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Models of Neutrino Mass. Introduction (neutrino masses,mixings) Theory of neutrino mass (Majorana,Dirac,See-saw,Majorana matrices) Natural hierarchy (sequential right-handed neutrino dominance) Relation between neutrino factory CP violation and leptogenesis?

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Models of neutrino mass

Models of Neutrino Mass

  • Introduction (neutrino masses,mixings)

  • Theory of neutrino mass (Majorana,Dirac,See-saw,Majorana matrices)

  • Natural hierarchy (sequential right-handed neutrino dominance)

  • Relation between neutrino factory CP violation and leptogenesis?

  • SUSY and lepton flavour violation: see-saw vs. SUGRA

  • GUTs and Family Symmetry

Steve King, Coseners House


Possible three neutrino mass patterns with LMA and .

“Normal”

“Inverted”

Steve King, Coseners House


Large Mixing Angles and .

solar LMA MSW

atmospheric

CHOOZ

Steve King, Coseners House


The neutrino mixing matrix u
The Neutrino Mixing Matrix U and .

Majorana matrix

Constructing

Parametrising

Steve King, Coseners House


Origin of neutrino mass and .

In the Standard Model neutrinos are massless, and a neutrino and anti-neutrino are distinguished by a (total) conserved lepton number L.

CP conjugate of left-handed neutrino

Majorana or Dirac?

Majorana mass

(violates L)

Right-handed neutrinos

Dirac mass

from Yukawa couplings

(conserves L)

Steve King, Coseners House


See saw mechanism
See-saw mechanism and .

Diracmatrix

Heavy Majorana matrix

Diagonalise

Light Majorana matrix

Steve King, Coseners House


Leading order consistent with lma msw barbieri hall smith strumia weiner altarelli feruglio
Leading order consistent with LMA MSW and . Barbieri,Hall,Smith,Strumia,Weiner;Altarelli,Feruglio;…

Natural cases: SFK hep-ph/0204360

Type A (zero in 11)

Type B (non-zero 11)

Hierarchy

Large neutrinoless double beta decay (Petcov,…)

Inverted hierarchy

Pseudo-Dirac

Degenerate

Steve King, Coseners House


Natural Neutrino Hierarchy? and .

Natural eigenvalues are why ?

Technically need a small 23 sub-determinant:

  • But why should the sub-determinant be small ?

  • How can we get this from the see-saw mechanism?

Steve King, Coseners House


See saw with diagonal heavy majorana matrix
See-saw with and . diagonal heavy Majorana matrix

Columns can be re-ordered without loss of generality

If one right-handed neutrino of mass Y dominates then sub-determinant is naturally small: single right-handed neutrino dominance (SFK PLB 98, NPB 99)

Sequential dominance(SFK NPB2000)

Steve King, Coseners House


Analytic estimates for neutrino masses and mixing angles and . (valid for sequential dominance) SFK hep-ph/0204360

Sequential dominance

(set d=0 below)

Mass hierarchy and large mixing angles naturally!

Phases fixed by real 12 angle condition

where

and is fixed by the real 13 angle condition

Steve King, Coseners House


Light or heavy sequential dominance
Light and . or Heavy Sequential Dominance?

Heavy Sequential Dominance (HSD)

“Lop-sided” (large 23 element)

Light Sequential Dominance (LSD)

“Quark-like” (no large off-diagonal entries)

Note that X’ is irrelevent for neutrino masses, mixings (and leptogenesis-see later), and the model reduces to an effective 2 right-handed neutrino modelSFK 2000;Frampton,Glashow,Yanagida 2002; Raidal,Strumia 2002.

Steve King, Coseners House


Fukugita,Yanagida; Buchmuller,Plumacher; Di Bari, Davidson…

Leptogenesis

  • Right-handed neutrinos are produced in early universe and decay out of equilibrium giving net lepton number L

  • CP violation from complex Yukawa couplings

  • L is processed into B via B-L conserving sphalerons

Steve King, Coseners House


Relation between cp violation at a neutrino factory and in leptogenesis sfk hep ph 0211228
Relation between CP violation at a neutrino factory and in leptogenesis? SFK hep-ph/0211228

LSD

Assume 11 texture zero (see later)

Di Bari,Buchmuller,Plumacher

Heavy RH neutrino of mass X’ is irrelevant for both leptogenesis and neutrino masses, mixings

Neutrino factory phase and leptogenesis phase are linked in terms of two invariant see-saw phases

Remarkably the leptogenesis phase is equal to the phase which enters neutrinoless double beta decay !

In HSD (Hirsch,SFK) and gravitino bound may be respected (but no leptogenesis-MNS link since X’ couplings are relevant for leptogenesis but not neutrino masses, mixings)


Susy and lepton flavour violation

Borzumati, Masiero; Hisano, Moroi, Tobe, Yamaguchi; SFK, Oliveira; Casas, Ibarra; Lavignac, Masina, Savoy;Blazek,SFK

SUSY and Lepton Flavour Violation

If SUSY is present then neutrino masses inevitably lead to lepton flavour violation due to radiatively generated off-diagonal slepton masses

HSD/lopsided will lead to large due to large 23 Yukawa.

Blazek, SFK

Steve King, Coseners House


Steve King, Coseners House Oliveira; Casas, Ibarra; Lavignac, Masina, Savoy;Blazek,SFK


Lepton flavour violation in constrained minimal supersymmetric standard model
Lepton Flavour Violation in Constrained Minimal Supersymmetric Standard Model

Blazek,SFK hep-ph/0211368

HSD parametrisation with dominant heaviest RH neutrino in 33 position

LSD parametrisation with dominant lightest RH neutrino in 11 position

Large 23 element (lop-sided)

Steve King, Coseners House


Blazek,SFK hep-ph/0211368 Supersymmetric Standard Model

13 angle depends on a ratio of Yukawa couplings

HSD

Steve King, Coseners House


HSD predictions for constrained MSSM Supersymmetric Standard Model

Blazek,SFK hep-ph/0211368

Steve King, Coseners House


LSD predictions for constrained MSSM Supersymmetric Standard Model

Blazek,SFK hep-ph/0211368

Steve King, Coseners House


Iain Peddie, SFK (preliminary) Supersymmetric Standard Model

Supergravity LFV can mimic see-saw LFV

Steve King, Coseners House


The goal is to describe the quark and lepton mass hierarchies

t

Charge +2/3 quarks

Charge –1/3 quarks

u

d

c

Charged leptons

e

s

b

A neutrino hierarchy

Steve King, Coseners House


GUTs hierarchies

Steve King, Coseners House


Family symmetry
Family Symmetry hierarchies

Democracy, Fritzsch,…

Hierarchy Froggatt,Nielsen,Ross…

Nothing

Harrison, Scott

Steve King, Coseners House


G.Ross, SFK hierarchies

G.Ross, Velasco-Sevilla

Flavour Unification

Leads to approximately symmetric mass matrices

  • Allows a universal form for mass matrices

  • Example of Light Sequential Dominance (LSD)

  • Texture zero in 11 position  leptogenesis-neutrino factory link

Steve King, Coseners House


Conclusion
Conclusion hierarchies

  • Small neutrino masses can be elegantly explained by see-saw mechanism

  • Sequential dominance then provides a natural explanation of a neutrino mass hierarchy and large mixing angles

  • The dominant right-handed neutrino may be either the heaviest (HSD) or the lightest one (LSD)

  • LSD with 11 zero links leptogenesis phase and the CP phase which is measurable at a neutrino factory, but is inconsistent with SUSY models

  • HSD has no such link, but may be consistent with SUSY models

  • SUSY leads to lepton flavour violating processes, which can discriminate HSD from LSD

  • SUGRA LFV can mimic see-saw LFV

  • GUTs and family symmetry can solve flavour problem G.Ross talk

Steve King, Coseners House


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