MASSIVE NEUTRINOS: MODEL BUILDING M. Lola, HEP2006 funded by - - PDF document

MASSIVE NEUTRINOS: MODEL BUILDING

• M. Lola, HEP2006

funded by MEXT-CT-2004-014297 Neutrino data: By now convincing for mν = 0 and physics beyond SM What do we know? lower limit best value upper limit ∆m2

sun(10−5 eV 2)

5.4 6.9 9.5 ∆m2

atmo(10−3 eV 2)

1.4 2.6 3.57 sin2 θ12 0.23 0.30 0.39 sin2 θ12 0.31 0.52 0.72 sin2 θ13 0.006 0.1 Open questions:

• Is the atmospheric mixing maximal or close to maximal?
• How large is the solar mixing?
• What about θ13 ?
• What is the pattern of masses? (we know only ∆m)
• Phases? How large is leptonic CP-violation?

Origin of neutrino mass in SM extensions

• Family symmetries (abelian? non-abelian?)
• GUTs (which one?) / SUSY?

Use (i) multiplet structure (ii) known fermion mass and mixing parameters to predict those we know less Additional aspects to consider:

• Stability under quantum corrections (large effects possible)
• Leptonic CP-violation/Baryogenesis through leptogenesis?
• Rare charged-lepton decays, µ-e conversion on nuclei
• Collider Signatures/LHC

Combined analysis of the above for max. information

3× 3 mixing |νa >=

• i

Uai|νi >, a = e, µ, τ; i = 1, 2, 3 U = diag(eiδe, eiδµ, eiδτ).V.diag(e−iφ1/2, e−iφ2/2, 1) V =      c12c13 s12c13 s13e−iδ −c23s12 − s23s13c12eiδ c23c12 − s23s13s12eiδ s23c13 s23s12 − c23s13c12eiδ −s23c12 − c23s13s12eiδ c23c13      δ = −arg   

U∗

iiUijUjiU∗ jj

c12c2

13c23s13 + c12c23s13

s12s23    , i, j = 1, 2, 3 and i = j i.e. CP-violation ∝ Jarlskog invariant JCP = 1 2|Im(U ∗

11U12U21U ∗ 22)| = 1

2|Im(U ∗

11U13U31U ∗ 33)|

= 1 2|Im(U ∗

22U23U32U ∗ 33)| = 1

2|c12c2

13c23 sin δs12s13s23|

Different models predict different CP violation i.e. zero violation, for models with texture zeros in (1,3) entries

νR and See-Saw mechanism How can we generate naturally light neutrinos? Combine mD

ν and MνR to write a mass matrix

Mν =   0 mD

ν

mD

ν MνR

  If MνR ≫ mD

ν , a very heavy eigenvalue MN ≈ MνR

and a very light meff ≈

• (mD

ν )2

MνR

• VL

i VL j V R k VR m Φ H H

For (mD

ν )33 ≈ (200 GeV) (λN ≈ λt) and MN3 ≈ O(1013 GeV),

meff ≈ 1 eV

Mass hierarchies and flavour symmetries Start with L-R symmetric model, assume flavour symmetry (different generations of fermions have different charges) Invariance under symmetry, determines magnitude of masses Qi ¯ Ui ¯ Di Li ¯ Ei H2 H1 U(1) ai ai ai bi bi −2a3 wa3 LR + SU(2) ⇒ same charge for Qi, ¯ Ui, ¯ Di Up-mass matrix: Top coupling Q3 ¯ U3H2 0 charge ⇒ allowed All other couplings forbidden M up =      0 0 0 0 0 0 0 0 1     

• Suppose singlets θ with non-0 flavor-charges

(singlets expected in realistic models) Then: invariant terms Qi ¯ UjH2(< θ > /M)n n depending on flavour charges Hierarchical mass structures generated for ALL fermions

Example consistent with charged fermion hierarchies M u ∝      ǫ8 ǫ3 ǫ4 ǫ3 ǫ2 ǫ ǫ4 ǫ 1      , M d ∝      ¯ ǫ8 ¯ ǫ3 ¯ ǫ4 ¯ ǫ3 ¯ ǫ2 ¯ ǫ ¯ ǫ4 ¯ ǫ 1      Mℓ ∝      ¯ ǫ5 ¯ ǫ3 ¯ ǫ5/2 ¯ ǫ3 ¯ ǫ ¯ ǫ1/2 ¯ ǫ5/2 ¯ ǫ1/2 1      , Vtot =V †

ν Vℓ

• If mixing mostly dominated by Vℓ:
• naturally large neutrino mass hierarchies
• simplest constructions with too small solar mixing

(fixed by charged lepton hierarchies)

• If R-H neutrino sector relevant for mixing

see-saw 0-determinant cancellations, large solar mixing

• Models with more than one U(1)’s and more than one singlets
• less predictive, but often simulate well non-abelian structures

(very instructive to study them).

Minimal Models with Abelian Flavour Symmetries

• Large splitting between fermion masses

Naturally leads to large neutrino hierarchies

• Unknown phases/order unity coefficients ⇓

Difficult to obtain naturally degenerate neutrinos

• In many models lepton hierarchies consistent with mostly

SAMSW but LAMSW possible, ie by see-saw conditions Models with non-Abelian flavour symmetries

• Degenerate ν and ℓ± textures assuming

ie that the lepton fields are SO(3) triplets

• Subsequently break SO(3) so as:

large charged lepton splitting/ small neutrino splitting

• Favour almost-degenerate neutrino textures
• Textures with (almost)-bimaximal mixing predicted

LAMSW / VO oscillations for solar neutrinos

SU(5) (i) Assume the family symmetry is combined with SU(5) (ii) Use the GUT structure ONLY to constrain U(1) charges Under this group we have the following relations: Q(q,uc,ec)i = Q10

i

Q(l,dc)i = Q5

i

Q(νR)i = QνR

i

• Mup symmetric
• Mℓ± = M T

down

• L lepton mixing ≈ R down-quark one

Can we obtain acceptable patterns of masses/mixings? i.e. Mu mt =      ¯ ǫ6 ¯ ǫ5 ¯ ǫ3 ¯ ǫ5 ¯ ǫ4 ¯ ǫ2 ¯ ǫ3 ¯ ǫ2 1      , Mdown mb =      ¯ ǫ4 ¯ ǫ3 ¯ ǫ3 ¯ ǫ3 ¯ ǫ2 ¯ ǫ2 ¯ ǫ 1 1      Mℓ mτ =      ¯ ǫ4 ¯ ǫ3 ¯ ǫ ¯ ǫ3 ¯ ǫ2 1 ¯ ǫ3 ¯ ǫ2 1      Solar Mixing: more structure needs to be added!

Ellis, Gomez, ML: computerised scanning of viable constructions, in progress

0.5 1 1.5 2 2.5 3

φ

ν (Rad) 0.2 0.4 0.6 0.8 1 1.2

Neutrino Yukawa mixing (Rad)

θ12 θ13 θ23 10 x JCP FIT 2 0.5 1 1.5 2 2.5 3

φ

ν (Rad) 0.2 0.4 0.6 0.8 1 1.2

Neutrino Yukawa mixing (Rad)

θ12 θ13 θ23 100 x JCP FIT 3 1 2 3

φ

ν (Rad) 0.2 0.4 0.6 0.8 1 1.2

Neutrino Yukawa mixing (Rad)

θ12 θ13 θ23 100 x JCP FIT 4 0.5 1 1.5 2 2.5 3

φ

ν (Rad) 0.2 0.4 0.6 0.8 1 1.2

Neutrino Yukawa mixing (Rad)

θ12 θ13 θ23 10 x JCP FIT 5

Figure 1: Neutrino mixing angles and values JCP vs. the phase φν of the Dirac neutrino matrix Yν. The phase φX23 of the Ye is kept constant (and the results are almost independent of it). The texures corresponds to fits 2,3,4,5 of KKPV with the values of coef. aij provided in their tables 11 and 13.

SO(10)

• All L- and R-handed fermions in the 16 of SO(10)
• Both MSSM Higgs fields fit in a single 10 of SO(10) ⇓

For all fermions, L-R symmetric textures, similar structure (different expansion parameters due to Higgs mixing) Flipped SU(5) Q(q,dc,νc)i = Q10

i , Q(l,uc)i = Q5 i, ec singlet of SU(5)

• Symmetric Mdown
• mD

ν = M T up

SU(3)c ⊗ SU(3)L ⊗ SU(3)R Particles placed in (3, 3, 1), (¯ 3, 1, ¯ 3) and (1, 3, ¯ 3) as:      u d D     

L

• ¯

u ¯ d ¯ D

• L

     ℓc L e− Lc ℓ ν e+ νc N     

L

• Symmetric lepton mass matrices (as in L-R symm. models)
• Asymmetric up and down

Different predictions and correlations between observables

Baryogenesis through leptogenesis

• Neutrinos have masses and mix with each other
• Like quarks, CP violation in neutrino sector

L = ℓL Φ hν N c

L + 1

2N c

L M N c L + h.c.

• Lepton-number-violation

(i.e. in decays of heavy, RH Majorana neutrinos) N c

L → Φ + ℓ

N c

L → Φ + ℓ

REMEMBER: L/B-violating interactions in thermal equilibr. at high T Changes in lepton number ⇒ Changes in baryon number THUS: Generate ∆L = 0, which then transforms to ∆B = 0

Out-of-equilibrium condition: Decay rates smaller than Hubble parameter H at T ≈ MN1 Three-level width of N1: Γ = (λ†λ)11

8π MN1

Compare with: H ≈ 1.7 g1/2

∗ T 2 Mp

(gMSSM

∗

≈ 228.75, gSM

∗

= 106.75) ⇒ (λ†λ)11 14πg1/2

∗

Mp < MN1 More accurate by looking at Boltzmann equations CP-violating asymmetry, ǫ (interference between tree-level and 1-loop amplitudes) ǫj = 1 (8πλ†λ)11

• j

Im

• (λ†λ)2

1j

• f

m2

Nj

m2

N1

• f(y) = √y
• 1 − (1 + y) ln

1 + y y

• Plus self-energy corrections ˜

δ ∝

MN1 (MN2−MN1)

What can leptogenesis tell us about fermion mass patterns?

Effects of radiative corrections on neutrino masses and mixing For i, j, generation indices 1 mij

eff

d dtmij

eff =

1 8π2

• −cig2

i + 3λ2 t + 1

2(λ2

i + λ2 j)

• 16π2 d

dtsin2 2θ23 =2 sin2 2θ23(1 − 2 sin2 θ23)λ2

τ

m33

eff + m22 eff

m33

eff − m22 eff

sin22θ23 affected by quantum corrections if: (i) λτ large (large tan β) (ii) m33

eff − m22 eff small

Semi-analytic and numerical studies ⇒

• The mixing can even be amplified/destroyed

mij

eff

mij

eff,0

= exp 1 8π2 t

t0

• −cig2

i + 3λ2 t + 1

2(λ2

i + λ2 j)

• ≡ Ig · It ·
• Ii ·
• Ij
• 1. The relative structure in meff is only modified by the lep-

tonic Yukawa couplings

• 2. On the contrary, the gauge and top couplings give only an
• verall scaling factor

LFV IN RARE DECAYS AND CONVERSIONS In SM extensions with ∆Li = 0, non-zero rates for pro- cesses such as: µ → eγ τ → µγ µ − e conversion on nuclei Very good expected future BR sensitivities: µ → eγ 10−14 µ−Ti → e−Ti 10−18

• 1. µ → eγ in the SM with mνi = 0

µ µ e γ νi W + µ e e γ νi W + µ e γ νi W + νi = νµ cos θ + νe sin θ, Γ = 1

16 G2

F m5 µ α

128 π4

• m2

2−m2 1

m2

W

• sin2 θ cos2 θ

BR ≤ 10−50, for ∆m2

12 from neutrino data

too small!

• 2. µ → 3e et µ -e conversion on nuclei

µ e e γ, Z e−(q) e+(q) + ...(suppressed box-diagr.) BR ≤ 10−53 for ∆m2

12 from neutrino data

LFV in minimal SUSY MSSM: For each SM vertex, also the one with 2 particles → superparticles FOR ALSO µ(e) µ(e) γ, Z µ(e) ˜ µ(˜ e) ˜ χ0 If ˜ µ-˜ e (˜ νµ-˜ νe) mixing, large rates for: µ e γ ˜ ℓi ˜ χ0 µ e γ ˜ νi ˜ χ− The fermion in the loop is now a neutralino/chargino instead

• f a neutrino

( m˜

χ0, m˜ χ± ≫ mν ⇒ large rates)

The magnitude of the rates depends on: The mass of superparticles The mixing of superparticles For non-universality at mGUT, large rates

Massive neutrinos and SUSY Even if: MGUT : m˜

ℓ,˜ ν ∝

     1 0 0 0 1 0 0 0 1      , REGs − →      1 ⋆ ⋆ ⋆ 1 ⋆ ⋆ ⋆ 1     

• RGEs for the charged-lepton mass matrix

t d dt(m2

˜ ℓ)j i =

1 16π2

• (m2

˜ ℓλ† ℓλℓ)j i + (m2 ˜ ℓλ† νλν)j i + ...

• The corrections in the basis where (λ†

ℓλℓ)j i is diagonal, are:

δm˜

ℓ ∝

1 16π ln MGUT MN λ†

νλνm2 SUSY

(And similar corrections for δm˜

ν )

INFO: For big µ-e lepton mixing, big rates for µ → eγ Different predictions for the various solutions of the solar neu- trino deficit (with a small/large mixing angle and with eV or ≈ 0.01 eV neutrinos) If R-violation, tree-level µ → 3e and µ − e conversion!

100 200 300 400 500

m1/2

100 200 300 400 500

m0

mτ

∼R<mχ

∼

10−12

mχ

∼+=95 GeV

10−11

100 200 300 400 500

m1/2

100 200 300 400 500

m0

mτ

∼

R<mχ

∼

10−14

mχ

∼+=95 GeV

10−13 10−15

Predictions for µ → eγ and µ − e conversion for the (by now excluded) ”SAMSW” and mν3 ≫ mν1,2. For large solar mixing, naturally, even larger rates are predicted for the same set of parameters.

LFV at LHC: Most promising: LFV decay of ˜ χ0

2

˜ χ0

2 → ˜

ℓ+

i ℓ− j → ˜

χ0

1ℓ+ i ℓ− j

Background: ˜ χ0

2 → χ0 1Z(h) → ˜

χ0

1ℓ+ i ℓ− i

(˜ χ0

2 produced through ˜

q, ˜ g) decays

• 60% of 1st- and 2nd-generation LH-squarks decay in Wino-

like neutralino and chargino

• RH-slepton masses expected to be smaller than m˜

χ0

2

• If µ ≫ M, most parameter space excluded by rare muon

and tau decays.

• If µ relatively close to gaugino masses,

LHC covers range where rare decays suppressed (cancellations between chargino and neutralino diagrams)

200 300 400 500 600 700 800

m0 (GeV)

10

−9

10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

Γ (GeV)

Γ(χ2 −> ALL) Γ(χ2 −> χ τ µ) Γ(χ2 −> χ τ τ) Γ(χ2 −> χ µ µ) R(τµ/µµ)

a)

300 400 500 600 700 800

m0 (GeV)

10

−9

10

−8

10

−7

10

−6

10

−5

10

−4

10

−3

10

−2

10

−1

10 10

1

Γ (GeV)

Γ(χ2 −> ALL) Γ(χ2 −> χ τ µ) Γ(χ2 −> χ τ τ) Γ(χ2 −> χ µ µ) R(τµ/µµ)

b)

Figure 2: Comparison of flavour-changing and -conserving χ2 decay modes as functions of m0 for (a) tan β = 10, µ > 0, m1/2 = 600 GeV and (b) tan β = 40, µ > 0, m1/2 = 600 GeV. We assume for illustration a non-universality factor x = 0.9 and a mixing angle φ = π

6.

Carvahlo, Ellis, Gomez, ML, Romao, PLB2005

CONCLUSIONS Neutrino Oscillations Neutrino masses / ∆L = 0 ⇓ Extensions of SM (L-R, GUTS, R /p, ...) Phenomenological Textures Which solutions? Which correlations between different parameters? Further predictions? Implications for underlying theory Different models “prefer” different solutions. New data progressively helps us to exclude/constrain the models

In Patras, EXT EC grant for research and collaborations on these areas Available funding for:

• A PhD post
• A Post-doc
• Several research visits (2-3 months each)

Contact: Magda.Lola@cern.ch Web page: http://www.physics.upatras.gr/ magda/group/EXT.htm