Perspectives on Grand Unification in View of Neutrino Mass

March 2005Theme Group 2

Perspectives on Grand Perspectives on Grand Unification in View of Neutrino Unification in View of Neutrino

MassMass

R. N. Mohapatra

University of Maryland


S. Sakata and MNSP Neutrino Mixing matrixS. Sakata and MNSP Neutrino Mixing matrix

• -1956-Sakata model (p, n, )

-led to SU(3) symmetry and to quark model

• -concept of weak isospin used in modern gauge theories


Baryon-Lepton SymmetryBaryon-Lepton Symmetry

• Baryon-Lepton Symmetry-inspired by

Sakata Model

• Gamba, Marshak, Okubo (1959)• -Sakata called it ``Kiev Symmetry'‘

e

n

p


Isospin Unification and Electric ChargeIsospin Unification and Electric Charge

• GMO proposed generalized Gell-Mann-Nishijima Formula based on Baryon-Lepton Symmetry:

Q = I +

-``Baryon-Lepton Unification’’- Key ingredient of modern grand unified theories.

3 2

LBT


From Sakata Model to Nagoya ModelFrom Sakata Model to Nagoya Model

• 1960: Maki-Nakagawa-Ohnuki-Sakata propose composite model with B-matter:

-Precursor of modern composite models;

-1962: Brookhaven expt discovers second neutrino - Problem for Nagoya model.

BeBnBp ;;


Birth of Neutrino Mixing IdeaBirth of Neutrino Mixing Idea

• To fit two neutrinos into Nagoya model, Maki, Nakagawa, Sakata introduce neutrino mixings:

• true neutrino and weak neutrinos1 ,e


Maki-Nakagawa-Sakata-PontecorvoMaki-Nakagawa-Sakata-Pontecorvo Matrix Matrix

• For 3 generation, Majorana neutrinos, MNSPmatrix is U = VK, where

v =

(Thanks to Chlorine, S-K,Gallex,Sage,SNO,KamLand,K2K,MINOexpts)


A Hidden symmetry of Leptons ?

• Possible symmetries being discussed: S3,S4, A4.


NeutrinoNeutrino Masses Masses


Puzzles of Neutrino Mass PhysicsPuzzles of Neutrino Mass Physics

• Why

• Why are neutrino mixings so much larger than quark mixings ?

• How does neutrino mass physics fit into the big picture of grand unification, supersymmetry (and/or extra dimensions )?

• In any case, neutrino mass is first evidence of new physics beyond the standard model !!

?qmm


New standard model: Seesaw ParadigmNew standard model: Seesaw Paradigm

• Add right handed neutrinos to the standard model and give them a large mass:

Minkowski (77), Yanagida; Gell-Mann, Ramond, Slansky; Glashow; RNM, Senjanovic (79)


Seesaw MechanismSeesaw Mechanism

• Implies neutrinos are Majorana fermions. Predicts neutrinoless double beta decay.


Why Seesaw Theoretically Appealing ? Why Seesaw Theoretically Appealing ?

• Adding RH neutrino makes Standard model quark lepton symmetric; (unlike standard model)

• It makes B-L cubic anomaly free and expands the gauge group to the left-right symmetric group:

LBRL USUSU )1()2()2(


Other Implications:Other Implications:

1. Weak interactions become asymptotically parity conserving;

2.

Marshak and RNM (79); A. Davidson (79).

3. Implies lepton number violation and Majorana neutrino mass, since

RILB 32)(


Neutrino Mass Parity Violation ConnectionNeutrino Mass Parity Violation Connection

• Low energy weak interaction V-A type because neutrino mass is so small:


GRAND UNIFICATIONGRAND UNIFICATION(Pati,Salam; Georgi, Glashow,73)

• Grand unification: An important and interesting concept ; says that all matter (quarks and leptons) and all forces are one and the same

• Two simple theories :

• (A) Supersymmetric minimal standard model (with SUSY at TeV)- couplings unifiy;

• (B) G_{SM}->SU(2)_LX SU(2)_R X SU(4)_c (no susy)-> SO(10)


Unification of Couplings: two examplesUnification of Couplings: two examples

Weak scale susyWeak scale susy Non SUSY SO(10) with seesawNon SUSY SO(10) with seesaw


Advantages of High Scale in GUTAdvantages of High Scale in GUT

• Superheavy GUT scale goes well to address cosmological issues e.g inflation and baryon asymmetry etc.

• Coupling unification perhaps means a grand unifying symmetry and a predicitve theory for quark and lepton masses.

• Superheavy scale : just what one needs

to suppress proton decay predicted by GUT that unify quarks and leptons.

• Present limit: implies

(Close to the GUT scale.)

yrsp6.3310 GeVMU

1510


Simplest GUT Model: SU(5)Simplest GUT Model: SU(5)


SUSY GUT:SUSY GUT:

• Why SUSY ?

1. Stabilizes gauge hierarchy;

2.Explains EWSB;

3. Provides dark matter; lightest SUSY particle if stable.


SUSY NEEDS NEW PHYSICSSUSY NEEDS NEW PHYSICS

• For the lightest SUSY particle to be dark matter, a new symmetry (in addition to Supersymmetry) called R-parity must be imposed !

.Where does this symmetry come from ?

Neutrino mass may throw light on this.

Recall: seesaw mechanism generates the B-L symmetry- If B-L is broken, it can leave R-parity as a gauge symmetry of MSSM.


Neutrino mass: a hint of grand unification ?Neutrino mass: a hint of grand unification ?

• Seesaw explanation of neutrino mass has put grand unification back on center stage again !

• Why ? Atmospheric mass measured by Super-K using the seesaw formula

implies

SEESAW SCALE CLOSE TO GUT SCALE-:

R

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22

GeVM R1410


Minimal GUT Group for neutrinos: SO(10)Minimal GUT Group for neutrinos: SO(10)

• Georgi; Fritzsch, Minkowski (75)

1. {16}-dim spinor contains contains all std model fermions plus RH neutrino;

2. It contains B-L symmetry, which can lead to R-parity in MSSM and hence a naturally stable dark matter.

3. B-L explains why Seesaw scale is so much less than the Planck scale-


From SO(10) down to the Std ModelFrom SO(10) down to the Std Model

• SO(10) Nu mass

• Left-Right Sym. Theory

• Standard Model-> seesaw

M

0

0

0

M

m

m

0


NEW SEESAW FORMULA IN SO(10)NEW SEESAW FORMULA IN SO(10)

1. New contribution due to Higgs triplet (Fig. b)

The first term can dominate for some parameter range:


Fermion Masses in SO(10):Fermion Masses in SO(10):

• Matter in 16-spinor:

• 16 X 16 = 10 + 126 + 120

Matter Higgs

Minimal model: one each of 10+126+ 120.

A REALISTIC PREDICTIVE MODEL :

Better than minimal SU(5) and testable in neutrino sector.


Large neutrino mixings in minimal SO(10)Large neutrino mixings in minimal SO(10)

• How large mixings arise naturally in the minimal models:

Simple Example: Model with only one {10} and {126} Higgs:

• Has only 12 parameters (for CP conserving case)- all determined by quark masses and mixings and charged leptons; all neutrino mixings are predicted.

• Babu, RNM (92); Bajc, Senjanovic, Vissani (2003); Goh, Ng, RNM (2003).


A New sumrule for neutrino mass:A New sumrule for neutrino mass:

• Type II seesaw assumption leads to the sum rule at GUT scale:

• Note


Including CP violation:Including CP violation:

• In the 10+126 model, CP violation can arise from complex Yuakawas- (but works only for a narrow range of parameters)

• In the full minimal 10+126+120 model, CP is more natural.


Some predictions of the final model:Some predictions of the final model:

• Prediction for U_e3:


Predictions for long baseline experiments:Predictions for long baseline experiments:


Predictions for lepton flavor violationPredictions for lepton flavor violation


ConclusionConclusion

• Seesaw explanation of neutrino mass has several specific predictions for physics beyond the standard model:

A. B-L symmetry

B. Left-right symmetry of weak int.

C. High seesaw scale- a hint of SO(10)

Grand Unification;

A minimal SO(10) model with 126-Higgs predicts neutrino mixings and natural dark matter and is testable.


POSTSCRIPTPOSTSCRIPT

Sakata legacy very much manifest

in today’s neutrino physics !!

Perspectives on Grand Unification in View of Neutrino Mass

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