass Term ν (0) α ν(n) βr + α W µ + h.c. N=1 N a ν(n) α ν(n) αr

Flavor Models try to describe the structure of masses Enforce a G F symmetry non-abelian global Text discrete commute w/ gauge group spontaneously broken @ high energies need to extend the scalar sector (Flavon Fields) G F = A4, S4, Dn etc.. many models... constrains Yukawas : the pattern of mass and mixing

What should you take home?

What should you take home? Neutrinos are the only known particles that can have Majorana Mass violating

What should you take home? Neutrinos are the only known particles that can have Majorana Mass violating Effective Theory arguments indicate that mass is due to Physics Beyond the SM

What should you take home? Neutrinos are the only known particles that can have Majorana Mass violating Effective Theory arguments indicate that mass is due to Physics Beyond the SM The basic seesaw mechanisms are elegant ways to implement small masses in models beyond SM

Consequences of masses & mixings Decay: 2 1 happens in all models (harmless is m < few ev ) e happens in all models (constrain models where m is of rad. origin) Some models have new particles few x 100 GeV / NV interactions that can be observed @ HC eptogenesis is possible (next week)